ISSN 1854-6250 APEM journal Advances in Production Engineering & Management Volume 17 | Number 2 | June 2022 Published by CPE apem-journal.org Advances in Production Engineering & Management Identification Statement APEM journal ISSN 1854‐6250 | Abbreviated key title: Adv produc engineer manag | Start year: 2006 ISSN 1855‐6531 (on‐line) Published quarterly by Chair of Production Engineering (CPE), University of Maribor Smetanova ulica 17, SI – 2000 Maribor, Slovenia, European Union (EU) Phone: 00386 2 2207522, Fax: 00386 2 2207990 Language of text: English APEM homepage: apem‐journal.org University homepage: www.um.si APEM Editorial Editor‐in‐Chief Miran Brezocnik editor@apem‐journal.org, info@apem‐journal.org University of Maribor, Faculty of Mechanical Engineering Sme‐ tanova ulica 17, SI – 2000 Maribor, Slovenia, EU Desk Editor Website Technical Editor Martina Meh Lucija Brezocnik desk1@apem‐journal.org desk3@apem‐journal.org Janez Gotlih desk2@apem‐journal.org Editorial Board Members Eberhard Abele, Technical University of Darmstadt, Germany Bojan Acko, University of Maribor, Slovenia Joze Balic, University of Maribor, Slovenia Agostino Bruzzone, University of Genoa, Italy Borut Buchmeister, University of Maribor, Slovenia Ludwig Cardon, Ghent University, Belgium Nirupam Chakraborti, Indian Institute of Technology, Kharagpur, India Edward Chlebus, Wroclaw University of Technology, Poland Igor Drstvensek, University of Maribor, Slovenia Illes Dudas, University of Miskolc, Hungary Mirko Ficko, University of Maribor, Slovenia Vlatka Hlupic, University of Westminster, UK David Hui, University of New Orleans, USA Pramod K. Jain, Indian Institute of Technology Roorkee, India Isak Karabegović, University of Bihać, Bosnia and Herzegovina Janez Kopac, University of Ljubljana, Slovenia Qingliang Meng, Jiangsu University of Science and Technology, China Lanndon A. Ocampo, Cebu Technological University, Philippines Iztok Palcic, University of Maribor, Slovenia Krsto Pandza, University of Leeds, UK Andrej Polajnar, University of Maribor, Slovenia Antonio Pouzada, University of Minho, Portugal R. Venkata Rao, Sardar Vallabhbhai National Inst. of Technology, India Rajiv Kumar Sharma, National Institute of Technology, India Katica Simunovic, J. J. Strossmayer University of Osijek, Croatia Daizhong Su, Nottingham Trent University, UK Soemon Takakuwa, Nagoya University, Japan Nikos Tsourveloudis, Technical University of Crete, Greece Tomo Udiljak, University of Zagreb, Croatia Ivica Veza, University of Split, Croatia Subsidizer: The journal is subsidized by Slovenian Research Agency Creative Commons Licence (CC): Content from published paper in the APEM journal may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any fur‐ ther distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Statements and opinions expressed in the articles and communications are those of the individual contributors and not necessarily those of the editors or the publisher. No responsibility is accepted for the accuracy of information contained in the text, illustrations or advertise‐ ments. 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Advances in Production Engineering & Management is indexed and abstracted in the WEB OF SCIENCE (maintained by Clarivate Analytics): Science Citation Index Expanded, Journal Citation Reports – Science Edition, Current Contents – Engineering, Computing and Technology • Scopus (maintained by Elsevier) • Inspec • EBSCO: Academic Search Alumni Edition, Academic Search Complete, Academic Search Elite, Academic Search Premier, Engineering Source, Sales & Marketing Source, TOC Premier • ProQuest: CSA Engineering Research Database – Cambridge Scientific Abstracts, Materials Business File, Materials Research Database, Mechanical & Transportation Engineering Abstracts, ProQuest SciTech Collection • TEMA (DOMA) • The journal is listed in Ulrich’s Periodicals Directory and Cabell's Directory Chair of Production Engineering (CPE) Advances in Production Engineering & Management Volume 17 | Number 2 | June 2022 | pp 137–258 Contents Scope and topics A method for prediction of S-N curve of spot-welded joints based on numerical simulation 140 141 Sustainability and digitalisation: Using Means-End Chain Theory to determine the key elements of the digital maturity model for research and development organisations with the aspect of sustainability 152 Supply chain coordination based on the probability optimization of target profit 169 A bi-objective optimization of airport ferry vehicle scheduling based on heuristic algorithm: A real data case study 183 Ultrasonic abrasive polishing of additive manufactured parts: An experimental study on the effects of process parameters on polishing performance 193 Machinability analysis and multi-response optimization using NGSA-II algorithm for particle reinforced aluminum based metal matrix composites 205 Supply chain coordination contract design: The case of farmer with capital constraints and behavioral preferences 219 Numerical study of racking resistance of timber-made double-skin façade elements 231 A Plant Simulation approach for optimal resource utilization: A case study in the tire manufacturing industry 243 Calendar of events Notes for contributors 256 257 Yang, L.; Yang, B.; Yang, G.W.; Xiao, S.N.; Zhu, T.; Wang, F. Kupilas, K.J.; Rodríguez Montequín, V.; Díaz Piloñeta, M.; Alonso Álvarez, C. Jian, M.; Liu, T.; Hayrutdinov, S.; Fu, H. Han, X.; Zhao, P.X.; Kong, D.X. Liu, X.; Wang, J.; Zhu, J.; Liew, P.J.; Li, C.; Huang, C. Umer, U.; Mohammed, M.K.; Abidi, M.H.; Alkhalefah, H.; Kishawy, H.A. Wang, Y.L.; Yin, X.M.; Zheng, X.Y.; Cai, J.R.; Fang, X. Kozem Šilih, E.; Premrov, M. Butrat, A.; Supsomboon, S. Journal homepage: apem-journal.org ISSN 1854-6250 (print) ISSN 1855-6531 (on-line) Published by CPE, University of Maribor. Scope and topics Advances in Production Engineering & Management (APEM journal) is an interdisciplinary refereed international academic journal published quarterly by the Chair of Production Engineering at the University of Maribor. The main goal of the APEM journal is to present original, high quality, theoretical and application-oriented research developments in all areas of production engineering and production management to a broad audience of academics and practitioners. In order to bridge the gap between theory and practice, applications based on advanced theory and case studies are particularly welcome. For theoretical papers, their originality and research contributions are the main factors in the evaluation process. General approaches, formalisms, algorithms or techniques should be illustrated with significant applications that demonstrate their applicability to real-world problems. Although the APEM journal main goal is to publish original research papers, review articles and professional papers are occasionally published. Fields of interest include, but are not limited to: Additive Manufacturing Processes Advanced Production Technologies Artificial Intelligence in Production Assembly Systems Automation Big Data in Production Block Chain in Manufacturing Computer-Integrated Manufacturing Cutting and Forming Processes Decision Support Systems Deep Learning in Manufacturing Discrete Systems and Methodology e-Manufacturing Evolutionary Computation in Production Fuzzy Systems Human Factor Engineering, Ergonomics Industrial Engineering Industrial Processes Industrial Robotics Intelligent Manufacturing Systems Joining Processes Knowledge Management Logistics in Production 140 Machine Learning in Production Machine-to-Machine Economy Machine Tools Machining Systems Manufacturing Systems Materials Science, Multidisciplinary Mechanical Engineering Mechatronics Metrology in Production Modelling and Simulation Numerical Techniques Operations Research Operations Planning, Scheduling and Control Optimisation Techniques Project Management Quality Management Risk and Uncertainty Self-Organizing Systems Smart Manufacturing Statistical Methods Supply Chain Management Virtual Reality in Production Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 2 | June 2022 | pp 141–151 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.2.426 Original scientific paper A method for prediction of S-N curve of spot-welded joints based on numerical simulation Yang, L.a, Yang, B.a, Yang, G.W.a,*, Xiao, S.N.a, Zhu, T.a, Wang, F.a aState Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu, P.R. China ABSTRACT ARTICLE INFO Currently, △F-N curves are often used to predict the fatigue lives of spotwelded joints, but the method for obtaining these △F-N curves is timeconsuming, laborious, and non-universal. Tensile-shear fatigue tests were performed to obtain the fatigue lives and the corresponding normalized S-N curves of spot-welded joints. Subsequently, the force acting at the spotwelded joints was obtained by extracting the force and moment of the beam element in the shell-element-based finite element model, and the equivalent structural stress at the spot-welded joint was obtained based on the equivalent structural stress method. Finally, the S-N curves of the spot-welded joints were fitted using the least-squares method. A comparison of the S-N curves of the spot-welded joints with those of different materials revealed that the material type had a significant influence on the S-N curve. To avoid this influence, a method for predicting the S-N curve of the spot-welded joints was proposed based on the relationship between the ratio of the tensile strength and that of the fatigue limit of each material. This research provides guidance for predicting the fatigue life of spot-welded joints in engineering applications. Keywords: Spot-welded joints; Simulation; Numerical simulation; Finite element methods (FEM); S-N curve; Prediction method; Equivalent structural stress *Corresponding author: gwyang@home.swjtu.edu.cn (Yang, G.W.) Article history: Received 4 April 2022 Revised 16 August 2022 Accepted 20 August 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction Spot-welded structures are widely used in modern industrial production owing to their advantages of light weight, stable performance, and high automated production efficiency. This is an important connection mode in the mechanical manufacturing process [1]. Spot welding is mainly used in the fields of automobile manufacturing, rail-vehicle manufacturing, aerospace, and ship building, especially in automobile bodies and stainless-steel bodies of rail vehicles. According to statistics, a stainless-steel body of rail vehicles usually has up to 50000 spot-welded joints, and an automotive body has approximately 4000-6000 spot-welded joints [2]. As the spot-welding nugget is located between two relatively close plates and fatigue cracks often appear on the inner side of the plate, it becomes difficult to monitor the crack length and depth and perform non-destructive inspection [3-6]. Spot-welding fatigue-assessment methods mainly include the load-life, nominal stress, hot-spot stress, local, notch stress, fracture mechanics, and equivalent structural stress methods. At present, the load-life method specified in the standards ISO 14324-2003 [7], NF A89-571-2004 [8], JIS Z3138-1989 [9], KS B 0528-2001 [10], and GB/T 15111-1994 [11] are still used to predict the fatigue life of spot-welded joints. Howev141 Yang, Yang, Yang, Xiao, Zhu, Wang er, the △F-N (load-amplitude-life) curves corresponding to different types of spot-welded joints in these standards are limited, and it is impossible to establish △F-N curves for individual spotwelding structures; furthermore, the load-life method is an approximate estimation method [12]. Therefore, the limitations of the load-life method are evident. In addition, other spotwelding fatigue assessment methods have limitations, such as high sensitivity to finite element meshes and a small application range, while the equivalent structural stress method has been widely used owing to its insensitivity to meshes. Current spot-welding fatigue-life prediction methods based on equivalent structural stress include the Radaj [13], Rupp [14], Sheppard [15], Kang [16], and Dong methods [17]. In the early stages of fatigue research of spot-welded joints, Radaj [13] derived the formula for the maximum equivalent structural stress at the edge of a weld nugget. Based on the Roark stress-strain formula, Rupp [14] predicted the fatigue lives of spot-welded joints using the structural stress and verified the accuracy of the structural stress via tests. Sheppard [15] calculated the equivalent structural stress using the spot-welding finite element model and evaluated the fatigue lives of spot-welded joints according to the relationship between the structural stress and fatigue life. Kang [16] substituted the stress components in the von Mises equation with the local structural stresses in the vicinity of the spot weld and used the forces and moments that were determined via finite element analysis to calculate the structural stresses at the edges of the weld nugget in each sheet. Through a finite element simulation, Dong [17] transformed the nodal forces and moments at the edge of the spot-welding nugget into the linear membrane stress and bending stress and proposed a structural-stress calculation method that was insensitive to meshes. Subsequently, Yan [18] combined the Dong and Rupp methods and proposed a new fatigue characteristic parameter and simplified structural stress of the spot welding. Subsequently, the author determined the correlations of the spot-welding fatigue characteristic parameters of the Rupp, Kang, Dong, and Sheppard structure stresses on the fatigue performance of single and double spot welding [19]. Wu [20] used the classical, nonlinear generalized reduced-gradient algorithm to propose a process for optimizing the empirical parameter terms in the Rupp structural stress formula. The optimized Rupp structural-stress formula can effectively correlate the fatigue lives of spot-welded joints of various geometric sizes. The aforementioned studies have made significant contributions to the fatigue-life evaluation method, equivalent-structural-stress calculation method, finite element simulation method, fatigue characteristic parameters, and fatigue influence parameters of spot welding. However, there is insufficient research on the normalized-spot-welding S-N curve and the method for predicting the S-N curve. Different from the above studies, in this study, the quasi-static failure loads of spot-welded joints of different materials were obtained by carrying out quasi-static tensile tests. Based on the quasi-static failure loads, the load levels of tensile-shear fatigue tests were determined, and the fatigue lives of the spot-welded joints were obtained via tensile-shear fatigue tests. The equivalent structural stresses of the spot-welded joints were obtained based on the Rupp equivalent structural stress method, and the S-N curves of the spot-welded joints were fitted based on the least-squares method. Finally, based on the influence of the material on the S-N curve, a method for predicting the S-N curve of spot-welded joints was proposed, which provides a useful reference for engineering applications. 2. Materials, methods, and experimental testing In this study, tensile-shear fatigue tests were performed on spot-welded specimens to study the fatigue lives of spot-welded joints. Because the process of welding the stainless-steel body of rail vehicles often comprises the use of spot-welded joints, the SUS301L stainless steel commonly used in the stainless-steel body was selected as the specimen material. To avoid eccentricity in the fatigue test process of the plate welding specimens of various thicknesses, the upper and lower auxiliary plates were welded onto the plate to ensure that the spot-welded joint was stressed uniformly. The parameters of the spot-welded specimens are listed in Table 1, and the structural diagram is presented in Fig. 1. 142 Advances in Production Engineering & Management 17(2) 2022 A method for prediction of S-N curve of spot-welded joints based on numerical simulation Table 1 Parameters of spot-welded specimens Upper plate Lower plate Weld nugget Load Yield Tensile Thickness Thickness Type diameter ratio Material Material strength strength (mm) (mm) (mm) (MPa) (MPa) SUS301L_ SUS301L_ A1 1.5 2 380 690 6 0.1 1/8H 1/8H SUS301L_ SUS301L_ A2 2 2 380 690 7 0.1 1/8H 1/8H SUS301L_ SUS301L_ B 1.5 3 450 790 6 0.1 1/16H 1/16H SUS301L_ SUS301L_ C 2 2 515 860 7 0.1 1/4H 1/4H Note: Type-A1 and Type-A2 comprise the same material, and only their sizes are different. Type-A is the name used to indicate Type-A1 and Type-A2. a) Type-A1 b) Type-A2 c) Type-B d) Type-C Fig. 1 The structural diagram of spot-welded specimens Table 2 Quasi-static tensile test results of spot-welded specimens Failure load F (kN) Specimen serial number Type-A1 Type-A2 Type-B 1 20.66 23.42 26.24 2 21.01 22.98 26.77 3 20.50 23.57 26.84 4 23.31 23.29 26.93 5 22.26 22.75 26.72 21.548 23.202 26.70 Average failure load 𝐹𝐹 Type-C 40.53 41.61 42.01 41.98 41.74 41.574 First, the specimens presented in Fig. 1 were installed on a hydraulic universal testing machine (WE-30) for the quasi-static tensile test to determine the failure load of the spot-welded specimens. The test results are listed in Table 2. Based on the average failure load 𝐹𝐹 in Table 2, the tensile-shear fatigue tests were then performed under four sets of load levels (multiples of 𝐹𝐹) on a PLG-20C high-frequency tension-andcompression fatigue-testing machine for each spot-welded specimen. The group and the ladder test methods were used, the load form was an equal-amplitude sinusoidal curve, and the load ratio was 0.1 (Fmin/Fmax). The loading frequency gradually decreased with the crack propagation in the specimens, and the frequency range was 50-1000 Hz. While considering the fatigue fracture of the spot-welded specimens as the failure criterion, the fatigue lives of the spot-welded specimens were obtained, as shown in Table 3. Advances in Production Engineering & Management 17(2) 2022 143 Yang, Yang, Yang, Xiao, Zhu, Wang Table 3 Tensile-shear fatigue test loads and fatigue lives of spot-welded specimens Type-A1 Type-A2 Type-B Type-C Fmax (kN) N (cycle) Fmax (kN) N (cycle) Fmax (kN) N (cycle) Fmax (kN) 340800 186700 358500 495300 202600 400600 3.2322 kN 4.6404 kN 4.005 kN 4.1574 kN 671700 209000 418209 (15 % F) (20 % F) (15 % F) (10 % F) 997900 307843 433200 1085900 522400 537000 150900 36500 92100 199600 38300 97100 4.3096 kN 6.9606 kN 6.675 kN 8.3148 kN 205700 42900 105700 (20 % F) (30 % F) (25 % F) (20 % F) 218300 53500 120500 356100 55300 134700 35100 15300 32100 62800 16700 36600 5.387 kN 9.2808 kN 9.345 kN 12.4722 kN 85500 22200 40500 (25 % F) (40 % F) (35 % F) (30 % F) 91300 22300 57200 93300 25300 58800 22300 4700 14200 28300 7600 16100 6.4644 kN 11.6010 kN 12.015 kN 16.6296 kN 37800 8400 22400 (30 % F) (50 % F) (45 % F) (40 % F) 46900 9000 23100 50700 10600 28000 N (cycle) 373750 406659 419313 426488 497444 58208 59175 81142 152638 162663 14028 14133 14439 15123 15476 4986 5118 5366 5439 5817 The △F-N curves of the spot-welded specimens were obtained according to the test loads and tensile-shear fatigue lives of the specimens, as shown in Fig. 2. It can be observed that the overall dispersion of the data points was relatively high, and the correlations between the △F-N curves for each material were weak. It was found that the correlation between the load amplitude △F and fatigue life N of the spot-welded joint was weak, and the △F-N curves fitted appropriately only for the spot-welded joints of the same material. When predicting the fatigue lives of the spot-welded joints of different materials, fatigue tests were performed for each structure. This is time-consuming and laborious. Furthermore, the selection process also becomes cumbersome when too many curves are considered. Therefore, it is of greater engineering significance to plot the normalized S-N curves of spot-welded joints suitable for different steels and different weld sizes. Load amplitude △F (N) 104 103 Type-A1 test data Type-A1 △F-N curve Type-A2 test data Type-A2 △F-N curve Type-B test data Type-C test data Overall △F-N curve Type-B △F-N curve Type-C △F-N curve 104 105 Life N (cycles) 106 Fig. 2 △F-N curves 144 Advances in Production Engineering & Management 17(2) 2022 A method for prediction of S-N curve of spot-welded joints based on numerical simulation 3. Structural-stress calculation method 3.1 Structural-stress calculation model To fit the S-N curve, it was necessary to obtain the structural stress (S) of the spot-welded joints. The spot-welding equivalent structural stress proposed by Rupp based on Roark's stress-strain formula is widely used in the fatigue-strength evaluation of spot-welded joints; its equivalent structural stress calculation model is presented in Fig. 3. Fig. 3 Method for calculating equivalent-structural-stress of spot-welded joints The plate thickness of the spot-welded joint in this study satisfied the relation 𝑑𝑑 > 3.5√𝑡𝑡 (d is the diameter of the weld nugget, t is the thickness of sheet). According to the structural-stress calculation model, the equivalent structural stress of a spot-welded joint was obtained, as shown in Eqs. 1 to 7, respectively [14]. σ𝑣𝑣1 = −𝜎𝜎max (𝐹𝐹𝑥𝑥1 )cos𝜑𝜑 − 𝜎𝜎max �𝐹𝐹𝑦𝑦1 �sin𝜑𝜑 + 𝜎𝜎max (𝐹𝐹𝑧𝑧1 ) + 𝜎𝜎max (𝑀𝑀𝑥𝑥1 )sin𝜑𝜑 − 𝜎𝜎max �𝑀𝑀𝑦𝑦1 �cos𝜑𝜑 (1) where σmax (𝐹𝐹𝑥𝑥1 ) = σmax (𝐹𝐹𝑦𝑦1 ) = 𝐹𝐹𝑥𝑥1 𝜋𝜋𝜋𝜋𝑡𝑡1 𝐹𝐹𝑦𝑦1 𝜋𝜋𝜋𝜋𝑡𝑡1 1.872𝑀𝑀 σmax (𝑀𝑀𝑥𝑥1 ) = 𝐾𝐾1 ( 𝑑𝑑𝑡𝑡 2 𝑥𝑥1 ) 1 1.872𝑀𝑀𝑦𝑦1 σmax (𝑀𝑀𝑦𝑦1 ) = 𝐾𝐾1 ( ) 𝑑𝑑𝑡𝑡 2 1 (2) (3) (4) (5) where t1 is the thickness of sheet 1, 𝐾𝐾1 = 0.6√𝑡𝑡1 is an empirical correction factor, and φ is the radial stress angle. When the axial force on the weld nugget is a tensile force, it results in fatigue failure, and the influence of the axial force should be considered, that is, when 𝐹𝐹𝑧𝑧1 > 0: 1.774𝐹𝐹𝑧𝑧1 ) 𝑡𝑡12 σ(𝐹𝐹𝑧𝑧1 ) = 𝐾𝐾1 ( (6) When the axial force on the weld nugget is the result of a pressure, fatigue does not occur. At this time, the effect of the axial force is ignored, that is, when 𝐹𝐹𝑧𝑧1 ≤ 0: 3.2 Equivalent structural stress calculation σ(𝐹𝐹𝑧𝑧1 ) = 0 (7) To obtain the force and moment at the spot welding, a finite element model of the spot-welded joint was established in the software HyperMesh, wherein the base metal was simulated as the shell element and the weld nugget was simulated as the CBAR element. The weld nugget center nodes of the upper-plate and lower-plate nuggets were connected using a CBAR element. The mesh size of the model was 2 mm, and the load and boundary conditions were consistent with Advances in Production Engineering & Management 17(2) 2022 145 Yang, Yang, Yang, Xiao, Zhu, Wang those of the test. One end of the specimen was fully constrained, the other end was connected to the rbe2 rigid elements, and the specimen was unconstrained in the direction of the load. The time of finite element model simulation was 38 s, and the required storage space was 8.04 MB. The spot-welded shell-element-based finite element model is presented in Fig. 4. This finite element model can accurately simulate the actual stress of the spot welding and easily obtain the stress of the spot-welded structure [2, 19, 21]. Fig. 4 Spot-welded shell-element-based finite element model In the finite element simulation, first, the maximum and minimum loading forces Fmax and Fmin, respectively, of the different types of spot-welded specimens were applied to the finite element models. Then, the software NASTRAN was used to calculate the force and moment of the beam element nodes of the finite element models. Finally, the force and moment of the beam element nodes were introduced into Eqs. 1 to 7 to obtain the equivalent structural stresses of the spot-welded joints under tensile-shear loads. The calculation process is presented in Fig. 5 (A and B indicate the nodes at each end of the beam element). Fig. 5 Equivalent structural stress calculation process [22] 146 Advances in Production Engineering & Management 17(2) 2022 A method for prediction of S-N curve of spot-welded joints based on numerical simulation On considering the Type-B specimen, with Fmax = 6.675 kN, as an example, according to the calculation process shown in Fig. 5, the force and moment of the beam-element nodes in the model and the equivalent-structural-stress amplitude of the spot-welded joint were obtained, as shown in Table 4. Table 4 Force and moment of beam element nodes in the model and the equivalent-structural-stress amplitude of spot-welded joint Nodes Force and Fmax = 6675 N Fmin = 667.5 N σa_max, σb_max σa_min, σb_min △σa, △σb △σs moment (MPa) (MPa) (MPa) (MPa) M1 (N·mm) -11490 -1149 Node A M2 (N·mm) -2.929e-10 -2.884e-11 Axial (N) 85.4 8.54 Shear1 (N) Shear2 (N) Torque (N·mm) Node B M1 (N·mm) M2 (N·mm) Shear1 (N) Shear2 (N) Axial (N) Torque (N·mm) -6675 -4.897e-11 9.185e-15 3532 -1.827e-10 -6675 -4.897e-11 85.4 9.185e-15 -667.5 -4.608e-12 549.184 54.918 494.266 8.526e-16 580.166 353.2 -1.847e-11 -667.5 -4.608e-12 8.54 644.629 64.463 580.166 8.526e-16 4. S-N Curve and prediction method 4.1 Fitting S-N curve The test data were fitted in a double-logarithmic coordinate system using the least-squares method by plotting the equivalent-structural-stress amplitude △σs along the ordinate and the fatigue life N along the abscissa, and the S-N curves of the spot-welded joints of the same material and of different materials were obtained as shown in Fig. 6. In the processing of the fatigue test data, five times the lifespan (hereinafter referred to as “5×lifespan”) is typically used to evaluate the S-N curve. If the data points are within the 5×lifespan, the S-N curve is considered to have a high correlation [2, 20, 22, 23]. It can be observed from Fig. 6 that all the spot-welding data points of the same material were within the 5×lifespan, the data points were relatively compact, and the squared correlation coefficient (R2) of the S-N curves were greater than 0.8769; however, the spot-welding data points in the case of different materials were more dispersive, and R2 was only 0.8667 in the S-N curve. Thus, the S-N curve of the spot welding of the same material had a higher correlation and a better fitting effect. The dispersion of the spot-welding data points for different materials resulted in a weak correlation of the overall S-N curve with R2 of only 0.8742. It can be observed that the material had a significant influence on the S-N curve; therefore, the influence of the material cannot be ignored in the fatigue analysis of the spot-welded joints. It is necessary to distinguish the materials of spot-welded joints for the fatigue evaluation. Advances in Production Engineering & Management 17(2) 2022 147 Yang, Yang, Yang, Xiao, Zhu, Wang (a) 103 x5 4 10 6 101 7 10 10 Life N (cycles) 10 (d) Type-C test data Type-C S-N curve 103 104 105 106 Life N (cycles) x5 x5 x5 2 10 y = -0.27944x + 3.9004 R2 = 0.8967 104 105 106 Life N (cycles) y = -0.28096x + 3.8336 R2 = 0.8667 103 107 (e) 104 105 106 Life N (cycles) 107 All test data Overall S-N curve 103 ∆σs (MPa) 107 Test data for different materials S-N curve for different materials 103 x5 103 103 ∆σs (MPa) ∆σs (MPa) y = -0.28146x + 3.8806 R2 = 0.9296 5 104 (c) 101 x5 102 y = -0.26807x + 3.7385 R2 = 0.8769 10 102 x5 103 x5 3 Type-B test data Type-B S-N curve ∆σs (MPa) ∆σs (MPa) 102 104 (b) Type-A test data Type-A S-N curve x5 x5 2 10 y = -0.27029x + 3.7815 R2 = 0.8742 103 4.2 S-N curve prediction method 104 105 106 Life N (cycles) 107 Fig. 6 S-N curves of spot-welded joints The standard-power-function expression of the S-N curve is shown in Eq. 8, and all the spotwelding test fatigue lives N can be equivalent to the fatigue life Ne when the fatigue limit is 5e6 cycles as shown in Eq. 8 [24] and the equivalent equation is given by Eq. 9. 𝑆𝑆 𝑚𝑚 𝑁𝑁 = C (8) where m and C are parameters related to the material properties, specimen form, stress ratio, and loading mode, respectively. 𝑆𝑆 𝑁𝑁𝑒𝑒 = 𝑁𝑁( )𝑚𝑚 (9) 𝑆𝑆𝑒𝑒 where Se is the stress amplitude corresponding to the S-N curve of the spot welding when N is 5e6 cycles. The equivalent S-N curves are presented in Fig. 7, and it can be observed that the S-N curves of the spot-welded joints of all the materials after equivalence are almost parallel. The slopes and relative deviations of the S-N curves of the spot-welded joints are listed in Table 5. It can be 148 Advances in Production Engineering & Management 17(2) 2022 A method for prediction of S-N curve of spot-welded joints based on numerical simulation observed that the relative deviations of all the slopes are within 5 %. Within the acceptable error range, the S-N curves of the spot-welded joints of various materials were considered to be parallel. This indicates that the ratio of fatigue limit or that of the fatigue strength under different cycles of spot welding is a constant value, and the spot-welding S-N curve of one material can be derived from that of another material. Type-A S-N curve Type-B S-N curve Type-C S-N curve Fatigue limit of Type-A Fatigue limit of Type-B Fatigue limit of Type-C Equivalent life of Type-A under 5e6 cycles Equivalent life of Type-B under 5e6 cycles Equivalent life of Type-C under 5e6 cycles 3x102 ∆σs (MPa) 2x102 102 105 106 Life N (cycles) 107 Fig. 7 The equivalent S-N curves of spot-welded joints Because the fatigue limit of the material has a good correlation with the tensile strength [25], the tensile strength of the spot-welded joint material was compared with the fatigue limit, and the results are shown in Table 6. It can be observed that the ratio of the tensile strength of each material is very close to that of the fatigue limit, and the ratio deviation is within 3 %. This shows that the spot-welding S-N curve of other materials can be derived from the known spotwelding S-N curve of one material according to the ratio relationship of the tensile strength. Table 5 Slopes and relative deviations of S-N curves of spot-welded joints Spot welding type Slope relative deviation (%) Item Type-A versus Type-A versus Type-B versus Type-A Type-B Type-C Type-B Type-C Type-C Slope of S-N curve -0.26807 -0.28146 -0.27944 4.995 4.241 0.718 Table 6 Relationship between tensile strength of spot-welded joint material and S-N curve Ratio of Type-A Ratio of Type-A Ratio of Type-B Item Type-A Type-B Type-C to Type-B to Type-C to Type-C Tensile strength, MPa 690 790 860 0.873 0.802 0.919 Fatigue limit, MPa 87.641 98.880 106.768 0.886 0.821 0.926 Deviation (%) / / / 1.458 2.258 0.812 According to the ratio relationship of the tensile strength of spot-welding materials, the spotwelding S-N curve of other materials was derived from the known spot-welding S-N curve of one material, as shown in Table 7. It can be observed that the derived fatigue limit of the spot welding was very close to the fatigue limit fitted according to the test data, and the corresponding error was within 3 %. Therefore, according to the ratio relationship of the tensile strength of the spot-welding materials, the spot-welding S-N curve of other materials can be predicted relatively accurately from the known spot-welding S-N curve of one material. In engineering applications, it is not necessary to perform tests on spot-welded joints of each material individually. Using the S-N-curve prediction method, the predicted S-N curves of other materials can be obtained, which is timesaving, labor-saving, and more universal and provides references for the design of spotwelding structures and life predictions in engineering applications. Advances in Production Engineering & Management 17(2) 2022 149 Yang, Yang, Yang, Xiao, Zhu, Wang Table 7 Spot welding S-N curves were derived according to the ratio relationship of the tensile strength of spot-welding materials Type-B derives Type-C derives Type-A derives Type-C derives Type-A derives Type-B derives Item Type-A Type-A Type-B Type-B Type-C Type-C Derived S-N y = -0.28146 x + y = -0.27944 x + y = -0.26807 x + y = -0.27944 x + y = -0.26807 x + y = -0.28146 x + curves 3.8218 3.8048 3.7973 3.8635 3.8341 3.9175 Derived fatigue 86.363 85.662 100.343 98.077 109.234 107.641 limit (MPa) Fitted fatigue 87.641 87.641 98.880 98.80 106.768 106.768 limit (MPa) Error (%) -1.458 -2.258 1.479 -0.812 2.310 0.818 5. Results and discussion In this study, through fatigue tests and finite element simulations of spot-welded joints, the normalized S-N curve of spot-welded joints was studied based on the structural stress method, and a method for predicting the S-N curve was proposed. The following conclusions were drawn. The correlation of the △F-N curves of the spot-welded joints was weak, and the materials had a significant influence on the curves. When predicting the fatigue life of the spot-welded joints with different materials, fatigue tests had to be performed for each structure; therefore, the △FN curves were non-universal. The stress of the spot-welded joint can be easily obtained by extracting the force and moment of the beam-element nodes in the spot-welded shell-element model. Using the equivalentstructural-stress calculation model, the equivalent structural stress of the spot-welded joint can be accurately obtained. The correlation of the S-N curves of the spot-welded joints of the same material was satisfactory, and the correlation of the S-N curves of different materials was weak. Therefore, the material has a significant influence on the S-N curves, and the influence of materials cannot be ignored in the fatigue analysis of spot-welded joints. To avoid the influence of materials on the S-N curves of spot-welded joints, a method for predicting the S-N curve was proposed based on the relationship between the ratio of the tensile strength and that of the fatigue limit of each material, which provides references for the design of spot-welding structures and life prediction in engineering applications. Owing to the limitations of the test conditions and the amount of available test data, some data were dispersive and did not provide accurate solutions; therefore, supplementary tests should be conducted to improve the accuracy of the results. In the future, the influence of residual stress on the fatigue life and fatigue characteristics of spot-welded joints under tensile loads can be further investigated. Acknowledgement The authors are grateful for the financial support provided by the the National Natural Science Foundation of China (grant number 52175123) and the Independent Subject of State Key Laboratory of Traction Power (grant number 2022TPL_T03). References [1] [2] [3] [4] 150 Yang, L., Yang, B., Yang, G.W., Xiao, S.N., Zhu, T., Wang, F. (2020). S-N curve and quantitative relationship of single-spot and multi-spot weldings, International Journal of Simulation Modelling, Vol. 19, No. 3, 482-493, doi: 10.2507/IJSIMM19-3-CO11. Wang, F. (2018). Research on equivalent stress method of spot welding and ring welding, Master Thesis, Southwest Jiaotong University, Chengdu, China. Ismail, M.I.S., Afieq, W.M. (2016). Thermal analysis on a weld joint of aluminium alloy in gas metal arc welding, Advances in Production Engineering & Management, Vol. 11, No. 1, 29-37, doi: 10.14743/apem2016.1.207. Talabi, S.I., Owolabi, O.B., Adebisi, J.A., Yahaya, T. (2014). 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Characteristics and life expression of fatigue fracture of G105 and S135 drill pipe steels for API grade, Engineering Failure Analysis, Vol. 116, Article No. 104705, doi: 10.1016/ j.engfailanal. 2020.104705. Advances in Production Engineering & Management 17(2) 2022 151 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 2 | June 2022 | pp 152–168 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.2.427 Original scientific paper Sustainability and digitalisation: Using Means-End Chain Theory to determine the key elements of the digital maturity model for research and development organisations with the aspect of sustainability Kupilas, K.J.a, Rodríguez Montequín, V.a,*, Díaz Piloñeta, M.a, Alonso Álvarez, C.a aUniversity of Oviedo, Oviedo, Project Engineering Area, Spain ABSTRACT ARTICLE INFO Organisations are under pressure to digitally transform and become more sustainable. Thus, the convergence of digitalisation and sustainability is inevitable. There are several Digital Maturity models that help companies to develop their digital roadmaps, however, none of them have been developed for Research and Development (R&D) organisations. Additionally, none of these models include the dimension of sustainability. In this paper the authors used the Means-End Chain method to determine which are the key dimensions of the digital maturity model tailored for R&D, as well as to investigate the link between digital transformation and sustainability. The results show that although technologies are important, they cannot successfully transform the organisation on their own. They must be supported by people and culture change. The results also highlighted that sustainability is high on the agenda and cannot be ignored when progressing towards the higher level of Digital Maturity. The findings may serve as a reference for any organisation that is building or revising its digitalisation or sustainability strategies. It highlights the important dimensions that should be considered and prioritised when preparing the transformation roadmap. These dimensions are tailored for R&D but can be a good indication for any other type of organisation. Keywords: Sustainability; Digitalisation; Digital transformation; Means-End Chain Theory (MEC); Research and development (R&D) *Corresponding author: montequi@uniovi.es (Rodríguez Montequín, V.) Article history: Received 8 March 2022 Revised 15 August 2022 Accepted 18 August 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction To remain competitive in today’s market and to assure long-term survival, organisations must continuously develop innovative, high-quality products and services and renew their way of operating [1]. Therefore, they are under tremendous pressure to transform. It is the case for organisations from both developed and transitioning countries [2]. The majority of them are taking advantage of new technologies, pursuing their “digital transformations” [3–5]. At the same time, companies must reduce their carbon footprint and become more sustainable overall [6, 7]. These two strategies are interconnected and some of these connections have been demonstrated in [8], where the authors argue that they are positively related. It can be stated that a given company that transforms itself becomes more efficient and thus automatically more sustainable. On the other hand, new technologies offer resources that can be applied to accelerate sustainability [7, 9]. 152 Sustainability and digitalisation: Using Means-End Chain Theory to determine the key elements of the digital maturity … Additionally, recent events (mainly the global pandemic that started in early 2020) highlighted the growing need for organisations to become more digitally mature. This is supported by the emerging research including the study of Fletcher and Griffiths [10] suggesting that VUCA environments (VUCA stands for Volatility, Uncertainty, Complexity and Ambiguity) strengthen the need for digital transformation. After analysing the effects of global pandemic, they even suggest, that digital is no longer an option but became a necessity. Such events affect more severely less digitally mature organisations. Another research by Vandana and Ashutosh [11] supports this observation. The task of continuous reinvention of a given organisation in many cases is performed by Research and Development departments (R&D). As leaders of such creativity and innovation, R&D organisations are at the forefront of progress. They contribute towards new technologies, products, and manufacturing processes more than any other entity. It is their mission to apply innovation to make new processes more efficient, products more attractive and cheaper, and overall to help to become more efficient, generate less waste and reduce the impact on the environment, business, and society [12]. A good way to progress on such a transformational journey is to apply a concept of digital maturity. Assessing the state of digital maturity and deciding how to proceed to a higher maturity level can help to create transformation programs using a systematic approach and eliminate blind spots. Digital maturity models are used for prescriptive, descriptive and comparative purposes [13, 14]. Many of them have been developed by organisations to assess their processes, identify improvement areas and use them to drive the way they operate [15]. Maturity assessments can be applied to an entire organisation or part of it, and can also be specifically developed and applied to certain aspects of any business process. The usual way of employing a maturity model is to use it to assess an organisation’s current maturity and then prepare a strategy for the future to achieve a higher level. Although there are several publications about digital maturity within the existing literature, the authors noticed that there is a gap when it comes to digital maturity tailored to the needs of R&D organisations, and they hope that this publication can contribute towards closing this gap. It attempts to describe which digital maturity dimensions should be considered to fit into R&D specifics. It also tries to explore the relation between digital transformation and sustainability. The authors’ understanding of sustainability is based on the “Brundtland Report”, which was published in 1987 by the World Commission on Environment and Development (WCED) [16]. In this report sustainability or sustainable development is described as “development that meets the needs of the present without compromising the ability of future generations to meet their own needs”. It is based on three pillars: social, economic and environmental sustainability [17]. Currently, both sustainability and digitalisation strategies are at the top of most companies’ agenda. Even if this is the case, in many organisations both strategies are operating in parallel, being executed by separate departments with people with different skillsets. Recently, however, there is emerging scientific evidence that digitalisation and sustainability are interconnected [8, 18]. There is an emerging opportunity to join efforts to accelerate sustainability goals by using digital technologies. It is worth noticing the work of Gupta et al., who presented the Digitalisation‒Sustainability Matrix, where they researched how technologies impact Sustainable Development Goals (SDGs) [19]. The authors firmly believe that there is no responsible digitalisation without considering the dimension of sustainability. A digitally transformed company becomes more efficient, generates less waste and uses fewer resources, which makes it more sustainable. The first research goal of this study was to determine the key elements of a digital maturity model tailored for such an R&D organisation. The focus was on the model’s key dimensions (often also referred to as “goals” or “values”). The second goal was to conduct a preliminary study on the sustainability dimension as part of the digital maturity model, considering the fact that digital technologies have a big potential to accelerate sustainability [20]. The objectives were achieved by applying a 2-step approach. Firstly, the authors prepared an initial set of dimensions based on the literature review of the existing digital maturity models. Secondly, by using the Means-End Chain (MEC) method, they refined this initial set and suggested a usable comAdvances in Production Engineering & Management 17(2) 2022 153 Kupilas, Rodríguez Montequín, Díaz Piloñeta, Alonso Álvarez promise which can be used for an R&D digital maturity model. Information for the MEC was taken from the outputs from interviews conducted with experts from both inside and outside R&D. This paper starts with the literature review and the description of methods used. These are then followed by empirical data analysis, discussion of results and conclusions, with suggestions for further potential research areas. 2. Literature review The authors conducted the literature review according to the guidelines proposed by Kitchenham at Keele University [21]. They searched Google Scholar, SCOPUS, EBSCO and ProQuest for the terms “Digital AND Maturity AND Literature AND Review”. The initial result showed 292,000 entries in Google Scholar, 168 in SCOPUS, 834 in ProQuest and 32 in EBSCO. To limit the results to the most relevant ones, the authors applied several filters. As the various repositories were constructed in different ways, it was impossible to apply the same filters on all of them in the same way so, in order to ensure that the review was comprehensive, the authors applied filters where it was possible without changing the number of results in the repositories where such filters did not exist. For example, ProQuest offered the filter called “literature reviews” which reduced the number of papers initially found from 834 to 151, however, such filter did not exist in Google Scholar, SCOPUS and EBSCO. The next level of filters applied was the language (English), which reduced the number of results in SCOPUS from 168 to 164. An additional filter applied was to include results that were “peer reviewed”, which reduced the number of results in ProQuest to 149 and EBSCO to 27. The last filter applied was to look for results in the paper title and this reduced the number of results to 259 (Google Scholar 8, SCOPUS 3, ProQuest 149, EBSCO 99). The authors analysed these 259 results, eliminated overlaps across repositories and selected 8 publications which were relevant in the first stage of the research. These publications were used to find the existing most relevant digital maturity models, determine if there are gaps related to specifics of Research and Development organisations and which potential dimensions of the existing models could be adapted and used for building a model that is better tailored to R&D specifics. Table 1 lists the literature selected by the authors. The nine models shown in Table 2 represent the results of the authors’ analysis of the models developed by both academics and practitioners. More models were found but either their research was not completed or there were not enough details about the model, making it too open to individual interpretation and thus too difficult to use, making the result unpredictable. Table 1 Literature review output – selected publications Publication name Authors Multi-Attribute Assessment of Digital Kljajić Borštnar, M., Pucihar, A. Maturity of SMEs [22] Digital Maturity Models: a systematic Ochoa-Urrego, R.-L., Peña-Reyes, J.-I. literature review [23] Industry 4.0 Roadmap: Implementation for Small and Cotrino, A., Sebastián, M.A., González-Gaya, C. Medium-Sized Enterprises [24] Towards a Comprehensive Exploration and Mapping of Maturity Models in Digital Gandhi, A., Sucahyo, Y.G Business: A Systematic Literature Review [25] Digital Transformation Maturity: Teichert, R. A Systematic Review of Literature [26] Digital Maturity Models for Small and Medium-sized Enterprises: A Systematic Williams, C., Schallmo, D., Lang, K., Boardman, L. Literature Review [27] An Industry 4.0 maturity model proposal Santos, R.C., Martinho, J.L. [28] Development of an Assessment Model for Gökalp, E., Şener, U., Eren, P. Industry 4.0: Industry 4.0-MM [29] 154 Year published 2021 2021 2020 2020 2019 2019 2019 2017 Advances in Production Engineering & Management 17(2) 2022 Sustainability and digitalisation: Using Means-End Chain Theory to determine the key elements of the digital maturity … Model/Research name Table 2 Literature review output – Digital Maturity Models Maturity levels Dimensions Industry 4.0 / Digital Digital readiness for Operations Self-Assessment Industry 4.0 [31] 3 maturity levels (Vertical Integrator, Horizontal Collaborator, Digital Champion) SIMMI 4.0 [32] Industry 4.0 maturity Acatech Industry 4.0 Industry 4.0 maturity 5 maturity stages (Basic Digitisation, Crossdepartmental Digitisation, Horizontal and Vertical Digitisation, Full Digitisation, Optimised Full Digitisation) 6 dimensions (Business Models, Product & Service, Portfolio Market & Customer Access, Value Chains & Processes, IT Architecture, Compliance, Legal, Risk, Security & Tax, Organisation & Culture) IMPULS Industry 4.0 Readiness [30] Maturity Index [33] Research context Industry 4.0 readiness DREAMY (Digital REadiness Digital readiness for Assessment MaturitY Industry 4.0 model) [34] A maturity model for Industry 4.0 maturity Industry 4.0 Readiness [35] 360 Digital Maturity Assessment [36] 6 maturity levels (Outsiders, Beginner, Intermediate, Experienced, Expert, Top performers) 6 dimensions (Strategy & Organisation, Smart Factory, Smart Operations, Smart Products, Data-driven Services, Employees) 3 dimensions (Vertical Integration, Horizontal Integration, Cross-sectional Technology Criteria) 6 maturity stages (Computerisation, Connectivity, Visibility, Transparency, Predictive Capacity, Adaptability) 4 structural areas (Resources, Organisational Structure, Information Systems, Culture) Likert scale maturity levels (from rating 1= “not important” to rating 4 = “very important”) 9 dimensions (Strategy, Leadership, Customers, Products, Operations, Culture, People, Governance, Technology) 5 maturity stages (Initial, Managed, Defined, Integrated and Interoperable, Digital-Oriented) 5 structural areas (Design and Engineering, Production Management, Quality Management, Maintenance Management, Logistics Management) Digital readiness for Indus- 6 maturity stages (None, 5 digital dimensions (Govtry 4.0 Basic, Transparent, Aware, ernance, Technology, ConAutonomous, Integrated) nectivity, Value Creation, Competence) HADA Model developed by Spanhttp://hada.industriaconect ish Government ada40.gob.es/ Multi-Attribute Assessment Digital Maturity of SMEs of Digital Maturity [22] 6 maturity stages assigned by point system 0-1000 based on survey results (Static, Aware, Competent, Dynamic, Reference, Leader) 4 maturity stages (Lagging behind, Initial, Advanced, Digital winner) 5 dimensions (Strategy and business model, Processes, Organisation and people, Infrastructures, Products and services) 2 dimensions (Digital capability, Organisational capability) The authors found the literature review very insightful. It showed that the topic of digital maturity is increasingly on the agendas of researchers and practitioners. It was also interesting that there is a big overlap between digital maturity and Industry 4.0 readiness, and in many cases these terms were used as synonyms. They concluded, however, that while Industry 4.0 readiness Advances in Production Engineering & Management 17(2) 2022 155 Kupilas, Rodríguez Montequín, Díaz Piloñeta, Alonso Álvarez was mainly targeting industrial applications, digital maturity can be used across a wider set of organisations, including public services or non-profit. The review also showed that relevant research and adoption accelerated over the last 10 years, demonstrating the growing need for frameworks that would help organisations build their roadmaps and strategies in a structured and unbiased way. The further explanation of how authors used the outcomes from this literature review and arrived at the initial set of dimensions is described in more detail in chapter 3: “Research design”. It is also worth noticing that none of the existing maturity models described in the literature contains the sustainability dimension, which prompted the authors to include it in their proposed set of dimensions and then discuss further with experts whether it should or should not be considered. 3. Research design 3.1 General design To address the research questions, the work was organised into two main phases as shown in Fig. 1. In Phase 1, the authors wanted to find and analyse the research already available. This served two goals. Firstly, the authors wanted to validate if there is a gap in the existing literature in relation to R&D organisations to ensure the scientific value and contribution of their work. The second goal was to derive the initial set of dimensions to be validated in Phase 2. In this phase the authors conducted interviews with experts and applied the Means-End Chain method to arrive at the final set of dimensions addressing the needs of research and development. Fig. 1 The structure of the research To prepare the initial set of dimensions, the authors summarised and grouped the output from the literature review (dimension elements from Table 2) into three categories, namely, “External factors”, “Internal factors” and “Organisation” as shown in Table 3. From “External factors”, the authors suggested the following “Products” and “Services” as initial dimensions. From “Internal factors”, the most prevailing to be added to the initial list were “Operations” and “Facilities”, and from the “Organisation” side the authors suggested using “People” and “Strategy”. Additionally, the authors added the “Sustainability” dimension to test its 156 Advances in Production Engineering & Management 17(2) 2022 Sustainability and digitalisation: Using Means-End Chain Theory to determine the key elements of the digital maturity … viability as part of the digital maturity model of an R&D organisation. The rest of the elements in Table 2 did not need to form separate dimensions. For example, “Business Models” can be classified as part of “Operations” similarly to “Compliance, Legal, Risk, Security and Tax”. “IT architecture” can be part of “Facilities” and does not require a separate dimension to be formed. The authors believed that the initial proposed set of dimensions catered well for all the elements identified during the literature review. To verify this initial list of dimensions and to refine the findings, the authors applied the Means-End Chain (MEC) method. This method is widely known and used in marketing, but has not previously been used to compile and verify the elements of digital maturity. However, it was used in several studies outside of marketing that inspired the authors to apply it in their research. For example, in project management, in 2010 Verburg et al. used MEC to determine critical success factors for project managers in virtual work settings [37]. Later, in 2018, Chen et al. used MEC for innovation research program performance evaluation [38]. Model/Research name IMPULS Industry 4.0 / Digital Operations Self-Assessment Table 3 Initial grouping of the dimensions External factors Smart products Data-driven services Market & customer access SIMMI 4.0 Acatech Industry 4.0 Maturity Index DREAMY (Digital REadiness Assessment MaturitY model) A maturity model for Industry 4.0 Readiness 360 Digital Maturity Assessment HADA Multi-Attribute Assessment of Digital Maturity 3.2 Means-End Chain Customers product Products and services Internal factors Smart factory Smart operations Business models Product & service portfolio Compliance, legal, risk, security & tax IT architecture Value chains & processes Vertical integration Horizontal integration Digital product development Cross-sectional technology criteria Resources Information systems Process monitoring and control Technology Operations Technology Technology Connectivity Value creation Infrastructure Strategy and business model Processes Digital capability Organisation Employees Strategy and organisation Organisation & culture Resources Information systems Organisation Strategy Leadership Culture People Governance Governance Competence Strategy and business model Organisation and people Organisational capability The Means-End Chain (MEC) method is based on the attributes‒benefits‒values/goals sequence that forms a means-end chain. It was used initially by Gutman to understand the perceptions and motivations of consumers when they make their purchasing choices [39]. In that sense, it connects product or service attributes to the consequences produced by these and the latter to values. The MEC method is based on the sequence or hierarchy shown in Fig. 2 [40]. The links are identified by means of interviews conducted with the focus group individuals (customers, experts, etc.). The laddering interviewing technique is used for the elicitation. Laddering involves a Advances in Production Engineering & Management 17(2) 2022 157 Kupilas, Rodríguez Montequín, Díaz Piloñeta, Alonso Álvarez tailored reviewing format using a series of directed probes, typified by the “Why is it important to you that…” question [41]. The answers are explored further, and a ladder of constructs is created. The soft laddering method [42] is the recommended technique with a relatively small sample size (<50) and research of an exploratory nature [43]. In the case of this research, the values are the dimensions of the digital maturity model that are selected by experts for their attributes as well as their benefits. The links between products, values and attributes were identified through interviews conducted with subject matter experts following the laddering technique [41]. These interviews were conducted by asking about the attributes, why they are important (what benefits would be realised) and what values/goals they would serve. For example, if the goal is to have “Smart operations and research” in place, then products can be developed faster (benefit). To achieve this benefit, there is a need to “digitise information” (attribute) or have “digital platforms in place” (another attribute). Once the interviews were finished, the Implication Matrix (IM) and Hierarchical Value Map (HVM) were created by LadderUX software to analyse the results. The Implication Matrix is a tabular representation of the interview outcomes, while the Hierarchical Value Map (HVM) visually links attributes, benefits and goals. Examples of the HVMs created during this research can be found in the “Discussion” section (Figs. 3-6). To determine the order of importance for all the attributes, benefits and dimensions, the authors calculated their centrality as described in the following section. 3.3 Calculating centrality Fig. 2 The sequence flow of the Means-End Chain method Centrality is defined as the ratio of in-degrees plus out-degrees of a particular element over the sum of all cell-entries in the implication matrix [44]. It highlights those mentioned by most of the experts. The equations below represent the Implication Matrix (IM) and illustrate how the centrality is calculated. The columns of the IM are represented by index i – from 1 to the nth element, the rows by index j – from 1 to the nth element. Column S includes the sum of “out” elements in the row and column T includes the sum of “out” elements from both relevant rows and columns (the figure in column S). Column C displays the calculated centrality. 𝑎𝑎11 ⎡𝑎𝑎21 ⎢ ⋮ 𝐼𝐼𝐼𝐼 = ⎢ 𝑎𝑎 ⎢ 𝑗𝑗1 ⎢ ⋮ ⎣𝑎𝑎𝑛𝑛1 𝑎𝑎12 𝑎𝑎22 ⋮ 𝑎𝑎𝑗𝑗2 ⋮ 𝑎𝑎𝑛𝑛2 ⋯ ⋯ ⋱ ⋯ ⋯ ⋯ 𝑎𝑎1𝑖𝑖 𝑎𝑎2𝑖𝑖 ⋮ 𝑎𝑎𝑗𝑗𝑗𝑗 ⋮ 𝑎𝑎𝑛𝑛𝑛𝑛 ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ Calculation of the values of the elements is shown below: 158 𝑆𝑆𝑗𝑗 = ∑𝑛𝑛𝑗𝑗=1 𝑎𝑎𝑗𝑗𝑗𝑗 𝑎𝑎1𝑛𝑛 𝑎𝑎2𝑛𝑛 ⎤ ⋮ ⎥ ⎥ 𝑎𝑎𝑗𝑗𝑗𝑗 ⎥ ⋮ ⎥ 𝑎𝑎𝑛𝑛𝑛𝑛 ⎦ (1) (2) Advances in Production Engineering & Management 17(2) 2022 Sustainability and digitalisation: Using Means-End Chain Theory to determine the key elements of the digital maturity … 𝑇𝑇𝑗𝑗 = 𝑆𝑆𝑗𝑗 + ∑𝑛𝑛𝑗𝑗=1 𝑎𝑎𝑗𝑗𝑗𝑗 ∑ 𝑇𝑇 = ∑𝑛𝑛𝑗𝑗=1 𝑇𝑇𝑗𝑗 Finally, the centrality of each element is calculated as: 4. Empirical data analysis 𝐶𝐶𝑗𝑗 = 𝑇𝑇𝑗𝑗 ∑ 𝑇𝑇 (3) (4) (5) The process of interviewing started on 26 May 2020 and lasted until 2 February 2021. Considering the situation with the global pandemic (COVID-19) and the physical location of the experts, the authors conducted interviews using Microsoft Teams. All of them were recorded and stored in Microsoft Stream. At this stage, 32 senior experts (28 men and 4 women) from various functions and companies were interviewed, of whom two experienced technical difficulties and were not included further in the study. These experts are connected to digital transformation either within their own organisation or participating in the digital transformation of several organisations as a partner or consultant. They reside in both the Americas and Europe and work in companies of various sizes, from a single consultant to multinational corporations with over 200 000 employees. It was very important to ensure a wide representation of experts and not to limit the research to specific segments or industries. These segments and industries included tech startups, telecommunication, recruitment, research and development, fast-moving consumer goods (FMCG), manufacturing, management consulting, technology companies and academia. The authors wanted to collect both R&D views as well as external views to eliminate blind spots and biases. The interviewees resided in the following countries: Canada (1), Denmark (1), France (3), Luxembourg (2), Netherlands (2), Spain (2), UK (15) and USA (6). Authors’ criteria for selection were not specifically related to the countries but to the area of expertise of the interviewee and to the type of their organization. Authors wanted to get the view from both inside or outside the R&D, from small and big organisations and they believe that it has been achieved. When it comes to the question about the number of interviews to conduct in order to obtain meaningful results, the authors used the study conducted by Guest et al. [45]. In this publication they discuss the data saturation and variability in extracting information from interviews to determine how many interviews are enough to get meaningful results. In their experiment they concluded that to achieve meaningful themes and useful interpretation it takes as little as 6 to 12 interviews for this kind of study. They caution, however, that in some cases 12 interviews may not be enough. For example, if the "selected group is heterogeneous, the data quality is poor, and the domain of inquiry is diffuse and/or vague. Likewise, you will need larger samples if your goal is to assess variation between distinct groups or correlation among variables”. With that in mind, considering that the population selected for this research is relatively homogeneous (each of the interviewees has certain expertise in the field of digital transformation) and to accommodate a certain margin to eliminate insufficient data, the authors decided to conduct 30 interviews. Patterns were noticed after 12 of them, when the goals, attributes, and benefits started to repeat themselves (although some of them were named differently like “Employees” versus “People”, the meaning was the same). With the initial set of goals (dimensions), the in-depth interviews were conducted by asking the following questions: “Which attributes would need to be in place to become digitally mature?” and “Why are these attributes important?”. The purpose of the first question was to identify the attributes, the purpose of the second was to identify benefits and goals/values. After each interview, the values (goals) were noted down together with their links to the benefits, as well as the attributes that were mentioned by the experts. These links were entered into the LadderUX software [46], which generated the Implication Matrix (with calculated centralities) as well as the Hierarchical Value Map showing graphically these connections. After several interviews the set of values evolved to “Smart operations and research” (to include the scientific aspect as well as the organisational), “Smart facilities”, “Smart products and services”, “People”, “Strategy and organisation” and “Sustainability”, which was consistent throughout the majority Advances in Production Engineering & Management 17(2) 2022 159 Kupilas, Rodríguez Montequín, Díaz Piloñeta, Alonso Álvarez of the interviews. It also became evident that there is a need to standardise responses as much as possible to avoid overlap (for example, some experts referred to a dimension called “Employees”, some to “People” and some to “People and Culture”). To represent the degree of the central role of each element [47], the authors calculated the centrality. Centrality can be interpreted as a key element that determines the importance of the goals, benefits and attributes. Once calculated, the elements in each group were arranged from the largest to the smallest value of their centrality. Overall, the authors collected 111 elements that were grouped into 7 Goals (Dimensions), 47 Benefits and 57 Attributes. After calculating each element’s centrality, they were sorted by it. The tables below show each of the elements from the largest to the smallest value of centrality. The Goals are shown in Table 4 and Benefits and Attributes in Table 5. G1 G2 G3 G4 G5 G6 G7 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13 B14 B15 B16 B17 B18 B19 B20 B21 B22 B23 B24 B25 B26 B27 B28 B29 B30 B31 B32 B33 B34 B35 B36 B37 B38 160 Table 4 List of the Goals Goal Smart operations and research People Sustainability Strategy and organisation Smart facilities Smart products and services Smart innovation Table 5 Summary of Benefits and Attributes Benefit Faster product development Increased efficiency of operations Innovative workforce Faster process development Faster response to market dynamics Skilled workforce New revenues More value for customers Profitability Understand carbon footprint Increased competitiveness Understand the strategy Outcome-based pricing Driving reputation Increased customer satisfaction Lower energy consumption Lower emissions Less waste Operational flexibility Improved health and safety Educated workforce Lower carbon footprint Reduced time to market People understand emerging technologies Limit the negative consequences of operations Effective usage of available data New customers Market adaptability Increased employee satisfaction Making right decisions Longer asset lifecycle Product life cycle control Right pricing Improved quality of products and services Faster pace to sustainability Articulate and share organisational goals Proactiveness Enhanced product life Centrality 0.051 0.051 0.047 0.046 0.037 0.032 0.019 0.019 0.013 0.012 0.011 0.009 0.008 0.008 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.002 0.002 0.002 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28 A29 A30 A31 A32 A33 A34 A35 A36 A37 A38 Centrality 0.076 0.057 0.051 0.024 0.02 0.013 0 Attribute Data management Education of people Analytics tools Knowledge creation and management platform Smart platforms Communication Collaboration tools Digitalise the equipment Sharing scientific information Sharing experimental information Digital twins/simulations Access to right talent Sustainability score dashboard Efficiency dashboards Continuous improvement for process and culture Digitise information Product tracking technology Change management process Enabling experimentation Efficient and secure IT Sharing data with suppliers and customers Shared environmental data Shared customer data Predictive maintenance Smart horizontal and vertical integration Capturing value creation Meaningful data exchange Sourcing green energy Sustainability assessment process Innovation performance reviews Innovation workshops Innovation strategy Technology-based intelligence Innovation governance Process automation Usage of standards Automatic commissioning of the equipment Collaboration with academia Centrality 0.052 0.035 0.013 0.013 0.009 0.009 0.007 0.006 0.006 0.006 0.005 0.005 0.005 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 Advances in Production Engineering & Management 17(2) 2022 Sustainability and digitalisation: Using Means-End Chain Theory to determine the key elements of the digital maturity … B39 B40 B41 B42 B43 B44 B45 B46 B47 Benefit Data-driven decision-making Ability to measure impact Efficient resource usage Supply chain transparency Positive impact on supply chain Attract investors Common IT platforms Knowledge created and shared Optimised use of budget Table 5 (Continuation) Centrality 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0 0 A39 A40 A41 A42 A43 A44 A45 A46 A47 A48 A49 A50 A51 A52 A53 A54 A55 A56 A57 Attribute Measuring environmental impact Leadership fit Distributed team Agile strategy Carbon offsetting activities Rotating people across organisation Coaching/mentoring process Circular economy principles Supply chain carbon footprint Drone technology Image recognition Digital hiring tools Governance ISO 14001 Digitalise partnerships LIMS system in place Production data tracking and linking with product Leverage external partners Budget Centrality 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0 0 0 0 0 The Hierarchical Value Map (HVM) generated by Ladderux.org [29] consisted of 242 ladders with a total of 708 links. 475 of these links were direct and 233 were indirect. The number of elements and links made the visualisation of the entire HVM difficult for the purpose of this publication. To make the ladder examples presentable, the authors carried out a separate analysis for the top three dimensions and show them in more detail in chapter 5 “Discussion”. 5. Discussion After the round of interviews, the authors arrived at 6 dimensions. These dimensions are: “Smart operations and research”, “People”, “Sustainability”, “Strategy and organisation”, “Smart facilities” and “Smart products and services”. Due to the fact that the centrality of the “Smart innovation” dimension was 0, it was removed from the final list (see Table 4). Out of 47 collected benefits, the 5 most prevailing ones by centrality were “Faster product development”, “Increased efficiency of operations”, “Innovative workforce”, “Faster process development” and “Faster response to market dynamics”. Four of these are related to efficiency and the speed of the response to the market, but it is worth noticing that the third most central element was related to people and innovation. It could be said that an innovative workforce benefits from the technology and education, which in return helps to achieve the goals of the organisation. The 57 collected attributes are a mixture of technologies, tools, platforms (e.g. “Data management”, “Collaboration tools”, “Digital twins/simulations” etc.) and processes (e.g. “Collaboration with academia”, “Sustainability assessment process”, “Usage of standards”, etc.) The top ones by centrality are “Data management”, “Education of people”, “Analytics tools”, “Knowledge creation and management platform” and “Sustainable operations”. It is understandable that the “Data management” had the highest centrality score. This is required as a foundation for any operations to become “data- driven”. It was very interesting to see that the “Education of people” was placed in second position, which confirms that digitalisation is not purely dependent on technologies. On the contrary, the right education of people will be a critical attribute driving the culture shift required to move to the higher level of digital maturity. “Analytics tools” were placed in third position, which underlines the need for tools to act on the collected data. The explosion of various analytics tools offerings on the market confirms the importance of this attribute. Next in line, “Knowledge creation and management platform” seems an important attribute especially for R&D organisations where scientists create and share both scientific and organisational knowledge. As a side observation from the interviews, the authors noted that in many organisations the knowledge is scattered in various repositories, creating a challenge for people to find the right information. What is more, often there is not a single digital tool which would connect these separate pockets of knowledge. This was more visible in large organisaAdvances in Production Engineering & Management 17(2) 2022 161 Kupilas, Rodríguez Montequín, Díaz Piloñeta, Alonso Álvarez tions with various legacy knowledge repositories. However, the majority of them stated that deploying a digital tool that will connect various repositories and help to extract value from them was one of their priorities in order to speed up future development and accelerate research. To further focus on the first three dimensions, the authors separated them from the other elements in the LadderUX tool [46]. Fig. 3 shows the dimension “Smart operations and research”, focusing on the benefit B1 – “Faster product development”. The authors observed that “Data management” and “Analytics tools” were the first attributes contributing towards “Faster product development”. However, it is worth mentioning the “Knowledge creation and management platform” - although it is a technical tool, it fosters collaboration and teamwork as people will use it to document their work and to learn from what was already done in the past on any given topic or project. A very similar pattern could be observed for “Faster process development”. This is due to the fact that, usually, to produce any given product faster, the production or manufacturing process needs to be more efficient. Interestingly, taking a closer look at the three further benefits with the largest centrality, it can be concluded that their key attributes are the same as those previously described and illustrated in Figs 5 and 6. These benefits are “Increased efficiency of operations”, “Faster response to market dynamics” and “Faster pace to sustainability” (see Fig. 4). The important thing to notice in this ladder is the link between digital transformation and sustainability. It shows that, by achieving the goal of “Smart operations and research”, the organisation will not only become more efficient and faster in terms of product development and manufacturing. It clearly also accelerates the path to sustainability and proves that, by moving up on the digital maturity curve, companies become more sustainable. Fig. 5 shows the simplified HVM for the “People” dimension. The simplification eliminated elements with fewer than 5 connections. For this dimension the emphasis should be put on the education attribute. Arming people with the right skillset future-proofs the existence of the organisation. Education also makes people more aware of the context of digitalisation and its purpose, which makes it easier to accept change. Additionally, education, training and overall career development have a big influence on employee satisfaction and a significant impact on their performance, driving the performance of the organisation [48]. To visualise the sustainability, the authors disabled all other dimensions in the laddering tool and then set cut-off values for connections equal to or less than 2 for the attributes and benefits, ending up with the ladder shown in Fig. 6. Fig. 3 Simplified ladder diagram for “Smart operations and research” (Faster product development benefit) 162 Advances in Production Engineering & Management 17(2) 2022 Sustainability and digitalisation: Using Means-End Chain Theory to determine the key elements of the digital maturity … Fig. 4 Simplified ladder diagram for “Smart operations and research” Fig. 5 Simplified ladder diagram for “People” dimension Fig. 6 Simplified ladder diagram for “Sustainability” dimension Advances in Production Engineering & Management 17(2) 2022 163 Kupilas, Rodríguez Montequín, Díaz Piloñeta, Alonso Álvarez It was evident again that “Data management” is a key attribute, contributing to lower energy consumption, by enabling data-driven decision-making. It also allows a better understanding of the carbon footprint. As it forms the foundation for digitalisation, it is an important contributor towards better sustainability. In order to move to a higher stage of digital maturity, the data management (the attribute that comes with the highest centrality from all 59), supported by the analytics tools (the attribute that came third), should be the first ones considered when preparing the digital roadmap for the organisation. If the budget is limited and requires prioritisation, these should be the top priorities, contributing to most of the goals, including “Sustainability”. Finally, the authors carried out a sensitivity analysis to understand how each single attribute influences the dimensions. For this, they calculated the values of the dimensions’ maturity separately for each attribute, setting its value to 1 (full influence on the dimensions) while setting all the other attributes’ values to 0 (no influence on dimensions). The result is shown in Fig. 7. Such analysis can be very useful for selecting the areas of focus when creating plans and planning the resources needed for achieving higher levels of maturity. For example, focusing solely on “Realtime data collecting and sharing” and investing most of the effort in improving the data management has a major positive influence on the overall digital maturity for most of the dimensions. It could be imagined that the creators of roadmaps and strategies could place a “Threshold line” on the diagram and use it to plan their activities: moving the threshold line up or down on the vertical scale could help in filtering the attributes and optimise between the desired maturity levels and the resources available to invest in the selected attributes. Sustainability aspect Fig. 7 Attributes’ influence on dimensions One of the observations after conducting the initial review was that currently available Digital Maturity or Industry 4.0 Readiness models do not include the sustainability aspect. The authors asked themselves the following question: “why is sustainability important, and should it be included in digitalisation activities at all?” The conclusion was that it is impossible to be “digitally mature” without considering the sustainability aspect. This is true even more in the case of R&D organisations as they work to drive and secure the long-term future (and thus economic sustainability) of the company. This thinking was confirmed by the results from the interviews, where the dimension of “Sustainability” had the centrality of 0.045, placing it in third place after “Smart operations and research” and 164 Advances in Production Engineering & Management 17(2) 2022 Sustainability and digitalisation: Using Means-End Chain Theory to determine the key elements of the digital maturity … “People” and before “Strategy and organisation”, “Smart facilities” and “Smart products and services”. This clearly demonstrates that it is high on the agenda of the experts. It is also natural to think that an organisation that progresses on the digital maturity journey will become more efficient, generating less waste, becoming naturally more friendly to the environment and to society. There are other, non-tangible motivations like the simple fact that people care about sustainability more than they used to years ago, knowing more about how operations impact the environment and society. Such conclusions were also confirmed by emerging research which concludes that both digitalisation and sustainability are interconnected [8, 18, 19]. To further understand the current situation, separate interviews were conducted with both Sustainability and Digitalisation teams in one of the world’s leading manufacturing companies, concluding that even if companies include both Digital and Sustainability strategies in their operations, they are most likely executed in parallel by different teams. The skills of the teams are different or hardly overlapping, with the Digitalisation teams being more technical than the Sustainability teams. Another observation was that, while there is an initial appetite to merge both concepts from the Sustainability side, the Digitalisation tends to focus on narrower aspects related to shorter-term goals associated with ongoing projects like reducing energy consumption, CO2 emissions, diffuse dust pollution, etc.) 6. Conclusion In this study the authors attempted to determine the key elements of the Digital Maturity model applicable to R&D organisations, including the aspect of sustainability. Using the Means-End Chain method, the authors confirmed that digitalisation and sustainability are interconnected and that, by working together, they support each other. This is in line with conclusions from other research already available, including outcomes from studies carried out by Denicolai et al. [8] and Gupta et al. [19]. With this in mind, and the fact that the “Sustainability” dimension was the third most important one by centrality after “Smart operations and research” and “People”, the authors concluded that it should be included in the maturity model. The following dimensions of the R&D Digital Maturity model emerged from the research, listed from largest to smallest centrality: “Smart operations and research”, “People”, “Sustainability”, “Strategy and organisation”, “Smart facilities” and “Smart products and services”. Interestingly, looking into the centrality gap between these elements, it can be determined that “Smart operations and research” should be the most important element to address. The gap between this element and the next two (“People” and “Sustainability”) was 0.019. Expert opinion clearly stated that the way in which R&D is organised, how it conducts the experiments, how it collects, stores and uses data, how it generates and shares knowledge, and the way it collaborates with both customers and partners are the key factors to accelerate research outcomes. The next areas to review when considering the digital maturity roadmap are “People” and “Sustainability”. The centrality gap between them was only 0.006, which indicates that they are both of equal importance. The second highest centrality for the “People” dimension clearly indicates that culture and the people factor must be considered together with the technology factor during the setting up of the transformation program. Sustainability had the third highest centrality score, showing its growing importance. The last three dimensions, “Strategy and Organisation”, “Smart Facilities” and “Smart Products and Services”, were separated from the three first by 0.027. Such gap splits the dimensions into two clusters which can be used as an indication for priority when building the digital transformation roadmaps. It is possible that such distribution is specific and only visible for R&D organisations, as they usually rely on human potential enabling creativity and innovation based on the solid foundation of technology. Collaboration between digitalisation and sustainability is essential. R&D organisations should embrace and lead this effort as they are at the forefront of progress in all industries. The authors included the aspect of sustainability in the Digital Maturity model based on the results from the interviews, but also based on emerging trends, where both strategies are at the top of the agendas of companies as well as policy-makers in the majority of countries, companies and instituAdvances in Production Engineering & Management 17(2) 2022 165 Kupilas, Rodríguez Montequín, Díaz Piloñeta, Alonso Álvarez tions. The digitalisation will aid and accelerate the path to sustainability by the application of technologies, processes, and skills. Most likely those R&D organisations which progress on the digital maturity path and include the “Sustainability” dimension will be able to better carry out activities to innovate and introduce new products, services, and processes. They will also support their customers better and use innovative and effective ways to generate and share knowledge, which, in turn, will automatically help both their internal or external customers to become leaders in their respective markets and sectors. When it comes to further research, the authors suggest two paths built on their initial work. Path 1 focuses on continuing to build the Digital Maturity model for R&D organisations by further nurturing the attributes and benefits leading to the model, including levels of maturity, scores and the process of assessing digital maturity, as well as the process of monitoring progress. This could result in an assessment tool that could be used by various organisations to assess their maturity and build their digital roadmaps. Path 2 relates to the Sustainability dimension to further nurture how technologies can accelerate it. 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Effect of education and training, career development and job satisfaction of employee performance at the department of education office of Gowa, Journal of Education and Vocational Research, Vol. 7, No. 1, 14-20, doi: 10.22610/jevr.v7i1.1217. 168 Advances in Production Engineering & Management 17(2) 2022 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 2 | June 2022 | pp 169–182 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.2.428 Original scientific paper Supply chain coordination based on the probability optimization of target profit Jian, M.a, Liu, T.a,*, Hayrutdinov, S.b, Fu, H.a aSchool of Transportation and Logistics, Southwest Jiaotong University, Chengdu, P.R. China Development Institute of Singapore in Tashkent, Uzbekistan bManagement ABSTRACT ARTICLE INFO Supply chain management decision-making study mainly based on the expected utility theory and most of the studies are obtaining the average values in the statistical sense. For Supply Chain (SC) decision-making individuals the statistical-based optimal profitability brings decision conflicts in the particular market within a specific period. Moreover, the small and medium outsourcing participants face unexpected outcomes which are the main cause of SCs disruption. This study proposes a contractual coordination model that maximizes the probability of a pre-determined Profit Target (PT). The purpose of this paper is to reduce the influence of demand uncertainty with the high risk of unexpected outcomes. We constructed the Revenue Sharing (RS) and buyback contract models within the SC participants’ PT conditions and then discussed the SC overall performance. We simulated and analyzed the coordination conditions and the decision-making preferences of SC participants under the two contracts. From the comparison, under the PT strategy, the retailer is more willing to adopt the RS contract rather than the buyback contract. But the SC upstream supplier's contract selection decision depends on the specific contract parameters. Finally, numerical results indicated the contract selection decisions with the given PT of both SC participants. Keywords: Supply chain; Coordination; Contractual coordination; Revenue-sharing contract; Buyback contract; Profit target; Optimization; Probability optimization *Corresponding author: liutong_60@163.com (Liu, T.) Article history: Received 14 February 2022 Revised 8 August 2022 Accepted 12 August 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction Fast-growing market competition is increasing the SC market demand uncertainty which is one of the main causes of SCs disruption. Moreover, the healthcare industry and short life-cycle products’ SCs face unpredictable and unexpected market returns caused by the combination of industry competitiveness and perishability. The management of SC with the Profit Target based on decision-makers' incentivization has multiple advantages in today’s marketplace. The stability of a SC under the PT is one of the main advantageous motivations. Today’s healthcare industry requires a new strategy to deal with high risks and ensure their market's satisfaction stability. Moreover, the SCs engaged in socially responsible activities and jointly intend to exhibit Corporate Social Responsibility (CSR) with a pre-determined PT may be a compromise solution. The CSR participant’s profit may be negative and to keep their stability, the management of SC requires a PT level. However, the SCs with CSR solutions are under pressure of social and environmental issues [1]. The channels with a specific PT have unique profitability influence and the SCs who fail to 169 Jian, Liu, Hayrutdinov, Fu maximize their adoption of a new strategy will be disrupted by the market uncertainty. Additionally, a SC under the PT orientation can also ensure the profitability of chain participants within the demand uncertainty. PT might help the SC participants reduce risk and loss with a specified level of profit. PT is part of management strategies that SC participants use to manage the risks. “A profit target is a pre-determined point at which the SC participants can initiate conditional orders in a predictable and specified level as well as maximum loss constraints”. The existing research in SC are mainly based on the expected utility theory, with the utility maximization as the decision-making goal. The expected utility theory is a statistical-based mean concept, which brings unexpected outcomes for SC decision-makers. Therefore, decision-making studies based on PT are promising new approaches. In the SC decision-making study with the PT, the probability of realizing a PT is maximized as the decision-making goal. Compared with the expected utility theory, the SC decision-maker can cooperate more intuitively, and it can effectively reduce the loss caused by market fluctuations. The newsboy model is a single item inventory controlling problem within the single-period stochastic demand, where demand uncertainty is the main industry issue under inventory, pricing, and overall operational management studies [2]. Khouja investigated and reviewed the different single-period problem-based extensions [3]. The research on supply chain can be summarized into the following categories. The first is the research on the supply chain structure, which can be divided into two-level supply chain [4], three-level supply chain [5], and two-channel supply chain [6]. On this basis, there are also literature studies on the optimization of channel structure [7]. The second is to study the uncertainty risk in the supply chain [8]. Then there is the research on information asymmetry [9]. Lee et al. [10] defined the content of information sharing in the supply chain and constructed the basic model of information sharing in the supply chain [11]. Finally, the relevant research is based on the preference of decision makers. The common preferences are risk aversion [12], waste aversion [13], fairness concern [14], test aversion [15] and green preference [16]. The single-period problem or newsboy model-based first PT investigation with a two-product SC extension was proposed in [17]. Their study constructed a two-product SC model with a newsboy problem and investigated the effects of SC participants’ decision-making on achieving the PT. The newsboy problem-based research with pricing was proposed in [18]. Yang et al. research considered both profit and revenue targets under the single-period problem, the study discussed the effects of profit and revenue targets on the expected profits and the probability of achieving PT or revenue target respectively [19]. Available literature mainly considered the single decision maker’s behavior in a SC with the PT and the influence of various newsboy products on a SC. None of the literature considers the joint strategical decision-making of the SC participants in-between an upstream and a downstream chain participant with their PT. However, most of the research with the newsboy problem is concerned with profit maximization. Additionally, there is a lack of studies simultaneously engaged with the stability of a SC under the PT and profit maximization. Contractual coordination provides a viable alternative as a mechanism for coordination of the SC and proves to be an interesting research direction. Various decentralized SC processes have been coordinated aiming to improve the functionality. The concept of contractual coordination in improving the SC processes have been widely investigated. Researchers and practitioners used incentivization to motivate and coordinate their SC performance [20]. The contractual coordination mechanisms are important to have the decentralized SC’s decision-makers pursue channel coordination. The existing SC contractual coordination mechanism with the newsboy problem is proposed by Arrow and Harris [21]. The most common applied contractual coordination mechanisms include wholesale price contracts [21], RS contracts [22], buyback contracts [23], and quantity flexibility contracts [24]. Considering contractual coordination under the newsboy problem, the buyback contract is incentivizing to increase an order quantity by sharing the inventory risk of downstream in a SC. The RS contract with the newsvendor problem plays an important role in the coordination of SC and most of the studies focused on newsvendor given with exogenous retailing price. Several extensions to the earlier contract model with newsboy have been developed [25]. Upstream supplier maximizes the profit of whole decentralized SC as the coordinator, in this 170 Advances in Production Engineering & Management 17(2) 2022 Supply chain coordination based on the probability optimization of target profit case, the RS contract model can efficiently coordinate SC members’ performance. The position guarantees a contractual coordination improvement, whereas the sharing parameter determines SC total profit distribution in between members [26]. The literature on SC contract mainly focuses on profit allocation. No research investigates the PT orientated SC under the contractual coordination theory to reduce the influence of demand uncertainty. This study constructs a contractual coordination model based on the PT oriented chain participants' incentivization. We analyzed the RS and buyback contract models with a SC participant's PT and then discussed the contract selection within SC participants’ PT. Then, we characterized the decision-makers’ optimal profit realization and the contract selection conditions, to reduce the influence of demand uncertainty with the risk of unexpected loss. This paper expands the existing research scenarios of supply chain contracts, which is closer to the actual production situation of the market for decision makers, and also provides a reference for the design of diverse contracts. The rest of this paper is organized as follows. Section 2 provides the basic model description, establishment, and assumptions. Section 3 analyses of the RS contract with a specific PT and coordination conditions of SC. Section 4 provides the analyses under the buyback contract with SC PT and coordination conditions. Section 5 presents the numerical analysis of contract selection with the given PT. Section 6 summarizes and concludes the study results. 2. The basic model, description, and assumptions In this section, we construct a basic contract model with a PT similar to Yang et al. [19]. Consider a two-stage SC consisting of one upstream supplier and one downstream retailer. The market demand during the single-season is stochastic. To avoid an unexpected random demand outcome that will cause chain disruption, the SC participants will set a PT. The PT is pre-determined and expected to be achieved in advance. The probability of achieving a PT is SC participants’ decisionmaking variable as the self-interested on the stability and adoption in a SC. To facilitate this model, this paper has the following assumptions: Assumption 1: The SC upstream and downstream participants are rational decision-makers. Assumption 2: The SC participants will determine the optimal order quantity and the maximum probability of achieving the PT based on the pre-determined target point. Assumption 3: The SC shortage lost is not considered. Assumption 4: The SC downstream retailer has only one opportunity to decide the ordering variable. As the classical newsboy problem, there is only one chance to order at the beginning of a single season. We consider the SC contract parameters with a unit wholesale price 𝑤𝑤, a unit selling price 𝑝𝑝, and a unit salvage value 𝑣𝑣. The market demand is 𝑥𝑥 and we denote 𝐹𝐹(𝑥𝑥) as the distribution function of 𝑥𝑥 with its density 𝑓𝑓(𝑥𝑥). Expected profit of downstream retailer For the comparison, we first characterized a benchmark case with the retailer’s profit function. Within the classical newsboy problem, SC downstream retailer's order quantity 𝑞𝑞 is under the conditions of: 𝑝𝑝𝑝𝑝 + 𝑣𝑣(𝑞𝑞 − 𝑥𝑥) − 𝑤𝑤𝑤𝑤 𝑥𝑥 < 𝑞𝑞 � 𝑟𝑟 = � (1) 𝑝𝑝𝑝𝑝 − 𝑤𝑤𝑤𝑤 𝑥𝑥 ≥ 𝑞𝑞 Then, the expected profit of a SC downstream retailer under the newsboy problem is as follow: 𝑞𝑞 +∞ 𝐸𝐸𝜋𝜋𝑟𝑟 = � (𝑝𝑝𝑝𝑝 + 𝑣𝑣(𝑞𝑞 − 𝑥𝑥) − 𝑤𝑤𝑤𝑤)𝑓𝑓(𝑥𝑥)𝑑𝑑𝑑𝑑 + � 0 𝑞𝑞 (𝑝𝑝𝑝𝑝 − 𝑤𝑤𝑤𝑤)𝑓𝑓(𝑥𝑥)𝑑𝑑𝑑𝑑 (2) For the retailer's profit analysis, where the downstream retailer set a PT, we donate the constraint conditions of order quantity. When 𝑥𝑥 < 𝑞𝑞 the retailer’s profit increases with the increase of market demand; else when 𝑥𝑥 ≥ 𝑞𝑞 the retailer’s profit does not change with the change of market demand and the maximum profit can be reached when 𝑥𝑥 = 𝑞𝑞. If the retailer has a PT 𝑡𝑡𝑟𝑟 to Advances in Production Engineering & Management 17(2) 2022 171 Jian, Liu, Hayrutdinov, Fu 𝑡𝑡 𝑡𝑡 𝑟𝑟 𝑟𝑟 achieve, it cannot exceed the maximum profit, as 𝑡𝑡𝑟𝑟 ≤ 𝑝𝑝𝑝𝑝 − 𝑤𝑤𝑤𝑤 and 𝑞𝑞 ≥ 𝑝𝑝−𝑤𝑤 . Thus, if 𝑞𝑞 < 𝑝𝑝−𝑤𝑤 , 𝑡𝑡 then 𝑡𝑡𝑟𝑟 > 𝑝𝑝𝑝𝑝 − 𝑤𝑤𝑤𝑤, the probability of achieving the PT is 0. When 𝑞𝑞 ≥ 𝑟𝑟 , in order to achieve the 𝑝𝑝−𝑤𝑤 PT, the condition needs to satisfy 𝑝𝑝𝑝𝑝 + 𝑣𝑣(𝑞𝑞 − 𝑥𝑥) − 𝑤𝑤𝑤𝑤 ≥ 𝑡𝑡𝑟𝑟 . Hence, we can get 𝑥𝑥 ≥ (𝑤𝑤−𝑣𝑣)𝑞𝑞+𝑡𝑡𝑟𝑟 (𝑝𝑝−𝑣𝑣) (𝑤𝑤−𝑣𝑣)𝑞𝑞+𝑡𝑡𝑟𝑟 (𝑝𝑝−𝑣𝑣) and (𝑤𝑤−𝑣𝑣)𝑞𝑞+𝑡𝑡 the probability of 𝑥𝑥 ≥ is 1 − 𝐹𝐹 � (𝑝𝑝−𝑣𝑣) 𝑟𝑟 �. Therefore, the probability of the SC retailer’s 𝑡𝑡𝑟𝑟 0 𝑞𝑞 < 𝑝𝑝−𝑤𝑤 . PT is: 𝑃𝑃(𝑡𝑡𝑟𝑟 ) = � (𝑤𝑤−𝑣𝑣)𝑞𝑞+𝑡𝑡 𝑡𝑡 1 − 𝐹𝐹 � (𝑝𝑝−𝑣𝑣) 𝑟𝑟� 𝑞𝑞 ≥ 𝑟𝑟 𝑝𝑝−𝑤𝑤 𝑡𝑡𝑟𝑟 𝑡𝑡𝑟𝑟 When 𝑞𝑞 < 𝑝𝑝−𝑤𝑤, the probability of the SC retailer’s PT is 0; when 𝑞𝑞 ≥ 𝑝𝑝−𝑤𝑤 , the probability of the retailer achieving the PT increases with the increase of 𝑞𝑞. The optimal order quantity of the re𝑡𝑡 𝑡𝑡 tailer can be obtained as 𝑟𝑟 where the probability of the retailer’s PT is 1 − 𝐹𝐹 � 𝑟𝑟 �. 𝑝𝑝−𝑤𝑤 𝑝𝑝−𝑤𝑤 Definition 1: In the SC downstream retailer’s decision on maximizing the probability, he first sets a PT 𝑡𝑡𝑟𝑟 based on his actual situation. In order to achieve a PT, the retailer's optimal order quantity 𝑡𝑡 𝑡𝑡 is 𝑟𝑟 and the probability of achieving the PT is maximum 1 − 𝐹𝐹 � 𝑟𝑟 �. 𝑝𝑝−𝑤𝑤 𝑝𝑝−𝑤𝑤 Expected profit of upstream supplier SC upstream supplier has a unit production cost 𝑐𝑐 and the total profit of the supplier can be expressed as follow: � 𝑠𝑠 = 𝑤𝑤𝑤𝑤 − 𝑐𝑐𝑐𝑐 (3) Where the expected profit of the SC upstream supplier under the newsboy problem is as follow: +∞ 𝐸𝐸𝜋𝜋𝑠𝑠 = � 0 (𝑤𝑤𝑤𝑤 − 𝑐𝑐𝑐𝑐)𝑓𝑓(𝑥𝑥)𝑑𝑑𝑑𝑑 (4) For the SC upstream supplier, who does not face the market demand directly, the profit will not change with the change of market demand. Therefore, the profit that the supplier can achieve is 𝑤𝑤𝑤𝑤 − 𝑐𝑐𝑐𝑐, and the probability of achieving her PT is 100%. From the basic model analysis, we can get the following three aspects of the problem: • Comparing to the SC downstream retailer conditions, the upstream supplier does not bear the market risk, and her profit will not change with the change of market demand. The supplier only incentivized to get the downstream retailer’s order as much as possible, so that she can achieve higher profit; • When the SC retailer determines the PT, it can increase the probability of achieving the PT by adjusting his order quantity. There is an optimal order quantity under each specific PT for retailer, but the SC downstream's order quantity is not optimal from the point of supplier and the overall SC. • For the SC retailer and supplier, the level of PT that can be achieved by both participants are less under the decentralized decision-making control. Thus, the research of PT oriented SC contracts analyzes both participants' decision-making in order to find the overall SC coordination conditions. Definition 2: When the SC participants are making an uniform decision in order to maximize their probability of achieving PT with an optimal order quantity, we define this condition as the SC coordination. 172 Advances in Production Engineering & Management 17(2) 2022 Supply chain coordination based on the probability optimization of target profit 3. Revenue-sharing contract with a specific profit target In this section, we construct the RS contract with PT oriented SC retailer and supplier, then we consider the coordination conditions under the RS contract from the perspective of SC participants’ PT. The downstream retailer is a SC leader and the upstream supplier is a follower. Based on the Definition 1, the events of the decision-making process under the RS contract with SC participants’ PT and based on the Definition 2, the analyzes of the coordination conditions under the RS contract with SC participants’ PT are as follows: 1) SC downstream retailer and upstream supplier set their PT. 2) SC upstream supplier is committed to providing for the retailer a lower wholesale price, while the downstream retailer is committed to returning a certain percentage of sales revenue. 3) SC retailer and supplier will determine their PT and set the optimal order quantity. 4) According to Definition 2, obtaining the PT based RS contract coordination conditions. 5) Analyzing the RS contract conditions for the improvement of the overall SC profitability. 3.1 Analysis of the retailer’s decision Under the RS contract, the supplier charges wholesale price 𝑤𝑤𝜑𝜑 per unit product while the downstream retailer is committed to returning a certain percentage (1 − 𝜑𝜑) of sales revenue to the supplier for making up for the supplier’s profit loss due to the lower wholesale price to the retailer. Thus, the total profit of the downstream retailer can be expressed as: � 𝑟𝑟 = � 𝜑𝜑[𝑝𝑝𝑝𝑝 + 𝑣𝑣(𝑞𝑞 − 𝑥𝑥)] − 𝑤𝑤𝜑𝜑 𝑞𝑞 𝜑𝜑𝜑𝜑𝜑𝜑 − 𝑤𝑤𝜑𝜑 𝑞𝑞 𝑥𝑥 < 𝑞𝑞 𝑥𝑥 ≥ 𝑞𝑞 (5) Where 𝜑𝜑 assumed to be in the range of 0 < 𝜑𝜑 < 1, and the expected profit of the downstream retailer under the newsboy problem is as follow: 𝑞𝑞 +∞ 𝐸𝐸𝜋𝜋𝑟𝑟 = � �𝜑𝜑�𝑝𝑝𝑝𝑝 + 𝑣𝑣(𝑞𝑞 − 𝑥𝑥)� − 𝑤𝑤𝜑𝜑 𝑞𝑞�𝑓𝑓(𝑥𝑥)𝑑𝑑𝑑𝑑 + � 0 𝑞𝑞 �𝜑𝜑𝜑𝜑𝜑𝜑 − 𝑤𝑤𝜑𝜑 𝑞𝑞�𝑓𝑓(𝑥𝑥)𝑑𝑑𝑑𝑑 (6) For the retailer's PT analysis, when 𝑡𝑡𝑟𝑟 > �𝜑𝜑𝜑𝜑 − 𝑤𝑤𝜑𝜑 �𝑞𝑞，we have 𝑃𝑃(𝑡𝑡𝑟𝑟 ) = 0, that is, when 𝑞𝑞 < 𝑡𝑡 𝑃𝑃(𝑡𝑡𝑟𝑟 ) = 0; when 𝑡𝑡𝑟𝑟 = �𝜑𝜑𝜑𝜑 − 𝑤𝑤𝜑𝜑 �𝑞𝑞 , which is 𝑞𝑞 = 𝑟𝑟 , we have 𝑃𝑃(𝑡𝑡𝑟𝑟 ) = 1 − 𝐹𝐹(𝑞𝑞); and when 𝑡𝑡𝑟𝑟 𝜑𝜑𝜑𝜑−𝑤𝑤𝜑𝜑 𝑡𝑡𝑟𝑟 ≤ �𝜑𝜑𝜑𝜑 − 𝑤𝑤𝜑𝜑 �𝑞𝑞 , or equivalently 𝑞𝑞 > 𝑡𝑡𝑟𝑟 𝜑𝜑𝜑𝜑−𝑤𝑤𝜑𝜑 𝜑𝜑𝜑𝜑−𝑤𝑤𝜑𝜑 , we have 𝑃𝑃(𝑡𝑡𝑟𝑟 ) = 1 − 𝐹𝐹 � probability of the retailer’s PT under RS contracts is: 𝑃𝑃(𝑡𝑡𝑟𝑟 ) = � 1 − 𝐹𝐹 � �𝑤𝑤𝜑𝜑 −𝜑𝜑𝜑𝜑�𝑞𝑞+𝑡𝑡𝑟𝑟 𝜑𝜑(𝑝𝑝−𝑣𝑣) 0 �𝑤𝑤𝜑𝜑 −𝜑𝜑𝜑𝜑�𝑞𝑞+𝑡𝑡𝑟𝑟 𝜑𝜑(𝑝𝑝−𝑣𝑣) � . Therefore, the � 𝑞𝑞 < 𝑞𝑞 ≥ 𝑡𝑡 𝑡𝑡𝑟𝑟 𝜑𝜑𝜑𝜑−𝑤𝑤𝜑𝜑 𝑡𝑡𝑟𝑟 𝜑𝜑𝜑𝜑−𝑤𝑤𝜑𝜑 . 𝑟𝑟 Theorem 1: Under the RS contract, the optimal order quantity of the SC retailer is 𝜑𝜑𝜑𝜑−𝑤𝑤 and the probability of achieving PT is 1 − 𝑡𝑡𝑟𝑟 𝐹𝐹 �𝜑𝜑𝜑𝜑−𝑤𝑤 �. 𝜑𝜑 𝑡𝑡 𝜑𝜑 𝑟𝑟 Proof of Theorem 1: In the case where 𝑞𝑞 < 𝜑𝜑𝜑𝜑−𝑤𝑤 the probability of achieving retailer’s PT is 0. In 𝑡𝑡𝑟𝑟 the case where 𝑞𝑞 ≥ 𝜑𝜑𝜑𝜑−𝑤𝑤 , 𝜑𝜑 �𝑤𝑤𝜑𝜑 −𝜑𝜑𝜑𝜑�𝑞𝑞+𝑡𝑡𝑟𝑟 of 𝑞𝑞. 1 − 𝐹𝐹 � 𝜑𝜑(𝑝𝑝−𝑣𝑣) 𝜑𝜑 𝑤𝑤𝜑𝜑 − 𝜑𝜑𝜑𝜑 > 0 we have �𝑤𝑤𝜑𝜑 −𝜑𝜑𝜑𝜑�𝑞𝑞+𝑡𝑡𝑟𝑟 𝜑𝜑(𝑝𝑝−𝑣𝑣) which is increases with the increase � decreases with the increase of order quantity 𝑞𝑞. 𝐹𝐹(𝑥𝑥)is an increasing 𝑡𝑡 𝑟𝑟 , and the probability of achieving function. Therefore, the retailer's optimal order quantity is 𝜑𝜑𝜑𝜑−𝑤𝑤 𝑡𝑡𝑟𝑟 �. 𝜑𝜑𝜑𝜑−𝑤𝑤 PT is 1 − 𝐹𝐹 � Corollary 1: Under RS contract condition, 𝜑𝜑 > 𝑝𝑝−𝑤𝑤+𝑤𝑤𝜑𝜑 𝑝𝑝 �𝑤𝑤 > 𝑤𝑤𝜑𝜑 �, retailers can increase the prob- ability of achieving PT by increasing the RS contract coefficient 𝜑𝜑. Advances in Production Engineering & Management 17(2) 2022 173 Jian, Liu, Hayrutdinov, Fu Proof: To increase the probability of SC retailer’s PT achievement, the conditions of 1 − 𝑡𝑡 𝑡𝑡 𝑡𝑡 𝑡𝑡 𝑟𝑟 𝑟𝑟 𝑟𝑟 𝑟𝑟 𝐹𝐹 �𝜑𝜑𝜑𝜑−𝑤𝑤 � > 1 − 𝐹𝐹 �𝑝𝑝−𝑤𝑤 � must be satisfied. It is equivalent to 𝑝𝑝−𝑤𝑤 > 𝜑𝜑𝜑𝜑−𝑤𝑤 , thus we have 𝜑𝜑 > 𝑝𝑝−𝑤𝑤+𝑤𝑤𝜑𝜑 𝑝𝑝 𝑡𝑡 𝜑𝜑 �𝑤𝑤 > 𝑤𝑤𝜑𝜑 � . By taking the derivative of 1 − 𝑝𝑝𝑡𝑡 𝑡𝑡 𝐹𝐹 � 𝑟𝑟 � 𝜑𝜑𝜑𝜑−𝑤𝑤𝜑𝜑 𝜑𝜑 with respect to 𝜑𝜑 , we have 𝑡𝑡 𝑟𝑟 𝑟𝑟 𝑟𝑟 � ∗ (−𝑤𝑤+𝑝𝑝𝑝𝑝) 𝑓𝑓 �𝜑𝜑𝜑𝜑−𝑤𝑤 2 > 0 for any 𝜑𝜑. Therefore, the probability of achieving PT 1 − 𝐹𝐹 �𝜑𝜑𝜑𝜑−𝑤𝑤 � in𝜑𝜑 creases with the increase of RS contract coefficient 𝜑𝜑. 𝜑𝜑 Fig. 1 The probability of achieving the PT: different sharing coefficient vs. no contract Fig. 1 illustrates a comparison of the SC retailer’s probability of achieving the PT under different contract parameters and no contract case, where 𝑃𝑃𝐴𝐴 represents the probability of achieving the PT with no contract case; 𝑃𝑃𝐵𝐵 represents the probability of achieving a PT under the condition 𝑝𝑝−𝑤𝑤+𝑤𝑤 where the RS contract coefficient satisfied 𝜑𝜑 < 𝑝𝑝 𝜑𝜑. 𝑃𝑃𝐶𝐶 represents the probability of achieving a PT under where the RS contract coefficient is larger, i.e., 𝜑𝜑 > 𝑝𝑝−𝑤𝑤+𝑤𝑤𝜑𝜑 𝑝𝑝 . From Fig. 1 we can get the conditions of 𝑃𝑃𝐶𝐶 > 𝑃𝑃𝐴𝐴 > 𝑃𝑃𝐵𝐵 . Fig. 2 illustrates a comparison of retailer’s probability of achieving PT under different targets and no contract case respectively, where 𝑡𝑡01 = 𝑡𝑡𝑟𝑟1 < 𝑡𝑡02 = 𝑡𝑡𝑟𝑟2 . Consequently, Figs. 1 and 2 indicate 𝑝𝑝−𝑤𝑤+𝑤𝑤 that if 𝜑𝜑 < 𝑝𝑝 𝜑𝜑 retailer’s probability of achieving its PT will be significantly reduced. On the contrary, i.e., if 𝜑𝜑 > 𝑝𝑝−𝑤𝑤+𝑤𝑤𝜑𝜑 𝑝𝑝 retailer’s probability of achieving its PT will increase. Thus, the retail- ers prefer to use RS contract to increase their probability of achieving a PT when 𝜑𝜑 > 𝑝𝑝−𝑤𝑤+𝑤𝑤𝜑𝜑 𝑝𝑝 . Moreover, it can be seen from Fig. 1 that the condition where RS coefficient is larger, the retailer’s probability of obtaining PT increases. Fig. 2 The probability of achieving the PT: different PT vs. no contract 174 Advances in Production Engineering & Management 17(2) 2022 Supply chain coordination based on the probability optimization of target profit 3.2 Analysis of the supplier’s decision Under RS contract the total profit condition of SC upstream supplier can be expressed as follow: (1 − 𝜑𝜑)[𝑝𝑝𝑝𝑝 + 𝑣𝑣(𝑞𝑞 − 𝑥𝑥)] + 𝑤𝑤𝜑𝜑 𝑞𝑞 − 𝑐𝑐𝑐𝑐 𝑥𝑥 < 𝑞𝑞 � 𝑠𝑠 = � (7) (1 − 𝜑𝜑)𝑝𝑝𝑝𝑝 + 𝑤𝑤𝜑𝜑 𝑞𝑞 − 𝑐𝑐𝑐𝑐 𝑥𝑥 ≥ 𝑞𝑞 Let 𝑡𝑡𝑠𝑠 denote the expected PT of the supplier. For further analysis of the supplier’s profit func𝑡𝑡𝑠𝑠 , where the probability tion, we know: when 𝑡𝑡𝑠𝑠 > �(1 − 𝜑𝜑)𝑝𝑝 + 𝑤𝑤𝜑𝜑 − 𝑐𝑐�𝑞𝑞 equivalently 𝑞𝑞 < (1−𝜑𝜑)𝑝𝑝+𝑤𝑤 −𝑐𝑐 𝜑𝜑 𝑡𝑡 𝑠𝑠 is equal 𝑃𝑃(𝑡𝑡𝑠𝑠 ) = 0 ; and when 𝑡𝑡𝑠𝑠 = �(1 − 𝜑𝜑)𝑝𝑝 + 𝑤𝑤𝜑𝜑 − 𝑐𝑐�𝑞𝑞 which is equivalent to 𝑞𝑞 = (1−𝜑𝜑)𝑝𝑝+𝑤𝑤 have the probability of 𝑃𝑃(𝑡𝑡𝑠𝑠 ) = 1 − 𝐹𝐹(𝑞𝑞); where 𝑃𝑃(𝑡𝑡𝑠𝑠 ) = 1 − 𝐹𝐹 � 𝑡𝑡 𝑠𝑠 𝑞𝑞 > (1−𝜑𝜑)𝑝𝑝+𝑤𝑤 𝜑𝜑 −𝑐𝑐 , where we have 𝑃𝑃(𝑡𝑡𝑠𝑠 ) = 1 − 𝐹𝐹 � probability: 𝑃𝑃(𝑡𝑡𝑠𝑠 ) = � 1 − 𝐹𝐹 � 0 �𝑐𝑐−𝑤𝑤𝜑𝜑 �𝑞𝑞−(1−𝜑𝜑)𝑣𝑣𝑣𝑣+𝑡𝑡𝑠𝑠 (1−𝜑𝜑)(𝑝𝑝−𝑣𝑣) �𝑐𝑐−𝑤𝑤𝜑𝜑 �𝑞𝑞−(1−𝜑𝜑)𝑣𝑣𝑣𝑣+𝑡𝑡𝑠𝑠 � (1−𝜑𝜑)(𝑝𝑝−𝑣𝑣) 𝑡𝑡𝑠𝑠 𝑞𝑞 < (1−𝜑𝜑)𝑝𝑝+𝑤𝑤 𝑡𝑡𝑠𝑠 𝜑𝜑 −𝑐𝑐 𝑞𝑞 ≥ (1−𝜑𝜑)𝑝𝑝+𝑤𝑤 𝜑𝜑 −𝑐𝑐 �𝑐𝑐−𝑤𝑤𝜑𝜑 �𝑞𝑞−(1−𝜑𝜑)𝑣𝑣𝑣𝑣+𝑡𝑡𝑠𝑠 (1−𝜑𝜑)(𝑝𝑝−𝑣𝑣) 𝜑𝜑 −𝑐𝑐 , we � , which indicates �. Thus, we have the supplier’s PT . Theorem 2: Under the RS contract, the optimal order quantity of the upstream supplier is 𝑡𝑡𝑠𝑠 ，and the probability of achieving (1−𝜑𝜑)𝑝𝑝+𝑤𝑤𝜑𝜑 −𝑐𝑐 𝑡𝑡 𝑠𝑠 the PT is 1 − 𝐹𝐹 �(1−𝜑𝜑)𝑝𝑝+𝑤𝑤 𝑡𝑡 𝑠𝑠 Proof of Theorem 2: For a given order quantity, where 𝑞𝑞 is 𝑞𝑞 < (1−𝜑𝜑)𝑝𝑝+𝑤𝑤 bility of achieving the PT is equal to 0. When 𝑞𝑞 ≥ (1 − 𝜑𝜑)𝑣𝑣� > 0 always holds. Therefore, 1 − 𝐹𝐹 � �𝑐𝑐−𝑤𝑤𝜑𝜑 �𝑞𝑞−(1−𝜑𝜑)𝑣𝑣𝑣𝑣+𝑡𝑡𝑠𝑠 (1−𝜑𝜑)(𝑝𝑝−𝑣𝑣) 𝑡𝑡𝑠𝑠 (1−𝜑𝜑)𝑝𝑝+𝑤𝑤𝜑𝜑 −𝑐𝑐 �𝑐𝑐−𝑤𝑤𝜑𝜑 �𝑞𝑞−(1−𝜑𝜑)𝑣𝑣𝑣𝑣+𝑡𝑡𝑠𝑠 (1−𝜑𝜑)(𝑝𝑝−𝑣𝑣) 𝜑𝜑 −𝑐𝑐 𝜑𝜑 −𝑐𝑐 �. , the supplier’s proba- the inequation �𝑐𝑐 − 𝑤𝑤𝜑𝜑 − increases with the increase of 𝑞𝑞. And � decreases with the increase of the order quantity 𝑞𝑞. 𝐹𝐹(𝑥𝑥) is an increas𝑡𝑡 𝑠𝑠 ing function. Thus, the SC supplier's optimal order quantity is (1−𝜑𝜑)𝑝𝑝+𝑤𝑤 𝑡𝑡 𝑠𝑠 achieving the PT is 1 − 𝐹𝐹 �(1−𝜑𝜑)𝑝𝑝+𝑤𝑤 𝜑𝜑 −𝑐𝑐 �. 𝜑𝜑 −𝑐𝑐 and the probability of Corollary 2: With the increase of RS coefficient 𝜑𝜑 supplier's probability of achieving PT decreases. 𝑡𝑡 𝑠𝑠 Proof: By taking the derivative of 1 − 𝐹𝐹 �(1−𝜑𝜑)𝑝𝑝+𝑤𝑤 𝑝𝑝𝑡𝑡𝑠𝑠 �𝑐𝑐−𝑤𝑤𝜑𝜑 +𝑝𝑝(−1+𝜑𝜑)� 2 𝜑𝜑 −𝑐𝑐 𝑡𝑡 𝑠𝑠 � with respect to 𝜑𝜑, we have −𝑓𝑓 �(1−𝜑𝜑)𝑝𝑝+𝑤𝑤 𝑡𝑡 𝑠𝑠 < 0 for any 𝜑𝜑 . Thus, the probability of achieving the PT 1 − 𝐹𝐹 �(1−𝜑𝜑)𝑝𝑝+𝑤𝑤 creases with the increase of the RS contract coefficient 𝜑𝜑. 𝜑𝜑 −𝑐𝑐 𝜑𝜑 −𝑐𝑐 �∗ � de- Fig. 3 SC participant’s probability of achieving the PT under RS coefficient Advances in Production Engineering & Management 17(2) 2022 175 Jian, Liu, Hayrutdinov, Fu Fig. 3 illustrates a comparison of the SC participants’ PT probabilities with the RS coefficient changes. As can be seen from the Fig. 3 above, the probability of achieving the PT of the retailer increases with the increase of the RS coefficient, while the probability of achieving the PT of the supplier decreases. Moreover, the increasing probability point where the SC participants have the same PT decreases the actual PT. Therefore, an appropriate and coordinated PT will help to achieve a win-win situation. 3.3 Coordination conditions under the revenue-sharing contract In this subsection, we discussed the SC coordination conditions under the RS contract. To achieve overall SC coordination, the optimal order quantity of the SC participants should be coherent with their PT, so that the optimal order quantity based on the probability of achieving the PT. In this case, under the RS contract conditions, the SC participants can reach their optimal order quantity at the same time they both get the highest probability of achieving their PT. Considering the coordination conditions of the RS contract, we have the following Theorem 3. Theorem 3: Under the RS contract with SC participants’ PT, the SC coordination condition is 𝑡𝑡𝑟𝑟 = 𝑡𝑡 �𝑝𝑝𝑝𝑝−𝑤𝑤 � 𝑠𝑠 𝜑𝜑 − 𝑐𝑐−𝑝𝑝+𝑝𝑝𝑝𝑝−𝑤𝑤 where 0 < �𝑝𝑝𝑝𝑝 − 𝑤𝑤𝜑𝜑 � < 𝑝𝑝 − 𝑐𝑐 If the condition falls to 0 < �𝑝𝑝𝑝𝑝 − 𝑤𝑤𝜑𝜑 � < 𝜑𝜑 𝑝𝑝−𝑐𝑐 retailer can achieve the higher PT than the upstream supplier; otherwise, i.e., 2 𝑝𝑝 − 𝑐𝑐, the PT of retailer is less than that of the SC upstream supplier. 𝑝𝑝−𝑐𝑐 , 2 the SC < �𝑝𝑝𝑝𝑝 − 𝑤𝑤𝜑𝜑 � < Proof of Theorem 3: Under the conditions where the SC is coordinated, the optimal order quantity 𝑡𝑡𝑟𝑟 that the SC upstream supplier and downstream retailer can achieve the PT are equal = 𝑡𝑡𝑠𝑠 . (1−𝜑𝜑)𝑝𝑝+𝑤𝑤𝜑𝜑 −𝑐𝑐 𝑡𝑡𝑠𝑠 �𝑝𝑝𝑝𝑝−𝑤𝑤𝜑𝜑 � Thus, we obtain 𝑡𝑡𝑟𝑟 = − 𝑐𝑐−𝑝𝑝+𝑝𝑝𝑝𝑝−𝑤𝑤 . For 𝑡𝑡𝑟𝑟 > 0, 𝑡𝑡𝑠𝑠 > 0, we have 𝜑𝜑 𝜑𝜑𝜑𝜑−𝑤𝑤𝜑𝜑 �𝑝𝑝𝑝𝑝−𝑤𝑤𝜑𝜑 � 𝑝𝑝−𝑐𝑐−�𝑝𝑝𝑝𝑝−𝑤𝑤𝜑𝜑 � > 0, which is 0 < �𝑝𝑝𝑝𝑝 − 𝑤𝑤𝜑𝜑 � < 𝑝𝑝 − 𝑐𝑐 or 𝑝𝑝 − 𝑐𝑐 < �𝑝𝑝𝑝𝑝 − 𝑤𝑤𝜑𝜑 � < 0. However, 𝑝𝑝 − 𝑐𝑐 < 0 it does not hold; 𝑝𝑝−𝑐𝑐 𝑝𝑝−𝑐𝑐 we have 𝑡𝑡𝑟𝑟 > 𝑡𝑡𝑠𝑠 ; when < thus, we have 0 < �𝑝𝑝𝑝𝑝 − 𝑤𝑤𝜑𝜑 � < 𝑝𝑝 − 𝑐𝑐. When 0 < �𝑝𝑝𝑝𝑝 − 𝑤𝑤𝜑𝜑 � < 2 �𝑝𝑝𝑝𝑝 − 𝑤𝑤𝜑𝜑 � < 𝑝𝑝 − 𝑐𝑐 , therefore 𝑡𝑡𝑟𝑟 < 𝑡𝑡𝑠𝑠 . 2 According to Section 2 basic model analysis with the three aspects of the problem, this section analyzed the improved conditions of PT oriented SC under the RS contract. Fig. 4 illustrates SC participants’ probability of achieving PT under different conditions. The horizontal axes represent the PT and the order quantity, respectively. The vertical axes represent the probability of achieving PT. 𝑃𝑃1 , 𝑃𝑃2 indicate the maximum probability that the retailer will achieve his PT when no contract condition and under RS contract, respectively; 𝑃𝑃3 indicates the maximum probability that the supplier will achieve her PT under the RS contract condition; 𝑃𝑃4 , 𝑃𝑃5 indicate the probability of retailer’s achieving his PT under the different order quantity, when no contract condition and the RS contract condition, respectively; 𝑞𝑞1 , 𝑞𝑞2 indicate the retailer’s optimal order quantity to achieve a specific PT, under the no-contract condition and the RS contract condition, respectively; 𝑃𝑃𝑟𝑟0 , 𝑃𝑃𝑟𝑟1 indicate the retailer’s probability of achieving a specific PT under the no-contract condition and the RS contract condition, respectively; 𝜆𝜆𝑠𝑠0 , 𝜆𝜆𝑠𝑠1 indicate the range of PT that the supplier can achieve under the no-contract condition and the RS contract condition, respectively; 𝜆𝜆𝑟𝑟0 , 𝜆𝜆𝑟𝑟1 indicate the range of PT that the SC retailer can achieve under the no-contract condition and the RS contract condition, respectively. From the Fig. 4, the following conclusions can be seen: • For the SC retailer, under the RS contract the probability of achieving a specific PT is higher, 𝑃𝑃𝑟𝑟1 > 𝑃𝑃𝑟𝑟0 ; the range of PT that the retailer can achieve under the RS contract will also increase 𝜆𝜆𝑟𝑟1 > 𝜆𝜆𝑟𝑟0 ; • For the supplier, under the no-contract condition the probability of achieving specific PT is 100%, under RS contract condition the range of PT that the supplier can achieve will also increase 𝜆𝜆𝑠𝑠1 > 𝜆𝜆𝑠𝑠0 ; • Under the RS contract condition the SC retailer's optimal order quantity 𝑞𝑞2 is less than the optimal order quantity 𝑞𝑞1 when non-contractual condition. However, the SC retailer’s probability of achieving his PT will increase, because of the supplier’s RS portion. 176 Advances in Production Engineering & Management 17(2) 2022 Supply chain coordination based on the probability optimization of target profit Fig. 4 Analysis of PT oriented SC coordination conditions under the RS contract. 4. Buyback contract with a specific profit target In this section, we discussed the buyback contract under the SC participants’ PT. Firstly, we constructed the buyback contract conditions for the SC downstream retailer and upstream supplier respectively. Then we analyzed the coordination conditions under the buyback contract within SC participants’ PT. Based on the Definition 1, the events of the decision-making process under the buyback contract with SC participants’ PT and based on the Definition 2, the analyzes of the coordination conditions under the buyback contract with SC participants’ PT are as follows: 1) SC downstream retailer and upstream supplier set their PTs; 2) The upstream supplier shares the market risk and will buy back the unsold products. 3) SC retailer and supplier will determine their PT and set the optimal order quantity. 4) According to Definition 2, obtaining the PT based RS contract coordination conditions. 5) Analyzing the RS contract conditions for the improvement of the overall SC profitability. 4.1 Analysis of the retailer’s decision Under the buyback contract, the supplier charges a retailer wholesale price 𝑤𝑤𝑏𝑏 for each unit ordered product and provides the buyback credit 𝑏𝑏 for each unit remaining product at the end of a selling season. Thus, the profit conditions of the SC downstream retailer can be expressed as follow: 𝑝𝑝𝑝𝑝 + (𝑏𝑏 + 𝑣𝑣)(𝑞𝑞 − 𝑥𝑥) − 𝑤𝑤𝑏𝑏 𝑞𝑞 𝑥𝑥 < 𝑞𝑞 � 𝑟𝑟 = � (8) 𝑝𝑝𝑝𝑝 − 𝑤𝑤𝑏𝑏 𝑞𝑞 𝑥𝑥 ≥ 𝑞𝑞 Considering the contract conditions within PT probability we can get the followings. When the 𝑡𝑡𝑟𝑟 , the retailer’s PT probability is equal to 𝑃𝑃(𝑡𝑡𝑟𝑟 ) = 0 retailer’s PT is 𝑡𝑡𝑟𝑟 > (𝑝𝑝 − 𝑤𝑤𝑏𝑏 )𝑞𝑞 which is 𝑞𝑞 < 𝑝𝑝−𝑤𝑤 𝑡𝑡 𝑏𝑏 𝑟𝑟 , we have the retailer’s PT probability 𝑃𝑃(𝑡𝑡𝑟𝑟 ) = 1 − 𝐹𝐹(𝑞𝑞) When PT is 𝑡𝑡𝑟𝑟 = (𝑝𝑝 − 𝑤𝑤𝑏𝑏 )𝑞𝑞, which is 𝑞𝑞 = 𝑝𝑝−𝑤𝑤 when 𝑡𝑡𝑟𝑟 ≤ (𝑝𝑝 − 𝑤𝑤)𝑞𝑞 i.e. 𝑞𝑞 > 𝑡𝑡𝑟𝑟 𝜑𝜑𝜑𝜑−𝑤𝑤𝑏𝑏 𝑏𝑏 we have 𝑃𝑃(𝑡𝑡𝑟𝑟 ) = 1 − 𝐹𝐹 � probability condition of retailer’s PT as follow: 𝑃𝑃(𝑡𝑡𝑟𝑟 ) = � (𝑤𝑤𝑏𝑏 −𝑏𝑏−𝑣𝑣)𝑞𝑞+𝑡𝑡𝑟𝑟 𝑝𝑝−𝑏𝑏−𝑣𝑣 1 − 𝐹𝐹 � 0 � . Thus, we have overall (𝑤𝑤𝑏𝑏 −𝑏𝑏−𝑣𝑣)𝑞𝑞+𝑡𝑡𝑟𝑟 𝑝𝑝−𝑏𝑏−𝑣𝑣 � 𝑞𝑞 < 𝑞𝑞 ≥ 𝑡𝑡𝑟𝑟 𝑝𝑝−𝑤𝑤𝑏𝑏 𝑡𝑡𝑟𝑟 . 𝑝𝑝−𝑤𝑤𝑏𝑏 Theorem 4: Under the buyback contract, the SC retailer’s optimal order quantity with his PT is 𝑡𝑡𝑟𝑟 𝑡𝑡𝑟𝑟 ，and the probability of achieving the PT is 1 − 𝐹𝐹 �𝑝𝑝−𝑤𝑤 �. 𝑝𝑝−𝑤𝑤 𝑏𝑏 𝑏𝑏 𝑡𝑡 𝑟𝑟 Proof of Theorem 4: In the case where order quantity 𝑞𝑞 < 𝑝𝑝−𝑤𝑤 , retailer’s probability of achieving 𝑏𝑏 𝑡𝑡 𝑟𝑟 the PT is equal to 0. In the next case where order quantity 𝑞𝑞 ≥ 𝑝𝑝−𝑤𝑤 , the probability Advances in Production Engineering & Management 17(2) 2022 𝑏𝑏 𝑤𝑤𝑏𝑏 −𝑏𝑏−𝑣𝑣 𝑝𝑝−𝑏𝑏−𝑣𝑣 > 0. 177 Jian, Liu, Hayrutdinov, Fu Thus, (𝑤𝑤𝑏𝑏 −𝑏𝑏−𝑣𝑣)𝑞𝑞+𝑡𝑡𝑟𝑟 𝑝𝑝−𝑏𝑏−𝑣𝑣 increases with the increase of 𝑞𝑞. And 1 − 𝐹𝐹 � (𝑤𝑤𝑏𝑏 −𝑏𝑏−𝑣𝑣)𝑞𝑞+𝑡𝑡𝑟𝑟 𝑝𝑝−𝑏𝑏−𝑣𝑣 � decreases with increase of order quantity 𝑞𝑞. 𝐹𝐹(𝑥𝑥) is an increasing function. Therefore, retailer's optimal order quantity is 𝑡𝑡𝑟𝑟 𝑡𝑡𝑟𝑟 and the probability of achieving PT is 1 − 𝐹𝐹 �𝑝𝑝−𝑤𝑤 �. 𝑝𝑝−𝑤𝑤 𝑏𝑏 𝑏𝑏 Corollary 3: The SC retailer's probability of achieving his PT cannot increase under the buyback contract conditions. Proof: In case of no contract, the supplier charges downstream retailer with the wholesale price 𝑤𝑤 for unit product. While under the buyback contract, supplier charges downstream retailer the wholesale price 𝑤𝑤𝑏𝑏 for unit product and provides buyback credit 𝑏𝑏 for remaining product at the end of selling season. Compared to the case where the contract is not applied, the supplier will generate a transfer payment to the downstream retailer at the end of selling season due to the buyback contract conditions. Therefore, to ensure the profit, the upstream supplier must charge higher wholesale price, i.e., 𝑤𝑤𝑏𝑏 > 𝑤𝑤. Similarly, under the RS contract, the upstream supplier will receive a portion of the retailer’s revenue for each unit sold, so the supplier will be willing to sell at a lower wholesale price, i.e., 𝑤𝑤𝜑𝜑 < 𝑤𝑤. Consequently, we have 𝑤𝑤𝜑𝜑 < 𝑤𝑤 < 𝑤𝑤𝑏𝑏 . In order to increase the retailer’s PT probability, the contract condition has to satisfy 1 − 𝑡𝑡 𝑡𝑡 𝑡𝑡 𝑡𝑡 𝐹𝐹 � 𝑟𝑟 � > 1 − 𝐹𝐹 � 𝑟𝑟 �, that is 𝑟𝑟 > 𝑟𝑟 . Thus, we have 𝑤𝑤𝑏𝑏 < 𝑤𝑤 which is a contradiction with 𝑝𝑝−𝑤𝑤 𝑝𝑝−𝑤𝑤 𝑝𝑝−𝑤𝑤 𝑝𝑝−𝑤𝑤 𝑏𝑏 𝑏𝑏 the premise 𝑤𝑤𝜑𝜑 < 𝑤𝑤 < 𝑤𝑤𝑏𝑏 . Hence, the probability that the retailer achieves his PT cannot increase using a buyback contract. Therefore, compared with the situation under the RS and buyback contracts, the SC downstream retailer prefers to choose the RS contract rather than the buyback contract. 4.2 Analysis of the supplier’s decision Under the buyback contract the total profit of the SC upstream supplier within the newsboy problem can be expressed as follow: −𝑏𝑏(𝑞𝑞 − 𝑥𝑥) + 𝑤𝑤𝑏𝑏 𝑞𝑞 − 𝑐𝑐𝑐𝑐 𝑥𝑥 < 𝑞𝑞 � 𝑠𝑠 = � (9) 𝑤𝑤𝑏𝑏 𝑞𝑞 − 𝑐𝑐𝑐𝑐 𝑥𝑥 ≥ 𝑞𝑞 𝑡𝑡𝑠𝑠 With the supplier’s PT, when 𝑡𝑡𝑠𝑠 > (𝑤𝑤𝑏𝑏 − 𝑐𝑐)𝑞𝑞, i.e., 𝑞𝑞 < , we have 𝑃𝑃(𝑡𝑡𝑠𝑠 ) = 0; and when 𝑡𝑡𝑠𝑠 = 𝑡𝑡𝑠𝑠 (𝑤𝑤𝑏𝑏 − 𝑐𝑐)𝑞𝑞 , i.e., 𝑞𝑞 = , we have 𝑃𝑃(𝑡𝑡𝑠𝑠 ) (𝑤𝑤𝑏𝑏 −𝑐𝑐) 𝑡𝑡𝑠𝑠 (𝑤𝑤𝑏𝑏 − 𝑐𝑐)𝑞𝑞, i.e., 𝑞𝑞 > , we have 𝑃𝑃(𝑡𝑡𝑠𝑠 ) = (𝑤𝑤𝑏𝑏 −𝑐𝑐) probability: 𝑃𝑃(𝑡𝑡𝑠𝑠 ) = � 1 − 𝐹𝐹 � 0 (𝑤𝑤𝑏𝑏 −𝑏𝑏−𝑐𝑐)𝑞𝑞−𝑡𝑡𝑠𝑠 𝑏𝑏 � (𝑤𝑤𝑏𝑏 −𝑐𝑐) = 1 − 𝐹𝐹(𝑞𝑞) ; finally, when the supplier’s PT is 𝑡𝑡𝑠𝑠 ≤ (𝑤𝑤𝑏𝑏 −𝑏𝑏−𝑐𝑐)𝑞𝑞+𝑡𝑡𝑠𝑠 1 − 𝐹𝐹 � 𝑞𝑞 < (𝑤𝑤 𝑡𝑡𝑠𝑠 𝑏𝑏 −𝑐𝑐) 𝑞𝑞 ≥ (𝑤𝑤 𝑡𝑡𝑠𝑠 𝑏𝑏 −𝑐𝑐) . 𝑏𝑏 �. Thus, we have the supplier’s PT Theorem 5: Under the buyback contract, the optimal order quantity for the supplier is 𝑞𝑞 = (𝑤𝑤 and the SC supplier’s PT probability is 𝑃𝑃(𝑡𝑡𝑠𝑠 ) = 1 − 𝐹𝐹 �(𝑤𝑤 𝑡𝑡𝑠𝑠 �. 𝑏𝑏 −𝑐𝑐) Proof of Theorem 5: For given order quantity 𝑞𝑞, when 𝑞𝑞 < (𝑤𝑤 ity of PT is equal to 0. When 𝑞𝑞 ≥ (𝑤𝑤 (𝑤𝑤𝑏𝑏 −𝑏𝑏−𝑐𝑐)𝑞𝑞−𝑡𝑡𝑠𝑠 𝑡𝑡𝑠𝑠 𝑡𝑡𝑠𝑠 𝑏𝑏 −𝑐𝑐) 𝑡𝑡𝑠𝑠 𝑏𝑏 −𝑐𝑐) SC upstream supplier’s probabil- the inequation (𝑤𝑤𝑏𝑏 − 𝑏𝑏 − 𝑐𝑐) > 0 always holds. Therefore, 𝑏𝑏 −𝑐𝑐) (𝑤𝑤 −𝑏𝑏−𝑐𝑐)𝑞𝑞−𝑡𝑡 𝑠𝑠 increases with the increase of order quantity. 1 − 𝐹𝐹 � 𝑏𝑏 𝑏𝑏 � decreases with the increase of order quantity 𝑞𝑞. 𝐹𝐹(𝑥𝑥) is an increasing function. Thus, the supplier's optimal order 𝑡𝑡 𝑡𝑡 quantity is (𝑤𝑤 𝑠𝑠 and the probability of achieving PT is 1 − 𝐹𝐹 � 𝑠𝑠 �. 𝑏𝑏 𝑏𝑏 −𝑐𝑐) 𝑤𝑤𝑏𝑏 −𝑐𝑐 Compared to the case under RS contract where the supplier ‘s optimal order quantity is 𝑡𝑡𝑠𝑠 (1−𝜑𝜑)𝑝𝑝+𝑤𝑤𝜑𝜑 −𝑐𝑐 178 𝑡𝑡 𝑠𝑠 the probability of achieving PT is 1 − 𝐹𝐹 �(1−𝜑𝜑)𝑝𝑝+𝑤𝑤 𝜑𝜑 −𝑐𝑐 �. Advances in Production Engineering & Management 17(2) 2022 Supply chain coordination based on the probability optimization of target profit When 𝑤𝑤𝑏𝑏 > (1 − 𝜑𝜑)𝑝𝑝 + 𝑤𝑤𝜑𝜑 the supplier’s probability of PT under the buyback contract is greater than under the usage of a RS contract, otherwise, i.e., 𝑤𝑤𝑏𝑏 < (1 − 𝜑𝜑)𝑝𝑝 + 𝑤𝑤𝜑𝜑 , the supplier’s probability of PT under the buyback contract is less than the RS contract condition. 4.3 Coordination condition under the buyback contract PT oriented SC coordination conditions under the buyback contract are the same as the RS contract condition, where the optimal order quantity of the SC participants should be coherent with their predetermined PT. In this case, the SC participants can reach their optimal order quantity and achieve a higher probability of their PT. Theorem 6: Under the buyback contract parameters within the PT, the SC coordination condition 𝑡𝑡 (𝑝𝑝−𝑤𝑤 ) 𝑝𝑝+𝑐𝑐 is 𝑡𝑡𝑟𝑟 = 𝑠𝑠(𝑤𝑤 −𝑐𝑐)𝑏𝑏 . When 𝑤𝑤𝑏𝑏 > the SC downstream retailer’s achieving PT is higher than the 2 𝑏𝑏 upstream supplier; otherwise, i.e., 𝑤𝑤𝑏𝑏 < 𝑝𝑝+𝑐𝑐 , 2 the downstream retailer’s achieving PT is smaller. Proof of Theorem 6: When SC is coordinated under the buyback contract, the optimal order quan𝑡𝑡 𝑡𝑡 tity that the SC participants can achieve the PT is equal, i.e., 𝑟𝑟 = (𝑤𝑤 𝑠𝑠 . Thus, the coordination condition is 𝑡𝑡𝑟𝑟 = 𝑡𝑡𝑠𝑠 (𝑝𝑝−𝑤𝑤𝑏𝑏 ) . (𝑤𝑤𝑏𝑏 −𝑐𝑐) 𝑝𝑝−𝑤𝑤𝑏𝑏 𝑏𝑏 −𝑐𝑐) 𝑝𝑝+𝑐𝑐 When 𝑤𝑤𝑏𝑏 > , the SC retailer can achieve a higher PT than the up2 𝑝𝑝+𝑐𝑐 𝑡𝑡𝑠𝑠 ; When 𝑤𝑤𝑏𝑏 < , the PT of the downstream retailer is less than that 2 stream supplier, i.e., 𝑡𝑡𝑟𝑟 > of the SC upstream supplier, i.e., 𝑡𝑡𝑟𝑟 < 𝑡𝑡𝑠𝑠 . 5. Numerical analysis In this section, we numerically analyzed the contract selection with the given PT for both SC participants. We assumed that 𝑐𝑐 = 30, 𝑝𝑝 = 50, 𝑣𝑣 = 15 and market demand 𝑥𝑥 is uniformly distributed with 𝑈𝑈(0,200). The density function and the cumulative distribution function of the stochastic de1 𝑥𝑥 mand 𝑥𝑥 are respectively 𝑓𝑓(𝑥𝑥) = , 𝐹𝐹(𝑥𝑥) = . We assumed that the SC downstream retailer's 200 200 PT is 𝑡𝑡𝑟𝑟 = 800 and the upstream supplier's PT is 𝑡𝑡𝑠𝑠 = 1000. Following the Theorem 3, we assumed 𝑝𝑝−𝑐𝑐 with the difference of 𝑡𝑡𝑟𝑟 = 800 < 𝑡𝑡𝑠𝑠 = 1000, where < �𝑝𝑝𝑝𝑝 − 𝑤𝑤𝜑𝜑 � < 𝑝𝑝 − 𝑐𝑐 , and where we 2 have 30 < 𝑤𝑤𝜑𝜑 < 40. For the RS contract analysis, the SC downstream retailer's optimal order quantity is assumed 800 4 as following to Theorem 1. Where the probability of achieving the PT of 800 is 1 − ; 50𝜑𝜑−𝑤𝑤𝜑𝜑 50𝜑𝜑−𝑤𝑤𝜑𝜑 1000 For the SC upstream supplier, following to Theorem 2 the optimal order quantity is 50(1−𝜑𝜑)+𝑤𝑤 −30 𝜑𝜑 5 and the probability of achieving the PT of 1000 is 1 − . Thus, we can analyze the RS 50(1−𝜑𝜑)+𝑤𝑤𝜑𝜑 −30 80+9𝑤𝑤𝜑𝜑 condition 𝜑𝜑 = 450 . In Table 1, the first-row numerical values show the condition where the RS contract can coordinate the PT based SC. In this case, the probability that the SC retailer and supplier can achieve their PT are equal. With the same wholesale price but under the different RS coefficient the probability of the SC retailer’s PT is increasing with the increase of the RS coefficient. The probability of supplier’s PT decreases with the increase of the RS coefficient and increases with the increase of the wholesale price. This table shows that retailers prefer the contract parameters combination with high revenue sharing coefficient and low wholesale price, while suppliers prefer the opposite. For the buyback contract analysis, the SC downstream retailer's optimal order quantity is as800 4 sumed as following to Theorem 4. Where the probability of achieving PT of 800 is 1 − ; 50−𝑤𝑤𝑏𝑏 50−𝑤𝑤𝑏𝑏 1000 and the 𝑏𝑏 −30) For the SC upstream supplier, following to Theorem 5 the optimal order quantity is (𝑤𝑤 5 . Then, according to Theorem 6, we can ana- Advances in Production Engineering & Management 17(2) 2022 179 probability of achieving the PT of 1000 is 1 − (𝑤𝑤 𝑏𝑏 −30) lyze the coordination condition under buyback contract as 𝑤𝑤𝑏𝑏 = 370 . 9 Jian, Liu, Hayrutdinov, Fu 𝑤𝑤𝜑𝜑 35.00 35.00 35.00 35.00 35.00 35.00 35.00 35.00 35.00 35.50 36.00 36.50 37.00 37.50 38.00 38.50 39.00 𝑤𝑤𝑏𝑏 41.11 40.50 40.00 39.50 39.00 38.50 38.00 37.50 37.00 36.50 36.00 Table 1 SC participants PT probabilities within the RS contract parameters 𝜑𝜑 𝑞𝑞∗ 𝑃𝑃(𝑡𝑡𝑟𝑟 ) 0.88 90.00 0.55 0.89 84.21 0.58 0.90 80.00 0.60 0.91 76.19 0.62 0.92 72.73 0.64 0.93 69.57 0.65 0.94 66.67 0.67 0.95 64.00 0.68 0.96 61.54 0.69 0.88 94.12 0.53 0.88 100.00 0.50 0.88 106.67 0.47 0.88 114.29 0.43 0.88 123.08 0.38 0.88 133.33 0.33 0.88 145.45 0.27 0.88 160.00 0.20 Table 2 SC participants PT probabilities within the buyback contract parameters 𝑞𝑞 ∗ 90.00 84.21 80.00 76.19 72.73 69.57 66.67 64.00 61.54 59.26 57.14 𝑃𝑃(𝑡𝑡𝑟𝑟 ) 0.55 0.58 0.60 0.62 0.64 0.65 0.67 0.68 0.69 0.70 0.71 𝑃𝑃(𝑡𝑡𝑠𝑠 ) 0.55 0.52 0.50 0.47 0.44 0.41 0.38 0.33 0.29 0.57 0.58 0.60 0.62 0.63 0.64 0.66 0.67 𝑃𝑃(𝑡𝑡𝑠𝑠 ) 0.55 0.52 0.50 0.47 0.44 0.41 0.38 0.33 0.29 0.23 0.17 In Table 2, the first-row numerical values show the condition where the buyback contract can achieve coordination. At this point, the probabilities that the SC participants can achieve their PT are equal. Table 2 shows that under the buyback contract parament 𝑤𝑤𝑏𝑏 , the probability of SC downstream retailer’s PT increases with the increase of the wholesale price, while the probability of the SC upstream supplier PT decreases. This table shows that retailers prefer contract parameters with high wholesale prices, while suppliers prefer the opposite. 6. Conclusion The traditional SC research is based on the expected utility theory, where the expected utility maximization as the decision-making goal. Most of the studies are based on the statistical average value and thus cannot avoid the low returns or large fluctuations in profitability. For decisionmakers, maximizing the probability of achieving the PT can effectively reduce their own risk. However, from the perspective of SC, each decision-maker has its own goal. There is a certain conflict between the goal of decentralized decision-making and the overall optimization of the SC. Therefore, this paper proposes the research of SC contracts based on PT. In this study, we investigated the RS and buyback contracts based on the SC participants’ PT. Different from the traditional SC contracts, it has valuable advantages for SC participants to deal with market risk. Through the research of SC contractual coordination under the PT, our main findings can be summarized as follows: 180 Advances in Production Engineering & Management 17(2) 2022 Supply chain coordination based on the probability optimization of target profit • This study analyzed the RS contract and buyback contract with PT and obtained the optimal order quantity and the probability of achieving PT for both SC participants. Additionally, we analyzed the coordination conditions of the RS contract and buyback contract with the PT. • When the RS coefficient of the contract is within a certain range, the probability of achieving the PT can be increased for both SC participants. As the RS coefficient increases, the probability of SC retailer’s PT increases, and the upstream supplier’s probability of PT decreases. • From the comparison, it can be seen that under the buyback contract a SC retailer cannot increase the probability of achieving the PT by adjusting the contract parameters. Therefore, under the PT strategy, the retailer is more willing to adopt the RS contract rather than the buyback contract. • Under the buyback contract, the SC supplier can adjust the contract parameters within a certain range to increase the probability of achieving her PT. Compared with the RS contract, the SC upstream supplier's contract selection decision depends on the specific contract parameters. • Coordination conditions analyses under the two main contracts proved that the PT of the SC participants can be achieved based on the contracts’ parameters. This study found the unique condition where both SC participants can achieve their PT and coordinate overall SC. Acknowledgment The authors would like to thank to all referees, for their constructive comments and useful suggestions that help us to improve the quality of the paper. This work is supported by The National Social Science Fund of China (No. 18BGL104). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] Panda, S., Modak, N.M. (2016). Exploring the effects of social responsibility on coordination and profit division in a supply chain, Journal of Cleaner Production, Vol. 139, 25-40, doi: 10.1016/j.jclepro.2016.07.118. Yue, J., Chen, B., Wang, M.-C. (2006). 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Supply chain coordination with contracts, Handbooks in Operations Research and Management Science, Vol. 11, 227-339, doi: 10.1016/S0927-0507(03)11006-7. 182 Advances in Production Engineering & Management 17(2) 2022 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 2 | June 2022 | pp 183–192 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.2.429 Original scientific paper A bi-objective optimization of airport ferry vehicle scheduling based on heuristic algorithm: A real data case study Han, X.a, Zhao, P.X.a,*, Kong, D.X.a aSchool of Management, Shandong University, Jinan, Shandong, P.R. China ABSTRACT ARTICLE INFO The optimization of ferry vehicle scheduling is the key factor to improve the punctuality of flights and passenger satisfaction at airports. Based on the airport reality, a bi-objective mixed integer linear programming model for airport ferry vehicle scheduling is proposed in this paper, in which the first objective is to minimize the number of vehicles used, and the second objective is to minimize the maximum number of flights per ferry vehicle serving under the constraint that the first objective takes the optimal value. For the optimization model of the second objective, this paper designs three heuristic algorithms: strict equalization algorithm, relaxed equalization algorithm and transplantation algorithm, and integrates them into a main algorithm. The actual flight data of Beijing Capital International Airport are used for numerical examples, and all the examples tested can obtain the exact solution or high-quality approximate solution using the designed algorithm, which verifies the effectiveness of the algorithm. This study can be used to inform decisions on the efficient and balanced use of airport ferry vehicles. Despite the system presented in the paper is designed for airport, it can be applied to solve similar vehicle scheduling problems. Keywords: Ferry vehicle; Vehicle routing; Bi-objective optimization; Heuristic algorithm; Strict equalization algorithm; Relaxed equalization algorithm; Transplantation algorithm *Corresponding author: pxzhao@sdu.edu.cn (Zhao, P.X.) Article history: Received 10 May 2022 Revised 9 August 2022 Accepted 16 August 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction In recent years, the rapid development of the civil aviation industry has made the scheduling and management of the limited ground resources at airports, such as parking positions, runways and ground support vehicles, gradually become important and complex. Among them, the ground support vehicles are special vehicles that provide a series of ground services for the aircraft, such as refuelling, air catering and ferrying. However, at present, the scheduling of airport ground support vehicles is still mainly manual, which is inefficient and easy to cause flight delays [1]. Flights parked at remote stands need ferry vehicles to transport passengers, so the scheduling level of ferry vehicles not only affects the punctuality of flights, but also directly affects the experience of passengers. The ferry service is characterized by time-consuming and different number of vehicles required for flights, which makes the ferry vehicle resources even more tight. In addition to completing all ferry services on time with as few ferry vehicles as possible, balancing the workload of each ferry vehicle as far as possible also facilitates driver scheduling and vehicle maintenance. 183 Han, Zhao, Kong The research on flight ground service scheduling mainly includes the scheduling optimization of ground service crew [2-8] and ground support vehicles. The ground support vehicle scheduling problem is a kind of vehicle routing problem, and the vehicle routing problem is widely used in the scheduling of vehicles such as electric vehicles [9], automated guided vehicles [10] and logistics vehicles [11]. For example, Norin et al. designed a greedy randomized adaptive search procedure to solve the de-icing vehicle scheduling problem [12]. Du et al. designed a column generation heuristic algorithm to solve the tractor scheduling problem [13]. Schyns designed an ant colony algorithm to solve the refuelling truck scheduling problem [14]. Padrón et al. proposed a decomposition framework and a sequence iterative method to solve the collaborative scheduling problem of multiple ground support vehicles [15]. Padrón and Guimarans [16] improved the algorithm proposed by Padrón et al. [15]. This paper focuses on the studies on ferry vehicle scheduling, as detailed in Table 1. As can be seen from Table 1, although there are existing studies involving optimization objectives in terms of balancing the workload of ferry vehicles, they are all nonlinear objective functions, which are solved using solvers or meta-heuristic algorithms. Solvers have difficulty solving large-scale nonlinear integer programming problems, and meta-heuristic algorithms often have difficulty obtaining the accuracy of the resulting solutions. This paper constructs a bi-objective optimization model for ferry vehicle scheduling, in which the first objective is to minimize the number of ferry vehicles used, and the programming model is a two-index arc-flow model based on a directed acyclic network, which is easy to obtain the optimal solution. The second objective is to minimize the maximum number of flights served by a single ferry vehicle under the constraint of using the minimum number of ferry vehicles, and the programming model is a threeindex mixed integer linear programming model. Since the model of the second optimization objective has large number of variables and is difficult to solve directly, three heuristic algorithms are designed and integrated into a main algorithm to solve the model. The analysis of numerical examples shows that the algorithm can solve 42 out of 60 examples to the optimum, and the Gap of the remaining examples is also very small. The rest of the paper is organized as follows. Section 2 constructs a bi-objective optimization model for ferry vehicle scheduling. Section 3 presents several heuristic algorithms for solving the optimization model of the second objective. Section 4 uses the actual flight data of Beijing Capital International Airport for numerical examples to verify the effectiveness of the designed heuristic algorithms. Section 5 provides conclusions and some possible directions for future research. Table 1 Studies related to ferry vehicle scheduling Programming Literature Optimization goal model [17] Maximize robustness ILP Minimize total costs, including vehicle usage costs and [18] LP driving costs Minimize the variance of the number of flights per ferry [19] QP vehicle serving Minimize the number of vehicles, the total vehicle mileage [20] and the variance of the number of flights per ferry vehicle Three-objective IP serving Minimize the number of vehicles and the total deviation of [21] Bi-objective MIP the number of flights per ferry vehicle serving [22] Minimize the number of vehicles MILP, LP Minimize the number of vehicles, the total vehicle mileage Three-objective [1] and the difference between the vehicle arrival time and MIP the earliest service time Minimize the number of vehicles and the total vehicle idle [23] Bi-objective MIP time [24] Minimize the number of vehicles ILP, LP 2. Problem description and model construction Solving method Column generation Shortest augmenting path algorithm Gurobi Two-stage heuristic algorithm Particle swarm optimization CPLEX Non-dominated sorting genetic algorithm Non-dominated sorting genetic algorithm Lingo Let there be |𝑁𝑁| flights requiring ferry services at an airport during a certain time period (including arriving flights and departing flights; if a flight arrives and then departs during this time 184 Advances in Production Engineering & Management 17(2) 2022 A bi-objective optimization of airport ferry vehicle scheduling based on heuristic algorithm: A real data case study period, it is considered as two flights), where 𝑁𝑁 is the set of these flights. Ferry vehicles for arriving flights are required to transport passengers from the parking positions to the terminal, while ferry vehicles for departing flights do the opposite. Let the time required for the ferry vehicle to travel from the end position of the ferry service of flight 𝑖𝑖 ∈ 𝑁𝑁 (the terminal if 𝑖𝑖 is an arriving flight, otherwise the parking position of 𝑖𝑖) to the start position of the ferry service of flight 𝑗𝑗 ∈ 𝑁𝑁 (the parking position of 𝑗𝑗 if 𝑗𝑗 is an arriving flight, otherwise the terminal) be 𝑡𝑡𝑖𝑖𝑖𝑖 . Let the ferry service start time window for flight 𝑖𝑖 ∈ 𝑁𝑁 be [𝑎𝑎𝑖𝑖 , 𝑏𝑏𝑖𝑖 ] and the required service time be 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖 , where 𝑎𝑎𝑖𝑖 and 𝑏𝑏𝑖𝑖 are determined according to the Scheduled Time of Arrival (STA) or Scheduled Time of Departure (STD) of flight 𝑖𝑖. Depending on the aircraft type, let the number of ferry vehicles required for flight 𝑖𝑖 ∈ 𝑁𝑁 be 𝐷𝐷𝑖𝑖 (if relevant data on the number of passengers on the flight are available, the number of passengers can be used instead of the aircraft type to determine the number of ferry vehicles required for the flight more accurately). To facilitate the algorithm design, this paper transforms the research problem into a vehicle scheduling problem with only one ferry vehicle for each flight by setting up virtual flights. Let flight 𝑖𝑖 ∈ 𝑁𝑁 correspond to 𝐷𝐷𝑖𝑖 virtual flights with the same time window, service time and other relevant time parameters as 𝑖𝑖. Denote the set of all virtual flights as 𝑁𝑁 𝑉𝑉 [19, 22, 24]. We use the service sequence and service time compatibility information in the flight service time window to construct the underlying network 𝐺𝐺 = (𝑉𝑉, 𝐴𝐴) of the ferry vehicle scheduling model, where 𝑉𝑉 = {0, |𝑁𝑁 𝑉𝑉 | + 1} ∪ {𝑖𝑖|𝑖𝑖 ∈ 𝑁𝑁 𝑉𝑉 } (Nodes 0 and |𝑁𝑁 𝑉𝑉 | + 1 can be regarded as ferry vehicle depot), 𝐴𝐴 = {(𝑖𝑖, 𝑗𝑗)|𝐴𝐴𝐴𝐴𝑖𝑖𝑖𝑖 = 1, 𝑖𝑖, 𝑗𝑗 ∈ 𝑉𝑉}. 𝐴𝐴𝐴𝐴𝑖𝑖𝑖𝑖 is an element of the adjacency matrix 𝐴𝐴𝐴𝐴 of network 𝐺𝐺. 𝐴𝐴𝐴𝐴𝑖𝑖𝑖𝑖 is calculated as follows. 1, if 𝑖𝑖 = 0 and 𝑗𝑗 ∈ 𝑁𝑁 𝑉𝑉 ⎧ ⎪ 1, if 𝑗𝑗 = |𝑁𝑁 𝑉𝑉 | + 1 and 𝑖𝑖 ∈ 𝑁𝑁 𝑉𝑉 𝐴𝐴𝐴𝐴𝑖𝑖𝑖𝑖 = (1) 𝑉𝑉 ⎨1, if 𝑖𝑖, 𝑗𝑗 ∈ 𝑁𝑁 and 𝑎𝑎𝑖𝑖 + 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖 + 𝑡𝑡𝑖𝑖𝑖𝑖 ≤ 𝑏𝑏𝑗𝑗 ⎪ 0, otherwise ⎩ For the ferry vehicle, the inequality 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖 + 𝑡𝑡𝑖𝑖𝑖𝑖 ≥ 𝑏𝑏𝑖𝑖 − 𝑎𝑎𝑖𝑖 holds for ∀𝑖𝑖, 𝑗𝑗 ∈ 𝑁𝑁 𝑉𝑉 , then 𝐺𝐺 is a directed acyclic network [22, 25]. The first objective of the ferry vehicle scheduling optimization is to minimize the number of ferry vehicles used. The decision variable 𝑥𝑥𝑖𝑖𝑖𝑖 ∈ {0,1} decides whether a ferry vehicle serves node 𝑗𝑗 immediately after serving node 𝑖𝑖, and the decision variable 𝑡𝑡𝑖𝑖 ∈ [𝑎𝑎𝑖𝑖 , 𝑏𝑏𝑖𝑖 ] decides the service start time of flight 𝑖𝑖. The two-index mixed integer linear programming model for the first optimization objective is constructed as follows. min � 𝑥𝑥0𝑗𝑗 (2) (0,𝑗𝑗)∈𝐴𝐴 � 𝑥𝑥𝑖𝑖𝑖𝑖 = 1, ∀ 𝑖𝑖 ∈ 𝑁𝑁 𝑉𝑉 (3) 𝑗𝑗|(𝑖𝑖,𝑗𝑗)∈𝐴𝐴 � 𝑥𝑥𝑗𝑗𝑗𝑗 = 1, ∀ 𝑖𝑖 ∈ 𝑁𝑁 𝑉𝑉 (4) 𝑗𝑗|(𝑗𝑗,𝑖𝑖)∈𝐴𝐴 𝑎𝑎𝑖𝑖 ≤ 𝑡𝑡𝑖𝑖 ≤ 𝑏𝑏𝑖𝑖 , ∀ 𝑖𝑖 ∈ 𝑁𝑁 𝑉𝑉 𝑡𝑡𝑖𝑖 + 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖 + 𝑡𝑡𝑖𝑖𝑖𝑖 ≤ 𝑡𝑡𝑗𝑗 + 𝑀𝑀�1 − 𝑥𝑥𝑖𝑖𝑖𝑖 �, ∀(𝑖𝑖, 𝑗𝑗) ∈ 𝐴𝐴, 𝑖𝑖, 𝑗𝑗 ∈ 𝑁𝑁 𝑉𝑉 (5) (6) 𝑥𝑥𝑖𝑖𝑖𝑖 ∈ {0,1}, ∀(𝑖𝑖, 𝑗𝑗) ∈ 𝐴𝐴 (7) The objective function Eq. 2 in the above model is to minimize the number of ferry vehicles dispatched. Constraints Eqs. 3 to 4 indicate that each virtual flight is served only once. Constraints Eqs. 5 to 6 are time window constraints. The second optimization objective is to minimize the maximum number of flights served by a single ferry vehicle under the constraint of using the minimum number of ferry vehicles. Let the optimal value of model 2 to 7 be 𝐾𝐾, that is, at least 𝐾𝐾 ferry vehicles are needed to serve all flights 𝑘𝑘 to decide on time. The second programming model uses the three-index decision variable 𝑥𝑥𝑖𝑖𝑖𝑖 whether ferry vehicle 𝑘𝑘 serves node 𝑗𝑗 immediately after serving node 𝑖𝑖, and introduces a new Advances in Production Engineering & Management 17(2) 2022 185 Han, Zhao, Kong decision variable 𝑧𝑧 to represent the maximum number of flights served by a single ferry vehicle. The mixed integer linear programming model for the second optimization objective is constructed as follows. min 𝑧𝑧 (8) � 𝑖𝑖,𝑗𝑗|(𝑖𝑖,𝑗𝑗)∈𝐴𝐴 𝑘𝑘 𝑥𝑥𝑖𝑖𝑖𝑖 ≤ 𝑧𝑧 + 1, ∀𝑘𝑘 ∈ {1,2, … , 𝐾𝐾} (9) 𝑘𝑘 � 𝑥𝑥0𝑖𝑖 = 1, ∀𝑘𝑘 ∈ {1,2, … , 𝐾𝐾} 𝑖𝑖|𝑖𝑖∈𝑁𝑁 𝑉𝑉 𝐾𝐾 � 𝑘𝑘=1 𝑘𝑘 � 𝑥𝑥𝑖𝑖𝑖𝑖 = 𝑗𝑗|(𝑖𝑖,𝑗𝑗)∈𝐴𝐴 (10) 𝑘𝑘 � 𝑥𝑥𝑖𝑖𝑖𝑖 = 1, ∀𝑖𝑖 ∈ 𝑁𝑁 𝑉𝑉 (11) 𝑗𝑗|(𝑖𝑖,𝑗𝑗)∈𝐴𝐴 � 𝑥𝑥𝑗𝑗𝑗𝑗𝑘𝑘 , ∀𝑖𝑖 ∈ 𝑁𝑁 𝑉𝑉 , 𝑘𝑘 ∈ {1,2, … , 𝐾𝐾} (12) 𝑗𝑗|(𝑗𝑗,𝑖𝑖)∈𝐴𝐴 𝑒𝑒𝑖𝑖 ≤ 𝑡𝑡𝑖𝑖 ≤ 𝑙𝑙𝑖𝑖 , ∀𝑖𝑖 ∈ 𝑁𝑁 𝑉𝑉 𝑡𝑡𝑖𝑖 + 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖 + 𝑡𝑡𝑖𝑖𝑖𝑖 ≤ 𝑡𝑡𝑗𝑗 + 𝑀𝑀�1 − 𝑘𝑘 𝑥𝑥𝑖𝑖𝑖𝑖 �, ∀𝑘𝑘 ∈ {1,2, … , 𝐾𝐾}, (𝑖𝑖, 𝑗𝑗) ∈ 𝐴𝐴且𝑖𝑖, 𝑗𝑗 ∈ 𝑁𝑁 𝑘𝑘 𝑥𝑥𝑖𝑖𝑖𝑖 ∈ {0,1}, ∀𝑘𝑘 ∈ {1,2, … , 𝐾𝐾}, (𝑖𝑖, 𝑗𝑗) ∈ 𝐴𝐴 𝑉𝑉 (13) (14) (15) The objective function Eq. 8 and constraint Eq. 9 in the above model minimize the maximum number of flights served by a single ferry vehicle. Constraint Eq. 10 indicates that each ferry vehicle is dispatched only once. Constraint Eq. 11 indicates that each virtual flight is served only once. Constraint Eq. 12 is the flow balance condition of the virtual flight node. Constraints Eqs. |𝑵𝑵𝑽𝑽 | ⌉ is 𝑲𝑲 13 to 14 are time window constraints. Obviously, ⌈ model in Eqs. 8 to 15. a lower bound for the optimal value of 3. Proposed approach: A heuristic algorithm Models in Eq. 2 to 7 can be solved quickly using the solver to obtain the exact solution [22]. Models 8 to 15 is a three-index arc-flow model with a large number of variables, which is difficult to solve directly using the solver for flight data with a 24-hour planning period. In this paper, three heuristic algorithms (see Algorithms 1, 2, and 3) are designed and integrated into a main algorithm (see Algorithm 0) to solve models in 8 to 15. The symbols involved in the algorithms are shown in Table 2. Symbol popsize 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖) 𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖) 𝑓𝑓𝑓𝑓1(𝑢𝑢, 𝑘𝑘) 𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝑘𝑘) 𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝑘𝑘) 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖′ 𝑓𝑓𝑓𝑓𝑓𝑓(𝑢𝑢) 𝑜𝑜𝑜𝑜𝑜𝑜(𝑢𝑢) 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠0(𝑖𝑖) 𝑠𝑠𝑠𝑠0(𝑖𝑖) 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠′ 𝑈𝑈𝑈𝑈 𝑈𝑈𝑈𝑈 max Table 2 The symbols used in the algorithms Meaning The number of solutions The ferry vehicle serving flight 𝑖𝑖 in solution 𝑢𝑢, 𝑢𝑢 = 1,2, … , popsize, 𝑖𝑖 = 1,2, … , |𝑁𝑁 𝑉𝑉 | The service start time of flight 𝑖𝑖 in solution 𝑢𝑢, 𝑢𝑢 = 1,2, … , popsize, 𝑖𝑖 = 1,2, … , |𝑁𝑁 𝑉𝑉 | The last flight that ferry vehicle 𝑘𝑘 has served in solution 𝑢𝑢, 𝑢𝑢 = 1,2, … , popsize, 𝑘𝑘 = 1,2, … , 𝐾𝐾 The service start time of the last flight that ferry vehicle 𝑘𝑘 has served in solution 𝑢𝑢, 𝑢𝑢 = 1,2, … , popsize, 𝑘𝑘 = 1,2, … , 𝐾𝐾 The number of flights that ferry vehicle 𝑘𝑘 has served in solution 𝑢𝑢, 𝑢𝑢 = 1,2, … , popsize, 𝑘𝑘 = 1,2, … , 𝐾𝐾 The set of ferry vehicles that can serve flight 𝑖𝑖 The set of ferry vehicles whose number of served flights satisfies a specific condition among ferry vehicles available for flight 𝑖𝑖 The number of flights served in solution 𝑢𝑢 The maximum number of flights served by a single ferry vehicle in solution 𝑢𝑢 The ferry vehicle serving flight 𝑖𝑖 in the optimal solution of models 2 to 7 The service start time of flight 𝑖𝑖 in the optimal solution of models 2 to 7 The set of solutions with the largest number of served flights The set of unserved flights in the solutions with the largest number of served flights The last flight unserved in the solutions with the largest number of served flights Firstly, all the flights in 𝑁𝑁 𝑉𝑉 are sorted in ascending order according to 𝑎𝑎𝑖𝑖 and respectively numbered as flight 1,2, … , |𝑁𝑁 𝑉𝑉 |. Then, if two flights are served by the same ferry vehicle, the vehicle must serve the flight with the smaller number first. Algorithms 1-3 all ensure that the con186 Advances in Production Engineering & Management 17(2) 2022 A bi-objective optimization of airport ferry vehicle scheduling based on heuristic algorithm: A real data case study straints on the time window and the number of ferry vehicles are not violated, then the resulting solution, if infeasible, is due to the fact that some flights are not served. Algorithm 2 has looser restrictions than Algorithm 1 in terms of the equilibrium degree of the ferry vehicle workload, so the main algorithm executes Algorithm 1 first, and if no feasible solution is obtained, Algorithm 2 is executed. If Algorithm 2 still fails to obtain a feasible solution, the time windows of the unserved flights are generally in the peak period of flight take-off and landing, during which there are fewer feasible vehicle scheduling schemes. Algorithm 3 transplants part of the ferry vehicle scheduling arrangement from the optimal solution of models 2 to 7, while taking into account the equilibrium degree of the ferry vehicle workload. If neither Algorithm 1 nor Algorithm 2 can get a feasible solution, Algorithm 3 can be executed. Algorithm 0: Main algorithm Input: popsize, 𝐾𝐾, |𝑁𝑁 𝑉𝑉 |, 𝑎𝑎𝑖𝑖 , 𝑏𝑏𝑖𝑖 , 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖 , 𝑡𝑡𝑖𝑖𝑖𝑖 , 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠0(𝑖𝑖), 𝑠𝑠𝑠𝑠0(𝑖𝑖) 1 Execute Algorithm 1, return 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖), 𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖), 𝑓𝑓𝑓𝑓𝑓𝑓(𝑢𝑢), 𝑜𝑜𝑜𝑜𝑜𝑜(𝑢𝑢); 2 If max𝑢𝑢∈{1,2,…,popsize} {𝑓𝑓𝑓𝑓𝑓𝑓(𝑢𝑢)} < |𝑁𝑁 𝑉𝑉 | 3 Execute Algorithm 2, return 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖), 𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖), 𝑓𝑓𝑓𝑓𝑓𝑓(𝑢𝑢), 𝑜𝑜𝑜𝑜𝑜𝑜(𝑢𝑢); If max𝑢𝑢∈{1,2,…,popsize} {𝑓𝑓𝑓𝑓𝑓𝑓(𝑢𝑢)} < |𝑁𝑁 𝑉𝑉 | 4 5 6 7 8 9 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠′ ← �𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖)�𝑖𝑖 ∈ {1,2, … , |𝑁𝑁 𝑉𝑉 |}, 𝑓𝑓𝑓𝑓𝑓𝑓(𝑢𝑢) = max𝑢𝑢∈{1,2,…,popsize} {𝑓𝑓𝑓𝑓𝑓𝑓(𝑢𝑢)}�; 𝑈𝑈𝑈𝑈 ← {𝑖𝑖 ∈ {1,2, … , |𝑁𝑁 𝑉𝑉 |}|𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖) ∈ 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠′ , 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖) = 0}; 𝑈𝑈𝑈𝑈 max ← max𝑖𝑖∈𝑈𝑈𝑈𝑈 {𝑖𝑖}; Execute Algorithm 3, return 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖), 𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖), 𝑓𝑓𝑓𝑓𝑓𝑓(𝑢𝑢), 𝑜𝑜𝑜𝑜𝑜𝑜(𝑢𝑢); Return 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖), 𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖), 𝑓𝑓𝑓𝑓𝑓𝑓(𝑢𝑢), 𝑜𝑜𝑜𝑜𝑜𝑜(𝑢𝑢) Algorithm 1 first makes ferry vehicles 1,2, … , 𝐾𝐾 serve flights 1,2, … , 𝐾𝐾 respectively (lines 1-7 of Algorithm 1). For flights 𝐾𝐾 + 1, 𝐾𝐾 + 2, … , |𝑁𝑁 𝑉𝑉 |, the set 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖 of the ferry vehicles that can serve it is determined in turn, and from the set, a ferry vehicle that has served the least number of flights is randomly selected to serve it (lines 8-18 of Algorithm 1). The time complexity of Algorithm 1 is 𝑂𝑂(popsize × (|𝑁𝑁 𝑉𝑉 | − 𝐾𝐾) × 𝐾𝐾 2 ). Algorithm 1: Strict equalization algorithm Input: popsize, 𝐾𝐾, |𝑁𝑁 𝑉𝑉 |, 𝑎𝑎𝑖𝑖 , 𝑏𝑏𝑖𝑖 , 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖 , 𝑡𝑡𝑖𝑖𝑖𝑖 1 For 𝑢𝑢 ← 1,2, … , popsize 2 For 𝑖𝑖 ← 1,2, … , 𝐾𝐾 3 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖) ← 𝑖𝑖; 4 𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖) ← 𝑎𝑎𝑖𝑖 ; 5 𝑓𝑓𝑓𝑓1(𝑢𝑢, 𝑖𝑖) ← 𝑖𝑖; 6 𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝑖𝑖) ← 𝑎𝑎𝑖𝑖 ; 7 𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝑖𝑖) ← 1; 8 For 𝑢𝑢 ← 1,2, … , popsize 9 For 𝑖𝑖 ← 𝐾𝐾 + 1, 𝐾𝐾 + 2, … , |𝑁𝑁 𝑉𝑉 | 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖 ← �𝑘𝑘 ∈ {1,2, … , 𝐾𝐾}�𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝑘𝑘) + 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑓𝑓𝑓𝑓1(𝑢𝑢,𝑘𝑘) + 𝑡𝑡𝑓𝑓𝑓𝑓1(𝑢𝑢,𝑘𝑘),𝑖𝑖 ≤ 𝑏𝑏𝑖𝑖 �; 10 11 If 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖 ≠ ∅ 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖′ ← �𝑘𝑘 ∈ 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖 �𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝑘𝑘) = min𝑘𝑘∈𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖 {𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝑘𝑘)}�; 12 Randomly select a ferry vehicle in 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖′ , denote as 𝓀𝓀; 13 14 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖) ← 𝓀𝓀; 𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖) ← max {𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝓀𝓀) + 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑓𝑓𝑓𝑓1(𝑢𝑢,𝓀𝓀) + 𝑡𝑡𝑓𝑓𝑓𝑓1(𝑢𝑢,𝓀𝓀),𝑖𝑖 , 𝑎𝑎𝑖𝑖 }; 15 𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝓀𝓀) ← max {𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝓀𝓀) + 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑓𝑓𝑓𝑓1(𝑢𝑢,𝓀𝓀) + 𝑡𝑡𝑓𝑓𝑓𝑓1(𝑢𝑢,𝓀𝓀),𝑖𝑖 , 𝑎𝑎𝑖𝑖 }; 16 17 𝑓𝑓𝑓𝑓1(𝑢𝑢, 𝓀𝓀) ← 𝑖𝑖; 18 𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝓀𝓀) ← 𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝓀𝓀) + 1; 19 𝑓𝑓𝑓𝑓𝑓𝑓(𝑢𝑢) ← ∑𝐾𝐾 𝑘𝑘=1 𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝑘𝑘); 𝑜𝑜𝑜𝑜𝑜𝑜(𝑢𝑢) ← max𝑘𝑘∈{1,2,…,𝐾𝐾} {𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝑘𝑘)}; 20 Return 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖), 𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖), 𝑓𝑓𝑓𝑓𝑓𝑓(𝑢𝑢), 𝑜𝑜𝑜𝑜𝑜𝑜(𝑢𝑢) The difference between Algorithm 2 and Algorithm 1 is that for flights 𝐾𝐾 + 1, 𝐾𝐾 + 2, … , |𝑁𝑁 𝑉𝑉 |, if |𝑁𝑁 𝑉𝑉 | there are ferry vehicles with the number of served flights less than or equal to ⌊ ⌋ in set 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖 , 𝐾𝐾 then a ferry vehicle is randomly selected from them (from the ferry vehicles with the number of |𝑁𝑁 𝑉𝑉 | served flights less than or equal to ⌊ 𝐾𝐾 ⌋) to serve flight 𝑖𝑖. Otherwise, the factor of ferry vehicle task volume is no longer considered, and a ferry vehicle is randomly selected from 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖 to serve flight 𝑖𝑖 (lines 9-27 of Algorithm 2). The time complexity of Algorithm 2 is 𝑂𝑂(popsize × (|𝑁𝑁 𝑉𝑉 | − 𝐾𝐾) × 𝐾𝐾). Advances in Production Engineering & Management 17(2) 2022 187 Han, Zhao, Kong Algorithm 2: Relaxed equalization algorithm Input: popsize, 𝐾𝐾, |𝑁𝑁 𝑉𝑉 |, 𝑎𝑎𝑖𝑖 , 𝑏𝑏𝑖𝑖 , 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖 , 𝑡𝑡𝑖𝑖𝑖𝑖 1 For ∀𝑢𝑢 ∈ {1,2, … , popsize}, 𝑖𝑖 ∈ {1,2, … , |𝑁𝑁 𝑉𝑉 |}, set 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖) ← 0; 2 For 𝑢𝑢 ← 1,2, … , popsize 3 For 𝑖𝑖 ← 1,2, … , 𝐾𝐾 4 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖) ← 𝑖𝑖; 5 𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖) ← 𝑎𝑎𝑖𝑖 ; 6 𝑓𝑓𝑓𝑓1(𝑢𝑢, 𝑖𝑖) ← 𝑖𝑖; 7 𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝑖𝑖) ← 𝑎𝑎𝑖𝑖 ; 8 𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝑖𝑖) ← 1; 9 For 𝑢𝑢 ← 1,2, … , popsize 10 For 𝑖𝑖 ← 𝐾𝐾 + 1, 𝐾𝐾 + 2, … , |𝑁𝑁 𝑉𝑉 | 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖 ← �𝑘𝑘 ∈ {1,2, … , 𝐾𝐾}�𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝑘𝑘) + 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑓𝑓𝑓𝑓1(𝑢𝑢,𝑘𝑘) + 𝑡𝑡𝑓𝑓𝑓𝑓1(𝑢𝑢,𝑘𝑘),𝑖𝑖 ≤ 𝑏𝑏𝑖𝑖 �; 11 12 If 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖 ≠ ∅ 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 |𝑁𝑁𝑉𝑉 | 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖′ ← �𝑘𝑘 ∈ 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖 �𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝑘𝑘) ≤ ⌊ ⌋�; 𝐾𝐾 If 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖′ ≠ ∅ Randomly select a ferry vehicle in 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖′ , denote as 𝓀𝓀; 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖) ← 𝓀𝓀; 𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖) ← max {𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝓀𝓀) + 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑓𝑓𝑓𝑓1(𝑢𝑢,𝓀𝓀) + 𝑡𝑡𝑓𝑓𝑓𝑓1(𝑢𝑢,𝓀𝓀),𝑖𝑖 , 𝑎𝑎𝑖𝑖 }; 𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝓀𝓀) ← max {𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝓀𝓀) + 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑓𝑓𝑓𝑓1(𝑢𝑢,𝓀𝓀) + 𝑡𝑡𝑓𝑓𝑓𝑓1(𝑢𝑢,𝓀𝓀),𝑖𝑖 , 𝑎𝑎𝑖𝑖 }; 𝑓𝑓𝑓𝑓1(𝑢𝑢, 𝓀𝓀) ← 𝑖𝑖; 𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝓀𝓀) ← 𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝓀𝓀) + 1; If 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖′ = ∅ Randomly select a ferry vehicle in 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖 , denote as 𝓀𝓀; 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖) ← 𝓀𝓀; 𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖) ← max {𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝓀𝓀) + 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑓𝑓𝑓𝑓1(𝑢𝑢,𝓀𝓀) + 𝑡𝑡𝑓𝑓𝑓𝑓1(𝑢𝑢,𝓀𝓀),𝑖𝑖 , 𝑎𝑎𝑖𝑖 }; 𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝓀𝓀) ← max {𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝓀𝓀) + 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑓𝑓𝑓𝑓1(𝑢𝑢,𝓀𝓀) + 𝑡𝑡𝑓𝑓𝑓𝑓1(𝑢𝑢,𝓀𝓀),𝑖𝑖 , 𝑎𝑎𝑖𝑖 }; 𝑓𝑓𝑓𝑓1(𝑢𝑢, 𝓀𝓀) ← 𝑖𝑖; 𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝓀𝓀) ← 𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝓀𝓀) + 1; 𝑓𝑓𝑓𝑓𝑓𝑓(𝑢𝑢) ← ∑𝐾𝐾 𝑘𝑘=1 𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝑘𝑘); 𝑜𝑜𝑜𝑜𝑜𝑜(𝑢𝑢) ← max𝑘𝑘∈{1,2,…,𝐾𝐾} {𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝑘𝑘)}; Return 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖), 𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖), 𝑓𝑓𝑓𝑓𝑓𝑓(𝑢𝑢), 𝑜𝑜𝑜𝑜𝑜𝑜(𝑢𝑢) Algorithm 3 relies on the optimal solution of models 2 to 7 and the parameter 𝑈𝑈𝑈𝑈 max determined by the solution obtained by Algorithm 2. For flights 1,2, … , 𝑈𝑈𝑈𝑈 max, the results of the ferry vehicle assignment for these flights in the optimal solution of models 2 to 7 are directly transplanted (lines 2-8 of Algorithm 3). For flights 𝑈𝑈𝑈𝑈 max + 1, 𝑈𝑈𝑈𝑈 max + 2, … , |𝑁𝑁 𝑉𝑉 |, the ferry vehicles continue to be assigned as in Algorithm 2. The time complexity of Algorithm 3 is 𝑂𝑂(popsize × (|𝑁𝑁 𝑉𝑉 | − 𝑈𝑈𝑈𝑈 max ) × 𝐾𝐾). Algorithm 3: Transplantation algorithm Input: popsize, 𝐾𝐾, |𝑁𝑁 𝑉𝑉 |, 𝑎𝑎𝑖𝑖 , 𝑏𝑏𝑖𝑖 , 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖 , 𝑡𝑡𝑖𝑖𝑖𝑖 , 𝑈𝑈𝑈𝑈 max , 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠0(𝑖𝑖), 𝑠𝑠𝑠𝑠0(𝑖𝑖) 1 For ∀𝑢𝑢 ∈ {1,2, … , popsize}, 𝑘𝑘 ∈ {1,2, … , 𝐾𝐾}, set 𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝑘𝑘) ← 0; 2 For 𝑢𝑢 ← 1,2, … , popsize 3 For 𝑖𝑖 ← 1,2, … , 𝑈𝑈𝑈𝑈 max 4 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖) ← 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠0(𝑖𝑖); 5 𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖) ← 𝑠𝑠𝑠𝑠0(𝑖𝑖); 6 𝑓𝑓𝑓𝑓1(𝑢𝑢, 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠0(𝑖𝑖)) ← 𝑖𝑖; 7 𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠0(𝑖𝑖)) ← 𝑠𝑠𝑠𝑠0(𝑖𝑖); 8 𝑓𝑓𝑓𝑓3�𝑢𝑢, 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠0(𝑖𝑖)� ← 𝑓𝑓𝑓𝑓3�𝑢𝑢, 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠0(𝑖𝑖)� + 1; 9 For 𝑢𝑢 ← 1,2, … , popsize 10 For 𝑖𝑖 ← 𝑈𝑈𝑈𝑈 max + 1, 𝑈𝑈𝑈𝑈 max + 2, … , |𝑁𝑁 𝑉𝑉 | 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖 ← �𝑘𝑘 ∈ {1,2, … , 𝐾𝐾}�𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝑘𝑘) + 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑓𝑓𝑓𝑓1(𝑢𝑢,𝑘𝑘) + 𝑡𝑡𝑓𝑓𝑓𝑓1(𝑢𝑢,𝑘𝑘),𝑖𝑖 ≤ 𝑏𝑏𝑖𝑖 �; 11 12 If 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖 ≠ ∅ 13 14 15 16 17 18 19 20 21 188 |𝑁𝑁𝑉𝑉 | 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖′ ← �𝑘𝑘 ∈ 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖 �𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝑘𝑘) ≤ ⌊ ⌋�; 𝐾𝐾 If 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖′ ≠ ∅ Randomly select a ferry vehicle in 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖′ , denote as 𝓀𝓀; 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖) ← 𝓀𝓀; 𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖) ← max {𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝓀𝓀) + 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑓𝑓𝑓𝑓1(𝑢𝑢,𝓀𝓀) + 𝑡𝑡𝑓𝑓𝑓𝑓1(𝑢𝑢,𝓀𝓀),𝑖𝑖 , 𝑎𝑎𝑖𝑖 }; 𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝓀𝓀) ← max {𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝓀𝓀) + 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑓𝑓𝑓𝑓1(𝑢𝑢,𝓀𝓀) + 𝑡𝑡𝑓𝑓𝑓𝑓1(𝑢𝑢,𝓀𝓀),𝑖𝑖 , 𝑎𝑎𝑖𝑖 }; 𝑓𝑓𝑓𝑓1(𝑢𝑢, 𝓀𝓀) ← 𝑖𝑖; 𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝓀𝓀) ← 𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝓀𝓀) + 1; If 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖′ = ∅ Advances in Production Engineering & Management 17(2) 2022 A bi-objective optimization of airport ferry vehicle scheduling based on heuristic algorithm: A real data case study 22 23 24 25 26 27 28 29 Randomly select a ferry vehicle in 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖 , denote as 𝓀𝓀; 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖) ← 𝓀𝓀; 𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖) ← max {𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝓀𝓀) + 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑓𝑓𝑓𝑓1(𝑢𝑢,𝓀𝓀) + 𝑡𝑡𝑓𝑓𝑓𝑓1(𝑢𝑢,𝓀𝓀),𝑖𝑖 , 𝑎𝑎𝑖𝑖 }; 𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝓀𝓀) ← max {𝑓𝑓𝑓𝑓2(𝑢𝑢, 𝓀𝓀) + 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑓𝑓𝑓𝑓1(𝑢𝑢,𝓀𝓀) + 𝑡𝑡𝑓𝑓𝑓𝑓1(𝑢𝑢,𝓀𝓀),𝑖𝑖 , 𝑎𝑎𝑖𝑖 }; 𝑓𝑓𝑓𝑓1(𝑢𝑢, 𝓀𝓀) ← 𝑖𝑖; 𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝓀𝓀) ← 𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝓀𝓀) + 1; 𝑓𝑓𝑓𝑓𝑓𝑓(𝑢𝑢) ← ∑𝐾𝐾 𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝑘𝑘); 𝑜𝑜𝑜𝑜𝑜𝑜(𝑢𝑢) ← max𝑘𝑘∈{1,2,…,𝐾𝐾}{𝑓𝑓𝑓𝑓3(𝑢𝑢, 𝑘𝑘)}; 𝑘𝑘=1 Return 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖), 𝑠𝑠𝑠𝑠(𝑢𝑢, 𝑖𝑖), 𝑓𝑓𝑓𝑓𝑓𝑓(𝑢𝑢), 𝑜𝑜𝑜𝑜𝑜𝑜(𝑢𝑢) 4. Numerical examples: Results and discussion This section takes 24 hours (0:00-23:59) as the planning period, and uses the flight data of Beijing Capital International Airport for 60 days from February 1 to April 1, 2018 as the numerical examples. The average number of virtual flights for these 60 data sets is 900. Models 2 to 7 can be solved directly using the CPLEX solver, and the results are shown in Table 3. The running conditions are a 2.7 GHz PC (Intel® CoreTM i7-7500U CPU), Windows 7 operating system, running with 8 GB RAM, and using CPLEX 12.9 solver. Serial number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Number of virtual flights 957 815 878 870 856 901 885 912 968 894 746 825 855 876 832 878 856 888 859 997 933 990 1016 931 923 884 838 897 858 841 Table 3 Results of solving models 2 to 7 Solving time Objective Serial Number of (s) value number virtual flights 34.04 76 31 905 64.27 58 32 844 133.89 61 33 889 102.51 74 34 876 45.35 60 35 884 137.72 72 36 968 216.34 61 37 844 105.71 75 38 898 34.63 76 39 839 121.24 62 40 1029 42.99 55 41 1040 91.09 64 42 1054 89.62 57 43 878 81.09 72 44 832 19.94 74 45 947 124.16 62 46 856 80.29 64 47 904 113.24 72 48 902 102.35 54 49 770 278.51 72 50 979 170.15 65 51 877 214.33 64 52 862 271.08 62 53 845 183.39 64 54 888 157.87 64 55 880 132.13 56 56 1012 102.57 66 57 1068 106.77 66 58 1033 125.05 62 59 791 75.93 60 60 939 Solving time (s) 68.16 94.07 131.92 38.92 129.76 152.71 120.32 59.25 21.14 180.03 226.7 269.23 117.8 72.57 32.96 99.97 104.13 27.81 226.68 203.46 107.53 106.35 105.75 135.85 130.92 175.3 181.98 177.51 1806.15 4276.94 Objective value 66 67 72 70 64 78 54 72 68 70 77 70 59 64 80 71 80 64 57 67 63 57 56 63 58 78 70 74 49 54 As can be seen from Table 3, for models 2 to 7, the optimal solutions can be obtained for all 60 groups of data, and the average time to solve the problem is 200 seconds. The optimal solutions for 58 groups of data can be obtained within 5 minutes. Algorithm 0 designed in Section 3 is implemented using MATLAB R2017b and used for these 60 groups of data. The solving results of models 8 to 15 are obtained as shown in Table 4 (popsize is set to 300). As can be seen from Table 4, the heuristic algorithms designed are very suitable for solving models 8 to 15. Among these 60 groups of data, the exact optimal solutions can be obtained for 42 groups of data (all obtained by Algorithm 1), and for the other 18 groups of data, the objec|𝑁𝑁 𝑉𝑉 | ⌉ of 𝐾𝐾 tive value differs from the lower bound ⌈ the model by only 1. There are 11 groups of data Advances in Production Engineering & Management 17(2) 2022 189 Han, Zhao, Kong that need to use Algorithm 2 and only 4 groups of data that need to use Algorithm 3, all of which can obtain the approximate optimal solution, and the maximum Gap with the lower bound of the model is only 7.69 %. Take the 60th group of data as an example to show the results of ferry vehicle scheduling. |𝑁𝑁 𝑉𝑉 | This group of data has a total of 939 virtual flights using 54 ferry vehicles with the ⌈ ⌉ value of 𝐾𝐾 18. The 60th group of data uses Algorithm 3 to obtain the final solution with the 𝑈𝑈𝑈𝑈 max value of 255, and a single ferry vehicle serves up to 19 virtual flights. The number of flights served by each ferry vehicle is shown in Table 5. Serial number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Ferry vehicle 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 190 |𝑁𝑁 𝑉𝑉 | ⌈ ⌉ 𝐾𝐾 13 15 15 12 15 13 15 13 13 15 14 13 15 13 12 15 14 13 16 14 15 16 17 15 15 16 13 14 14 15 Algorithm used 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Table 4 Results of solving models 8 to 15 Objective Gap Serial |𝑁𝑁 𝑉𝑉 | ⌈ ⌉ value (%) number 𝐾𝐾 13 0.00 31 14 15 0.00 32 13 15 0.00 33 13 12 0.00 34 13 15 0.00 35 14 13 0.00 36 13 15 0.00 37 16 13 0.00 38 13 13 0.00 39 13 15 0.00 40 15 14 0.00 41 14 13 0.00 42 16 15 0.00 43 15 13 0.00 44 13 12 0.00 45 12 15 0.00 46 13 14 0.00 47 12 13 0.00 48 15 16 0.00 49 14 14 0.00 50 15 15 0.00 51 14 16 0.00 52 16 17 0.00 53 16 15 0.00 54 15 15 0.00 55 16 16 0.00 56 13 13 0.00 57 16 14 0.00 58 14 14 0.00 59 17 15 0.00 60 18 Algorithm used 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 Table 5 Results of ferry vehicle scheduling on a certain day Number of flights Ferry Number of flights Ferry served vehicle served vehicle 15 19 18 37 18 20 13 38 17 21 18 39 19 22 18 40 19 23 14 41 19 24 19 42 18 25 18 43 15 26 18 44 14 27 17 45 18 28 18 46 17 29 18 47 19 30 19 48 19 31 19 49 19 32 19 50 18 33 19 51 19 34 15 52 19 35 17 53 19 36 19 54 Objective value 14 13 13 13 14 13 16 13 13 15 14 16 16 14 13 14 13 16 15 16 15 17 17 16 17 14 17 15 18 19 Gap (%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 6.25 7.14 7.69 7.14 7.69 6.25 6.67 6.25 6.67 5.88 5.88 6.25 5.88 7.14 5.88 6.67 5.56 5.26 Number of flights served 18 16 19 18 15 17 19 16 15 17 16 19 16 15 17 15 18 16 Advances in Production Engineering & Management 17(2) 2022 A bi-objective optimization of airport ferry vehicle scheduling based on heuristic algorithm: A real data case study 5. Conclusion This paper proposes a bi-objective optimization model for airport ferry vehicle scheduling to optimize the number of vehicles used and the equilibrium degree of the vehicle workload, in which the objective function designed for the second objective is to minimize the maximum number of flights served by a single ferry vehicle. For the second optimization objective, three concise and efficient heuristic algorithms are designed and tested using the actual flight data from an airport. The analysis of numerical examples shows that Algorithms 1 and 2, which do not depend on the optimal solution of the first optimization objective, have been able to solve most of the examples, and the effectiveness of these algorithms is verified by the fact that all three algorithms can obtain exact solutions or high-quality approximate solutions. Although the bi-objective optimization in this paper is designed for airports, its algorithms can also be applied to solve similar vehicle scheduling problems that balance the workload of vehicles. Possible future research directions also include the problem of real-time scheduling of ferry vehicles considering uncertain and unexpected conditions. Acknowledgement This work was supported by the National Natural Science Foundation of China (grant numbers 72071122, 72134004); the Natural Science Foundation of Shandong Province (grant number ZR2020MG002); and the Social Science Planning Research Project of Shandong Province (grant number 20CGLJ11). References Zeng, Z.H., Jia, L.Q. (2020). Research on airport special vehicle scheduling problem, In: Proceedings of 2020 International Conference on Virtual Reality and Intelligent Systems (ICVRIS), Zhangjiajie, China, 1076-1078. [2] Lv, H., Qin, Y., Tang, R., Luo, C. (2011). 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[24] Zhao, P., Han, X., Wan, D. (2021). Evaluation of the airport ferry vehicle scheduling based on network maximum flow model, Omega, Vol. 99, Article No. 102178, doi: 10.1016/j.omega.2019.102178. [25] Bertsimas, D., Jaillet, P., Martin, S. (2019). Online vehicle routing: The edge of optimization in large-scale applications, Operations Research, Vol. 67, No. 1, 143-162, doi: 10.1287/opre.2018.1763. 192 Advances in Production Engineering & Management 17(2) 2022 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 2 | June 2022 | pp 193–204 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.2.430 Original scientific paper Ultrasonic abrasive polishing of additive manufactured parts: An experimental study on the effects of process parameters on polishing performance Liu, X.a, Wang, J.a,*, Zhu, J.a, Liew, P.J.b, Li, C.c, Huang, C.d aMarine Engineering College, Dalian Maritime University, Ganjingzi District, Dalian, P.R. China Kejuruteraan Pembuatan, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, Durian Tunggal, Melaka, Malaysia cXinyu Key Laboratory of Materials Technology and Application for Intelligent Manufacturing, Xinyu University, P.R. China dCollege of Marine Engineering, Jimei University, Fujian, P.R. China bFakulti ABSTRACT ARTICLE INFO The rough surface of metal parts produced by the powder-based layered Additive Manufacturing (AM) technology such as Selective Laser Melting (SLM) is an important problem that needs to be solved. This study introduces obvious improvements in the surface quality of the AM parts by means of ultrasonic abrasive polishing (UAP), which uses cavitation collapse and microcut of abrasive particles for finishing surfaces. Experiments were conducted using the orthogonal experimental design method with an L9(34) orthogonal array to investigate the effects of ultrasonic power, machining time, abrasive particle size, and particle concentration on surface roughness Ra and material removal rate (MRR). The wear of the abrasive particles in the slurry was also studied. IN625 nickel-based alloy specimen manufactured by Selective Laser Melting (SLM) was chosen as the target workpiece. The results show that when the ultrasonic output power was too high, both surface quality and machining efficiency were deteriorated. And the surface roughness Ra was not further improved by just increasing the machining time. Severe cavitation erosion occurred in the polishing process and created leftover pits on the workpiece surface, which has a large influence on Ra. The size and amount of the abrasive particles should be within a certain range, which is helpful for material removal and improving the polishing performance. The work is useful for studying the influential process parameters involved in UAP and finding out the appropriate conditions. Keywords: Additive manufacturing; 3D printing; Selective laser melting (SLM); Ultrasonic abrasive polishing; Process parameters; Surface roughness; Material removal rate; Orthogonal array tests *Corresponding author: wjs@dlmu.edu.cn (Wang, J.) Article history: Received 19 January 2022 Revised 14 August 2022 Accepted 21 August 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction Additive Manufacturing (AM) technology is a process of joining materials layer by layer to make parts based on a pre-designed three-dimensional model data, which is distinguished from traditional subtractive machining techniques [1]. The manufactured components have high dimensional accuracy and long-term dimensional stability [2, 3] Therefore, the AM technology greatly reduces waste material, part weight, and production time. In addition, manufacturing components with no geometric limitations makes it attractive in various fields such as automotive, aerospace, and medicine [4-8]. 193 Liu, Wang, Zhu, Liew, Li, Huang Fig. 1 Stair-stepping effect, balling effect, and powder adhesion in SLM A laser beam can be focused to a small size which makes the energy density high and can minimize the molten pool and heat-affected zone. Therefore, lasers have been widely utilized in AM processes, especially for the metallic materials with high melting points [9-12]. The laserbased AM processes are classified into two categories [13]. One is the laser-based directed energy deposition (L-DED), where the material can be either wire or powder, and is melted and deposited simultaneously. The other one is the laser-based powder bed fusion (L-PBF), where the laser source selectively melts metallic powders layer by layer. Even though the L-DED has faster built speeds, the L-PBF is more popular due to its better manufacturing capability for producing compact features with greater geometrical accuracy and high specific strength [10, 12]. Selective laser melting (SLM) and Selective laser sintering (SLS) are typical L-PBF technologies. SLS technology has relatively low strength sintered parts. In addition, the mechanical properties and forming accuracy of SLS sintered parts are lower than that of SLM due to voids in process entities [14]. SLM acts as one of the most popular AM processes for metallic materials in industry now. However, the surface roughness of the SLM parts is still too high for direct uses. In the SLM process, stair-stepping effect, balling effect, and powder adhesion [15-18] are the three main factors leading to the poor quality as shown in Fig. 1. These not only affect the aesthetics, but also greatly limits the functional performance of the parts including fatigue life and friction properties [19]. To improve the surface quality of AM parts for practical uses, various post-process finishing techniques are implemented [20]. Today, manual polishing is still the main polishing method for AM parts, but it needs long operating time and high labor costs, and the accuracy is dependent on the experience of the personnel. Chemical polishing, electrochemical polishing, laser polishing, and abrasive flow machining have shown their capabilities in finishing AM parts [21-23]. However, they have their respective advantages and shortcomings when applied to surface polishing of AM parts. The larger thermal damage caused by laser polishing leads to the deformation of metal parts more easily. In the same way, chemical polishing causes great chemical damage. While electrochemical polishing is not suitable for polishing metal parts with deep inner holes. Abrasive flow machining is potential for surface finishing of internal channels, but it still has the limitations include damage to thin-walled structures due to excessive pumping pressures and abrasive contamination in the internal channels. The principle of ultrasonic abrasive polishing, abbreviated as UAP here, was proved effective in improving surface quality of AM parts in some recent studies [21, 24-26]. In this process, the materials are removed by the combination of cavitation and micro-cut of abrasive particles, which is feasible for finishing various AM parts with complex external and internal surfaces. Mass and dimensional losses are only significant for initially rough surfaces with numerous surface irregularities. Therefore, UAP has the potential to finish the surface without alteration of the original AM dimensions, which distinguishes it from other surface finishing techniques. Nevertheless, the machining capability of UAP for finishing AM surfaces is not totally understood. Many input parameters exist in UAP which would influence the polishing performance, and there is a lack of systematic study on this. In this study, UAP experiments of SLM manufactured 194 Advances in Production Engineering & Management 17(2) 2022 Ultrasonic abrasive polishing of additive manufactured parts: An experimental study on the effects of process … IN625 alloy specimen were conducted using the orthogonal experimental design method with an L9(34) orthogonal array to investigate the effects of ultrasonic power, machining time, abrasive size, and abrasive concentration on polishing results. The work is useful for studying the influential process parameters involved in UAP and improving the machining performance. 2. Basic principle of ultrasonic abrasive polishing (UAP) UAP uses an ultrasonic tool (horn) in conjunction with abrasive particles suspended in a liquid slurry for surface polishing, the ultrasonic tool tip should be at a specific distance away from the specimen surface to prevent a contact between them. According to the previous studies, three main material removal modes in the polishing process were concluded [25, 27] and schematically shown in Fig. 2. They include: • Cavitation erosion from the abrasive slurry, which is effective for removing partially melting powders on the AM surfaces. • Abrasion by the impact of the abrasive particles against the workpiece accelerated by the force of cavitation collapse. • Small-scale material removal by high frequency impact of abrasive particles excited by ultrasonic vibration of the tool. In addition, the cavitation effect is helpful for the circulation of abrasives and chip removal of the workpiece materials, which facilitate the material removal in UAP. The cavitation is mainly influenced by ultrasonic amplitude, ultrasonic frequency, and physical parameters of the liquid. Generally, ultrasonic frequency ranged from 20-40 kHz is appropriate for cavitation. The cavitation intensity increases with the increase of the ultrasonic amplitude. And an increase of the liquid viscosity would suppress the cavitation. On the other hand, the frequency and intensity of the abrasive impact would also be influenced by the input ultrasonic parameters and the characteristics of the particles. (a) (b) (c) Fig. 2 Schematic view of material removal in UAP: (a) cavitation erosion, (b) abrasive impact accelerated by cavitation collapse, (c) abrasive impact excited by ultrasonic vibration of the tool Advances in Production Engineering & Management 17(2) 2022 195 Liu, Wang, Zhu, Liew, Li, Huang Therefore, both the settings of the ultrasonic parameters and the composition of the slurry are important for the material removal in UAP, and accordingly influence the polishing efficiency and the surface quality. In the following sections, UAP experiments are introduced, discussions are also conducted based on the experimental results and previous studies. 3. Materials and methods 3.1 Materials The slurry composed of silicon carbide abrasive particles and purified water. The IN625 specimen was a cube with a side length of 20 mm, which was manufactured by a SLM equipment (FARSOON) with the scanning speed of 7.6 m/s. The metal powder size ranges from 15 μm to 53 μm. The powder-bed depth is 0.1 mm, and the material parameters are illustrated in Table 1. Surfaces built at 90° orientation were treated with UAP process. Element wt % C Si Mn S P Table 1 Material parameters Cr Ni Mo ≤ 0.1 ≤ 0.5 ≤ 0.5 ≤ 0.015 ≤ 0.015 20.0-23.0 ≥ 58.0 8.8-10.0 3.2 Experimental setup Al ≤ 0.4 Ti ≤ 0.4 Nb+Ta Co Fe 3.15-4.15 ˂ 1.0 ˂ 5.0 An ultrasonic generator with the output power ranging from 800-1800 W (Ningbo Scientz Biotechnology) was used in this work. The frequency is 19.5-20.5 kHz. The diameter of the horn tip is 25 mm. The ultrasonic amplitude can be adjusted purposely by changing the output power. 3.3 Design of experiments In this study, the surface roughness Ra and the material removal rate (MMR) were used for evaluating the polishing performance of UAP. To obtain the appropriate condition covering a wide range of factors in a more efficient way, the orthogonal experimental design was applied to reduce the number of experiments. Table 2 lists the specific conditions of an L9(34) orthogonal array used in this work, corresponding to four factors of three levels. As shown in Table 2, three levels of ultrasonic power were 900, 1200 and 1500 W. Three levels of machining time were 10 min, 20 min and 30 min. Three levels of abrasive size were 800, 1200, and 2000 grit sizes. Three levels of abrasive concentration were 5 %, 10 % and 15 %. Table 2 Experimental design using the L9 orthogonal array Experimental number Factors A (Ultrasonic power) B (Machining time) C (Abrasive size ) D (Abrasive concentration) 1 900 10 800 5 2 900 20 1200 10 3 900 30 2000 15 4 1200 10 1200 15 5 1200 20 2000 5 6 1200 30 800 10 7 1500 10 2000 10 8 1500 20 800 15 9 1500 30 1200 5 The orthogonal experimental results were studied with the range analysis, which is a statistical method to determine the sensitivity of the factors and to obtain the optimal process conditions. The analyzing process of range analysis is as follows: kXm = KXm / 3 (1) R = max(kX1, kX2, kX3) – min(kX1, kX2, kX3) (2) KXm and kXm means the sum and the average value of the experimental results of factor X with level m. R means the influence degree of the factor X, and the higher the value R is, the greater 196 Advances in Production Engineering & Management 17(2) 2022 Ultrasonic abrasive polishing of additive manufactured parts: An experimental study on the effects of process … the influence degree of factor X is. The tendency charts showing the influence of each parameter on the surface roughness and the MRR were also drawn based on the range analysis. 3.4 Experimental procedure As shown in Fig. 3, the workpiece to be polished was fixed in a container filled with the abrasive slurry. The ultrasonic tool was immersed in the slurry, the distance between the tool tip and the workpiece was adjusted to guarantee efficient polishing and prevent direct contact between the two. Meanwhile, cooling system was applied during the process to avoid a drastic increase in temperature of the horn. Repeated polishing experiments were conducted for each condition as shown in Table 2. After polishing, the surface roughness was tested by a hand-held roughness meter with the measurement accuracy of 0.002 μm (Mitutoyo), and the surface was observed with a scanning electron microscope (TESCAN). Due to the high standard deviations of AM surface, as least as 5 measurements of each specimen were conducted to calculate the average Ra value. The weight of the workpiece before and after polishing was measured by an electronic balance with the measurement accuracy of 0.1 mg. Thus, the MRR can be calculated as the difference of weight over the polishing time. In addition, the particle size distribution before and after machining was examined by a particle size analysis device (Mastersizer 3000, Malvern Panalytical) to study the wear of abrasive particles. Transducer X Z Horn and tool Slurry Workpiece Y Fig. 3 Schematic view of the experimental process 4. Results and discussions The obtained surface roughness Ra and MRR after ultrasonic polishing experiments are as shown in Table 3. The initial average Ra of the target SLM surface is 9.48 μm. After polishing, the surface roughness was decreased obviously ranging from 5.01 μm to 6.80 μm. The MRR ranges from 1.14 mg/min to 3.0 mg/min. Experimental number 1 2 3 4 5 6 7 8 9 Table 3 Results of surface roughness and MRR Surface roughness Ra (μm) 5.58 5.92 6.05 6.20 5.66 6.22 5.01 6.80 6.20 MMR (mg/min) 2.40 2.15 1.86 1.84 2.71 1.57 3.00 1.14 1.57 Range analysis results of surface roughness and MRR were presented in Table 4 and Table 5, respectively. Kj and kj represents the sum and average value of the measurement results of the roughness and the MRR for each factor (each column) with level j, j = 1, 2, 3, respectively. The results show that the main influence factor on surface roughness is abrasive concentration, and the influence order of different process parameters on Ra is: abrasive concentration > abrasive size > machining time > ultrasonic power based on the value R. The main influence factor on MRR is abrasive size, and the influence order of the parameters is: abrasive size > machining time > abrasive concentration > ultrasonic power using the same analysis method. In this work, Advances in Production Engineering & Management 17(2) 2022 197 Liu, Wang, Zhu, Liew, Li, Huang the surface roughness value is required to be as small as possible, which means the surface quality is improved. On the other hand, the MRR should be high, which is important to increase the machining efficiency. When the combination of the four process parameters is ultrasonic power at 900 W, machining time of 10 min, grit size at 2000, and abrasive concentration at 10 %, the analysis results show smallest Ra value (the corresponding level of minimum k for each factor) and highest MRR (the corresponding level of maximum k for each factor). Table 4 Range analysis on surface roughness Ultrasonic power Machining time Abrasive size Abrasive concentration (W) (min) (μm) (% wt) K1 17.55 16.79 18.60 17.44 K2 18.08 18.38 18.32 17.15 K3 18.01 18.47 16.72 19.05 k1 5.850 5.597 6.200 5.813 k2 6.027 6.127 6.107 5.717 k3 6.003 6.157 5.573 6.350 R 0.177 0.560 0.627 0.633 Order of priority Abrasive concentration ˃ Abrasive size ˃ Machining time ˃ Ultrasonic power Optimal level 900 10 2000 10 Optimal combination 900 W, 10 min, 2000 grit, 10 % Table 5 Range analysis on MRR Abrasive concentration Ultrasonic power Machining time Abrasive size (% wt) (W) (min) (μm) K1 6.41 7.24 5.11 6.68 K2 6.12 6.00 5.56 6.72 K3 5.71 5.00 7.57 4.84 k1 2.137 2.413 1.703 2.227 k2 2.040 2.000 1.853 2.240 k3 1.903 1.667 2.523 1.613 R 0.233 0.747 0.820 0.627 Order of priority Abrasive size ˃ Machining time ˃ Abrasive concentration ˃ Ultrasonic power Optimal level 900 10 2000 10 Optimal combination 900 W, 10 min, 2000 grit, 10 % 4.1 Effects of ultrasonic power Fig. 4 shows the effects of ultrasonic power on surface roughness and MRR. When the output power of the ultrasonic generator was 900 W, better surface roughness Ra and larger MRR were obtained compared to 1200 W and 1500 W. Based on our former research [25], when the ultrasonic power is among 400 W to 600 W, the surface becomes smoother with the increase of ultrasonic power. It is considered that with the increase of ultrasonic power, the cavitation intensity is enhanced which strengthens the cavitation erosion effects on the work surface and accordingly facilitates the removal of partially melted powders. In addition, abrasion against the workpiece due to the impact of abrasive particle that accelerated by cavitation collapse is also enhanced, so irregularities on the initially rough AM surfaces can be gradually smoothed. However, in this work, it is found that a too high ultrasonic power deteriorates both the surface quality and the machining efficiency. Existed studies have shown that the cavitation erosion effects on a solid surface increase with ultrasonic power up to a threshold and then decrease [28, 29]. The presence of a maximum in the ultrasonically enhanced erosion effects with increasing power is attributed to a peak in the cavitation intensity, which is supposed to increase with the enhancement of ultrasonic power if the collapse time allows the cavitation bubble to grow [30, 31]. Therefore, the condition produces maximum of cavitation erosion effects must be a function of power as well as frequency. On the other hand, it is commonly believed that the horn amplitude (here is controlled by the output power) has a significant effect on ultrasonic machining [32]. In this work, the output power has minimal impact on Ra and MRR compared to the other factors, which may be related to the choice of the three high output power levels. 198 Advances in Production Engineering & Management 17(2) 2022 Ultrasonic abrasive polishing of additive manufactured parts: An experimental study on the effects of process … Fig. 4 Effects of ultrasonic power on surface roughness and MRR 10 50 5 0 20 Particle size μm Relative distribution 15 100 After polishing with 900 W 5 50 0 0 10 20 Particle size μm 30 40 0 (a) 30 40 0 15 Relative distribution 10 Cumulative distribution 0 10 100 Before polishing Cumulative distribution Relative distribution 15 Cumulative distribution The wear of abrasive particles under 900 W and 1500 W were compared by examining particle size distribution before and after polishing process. Other conditions are the same: 2000 grit size abrasive particles, 5 % abrasive concentration, machining time of 20 min. The results are shown in Fig. 5. The maximum particle size that can be detected becomes smaller as indicated with the ellipse marks after polishing (maximum value shifted to the left). The mean particle size before polishing was found to be 8.98 μm, according to the measurement report. After polishing with 900 W and 1500 W, the mean particle size reduces to 8.74 μm and 8.16 μm, respectively. The wear of abrasive particles is increased due to the stronger cavitation effect at higher ultrasonic power. Therefore, more motion energy of the abrasive particles was consumed in the wear between the particles but not the material removal of the workpiece when the ultrasonic power was 1500 W, which accordingly influences the polishing efficiency and the surface quality. Fig. 6(a) shows the typical surface characteristics of the workpiece before polishing, and Fig. 6(b) is the same area after polishing. Obvious improvement of surface quality can be confirmed. The partially melted powders were almost removed as indicated in area A, and some larger discontinuities were also smoothed as shown in area B. On the other hand, tightly attached balls and irregular structures were challenging to be removed. In addition, some leftover pits due to cavitation erosion are found on the polished surface as shown in area C. With the increase of ultrasonic power, severe cavitation erosion may occur, which can leave more such leftover structures on work surface and increase the Ra value. 100 After polishing with 1500 W 10 5 50 0 0 10 20 Particle size μm 30 40 0 (b) (c) Fig. 5 Particle size distribution before (a) and after polishing with (b) 900 W and (c) 1500 W Advances in Production Engineering & Management 17(2) 2022 199 Liu, Wang, Zhu, Liew, Li, Huang A A B B C C Leftover pit Fig. 6 SEM images of the surfaces: (a) as-manufactured AM workpiece surface; (b) surface after ultrasonic abrasive polishing Therefore, although the machining capability of UAP could be enhanced at higher power, the increase in wear of abrasives and excessive erosion of surface occur simultaneously, which strongly influences the polishing process. In addition, large number of cavitation bubbles and broken abrasive particles between the horn and the workpiece may play a screening role that inhibits effective cavitation erosion and abrasion of particles against the workpiece at higher power. All these lead to the better surface roughness Ra and larger MRR at 900 W than 1200 W and 1500 W in this work. 4.2 Effects of machining time Fig. 7 shows the effects of machining time on surface roughness Ra and MRR. The machining time of 10 min resulted in minimum Ra and maximum MRR compared to 20 min and 30 min. At the initial stage of polishing, the partially melted powders were removed quickly, and the peak of material surface was easily to be ground. Therefore, the Ra value rapidly reduced, and the MRR was high. With the increase of polishing time, the peak of the surface was smoothed and became flat, which slowed down the MRR. And we found the similar tendency in the previous work [25] that the partially melted powders were predominately removed in the first several minutes and only slight material removal occurred in the remaining machining time. The surface was significantly modified in the initial stage (around several minutes or less) and converge to an equilibrium state. Normally, the Ra should not be worse because more powders and irregular structures might be removed with the increase of the machining time. However, the results show an obvious increase in the Ra value after 20 min and 30 min. The workpiece was an AM manufactured part and has its own surface features, large pits may be left on the surface as introduced in area C of Fig. 6 after the removal of tightly attached large balls and irregular structures due to severe cavitation erosion. This has a large effect on the surface roughness Ra. In addition, the existence of these pits may further negatively affect the polishing performance because it is easier to deepen the pits under cavitation erosion and abrasive impacts than to flatten them. It seems more necessary to finding out appropriate conditions to facilitate effective polishing action for further reducing the Ra value. 200 Fig. 7 Effects of machining time on surface roughness and MRR Advances in Production Engineering & Management 17(2) 2022 Ultrasonic abrasive polishing of additive manufactured parts: An experimental study on the effects of process … Surface roughness Ra (μm) 6.3 3 6.2 2.5 6.1 2 6 5.9 1.5 5.8 5.6 5.5 1 Ra MRR 5.7 400 800 1200 1600 0.5 2000 0 2400 Material removal rate (mg/min) On the other hand, with the increase of processing time, the wear of abrasive becomes more and more serious, which weakens the grinding capability of abrasive particles. And in the experiments, no new slurry was introduced in the machining area, the continuous high-power ultrasonic work leads to severe wear of abrasive particles and affects the UAP process. 4.3 Effects of abrasive size Fig. 8 shows the effects of abrasive size on surface roughness Ra and MRR. Using abrasive particles of 2000 grit size resulted in minimum Ra and maximum MRR compared to 1200 and 800 grit sizes. The abrasive particles act as bubble nucleation sites, compared to smaller particles, the larger particles have larger surface areas to compete for bubble nucleation, so the cavitation erosion against workpiece may be inhibited in the presence of larger particles. Accordingly, material removal process is influenced. The wear of abrasive particles of 2000 and 800 grit sizes were compared by examining particle size distribution before and after polishing process, respectively. Other conditions are the same: 900 W ultrasonic power, 5 % abrasive concentration, and machining time of 20 min. The results are shown in Fig. 9, the particles become smaller due to the wear for both cases. The mean particle size of 2000 and 800 grit abrasive particles decrease from 8.98 μm and 19 μm to 8.74 μm and 17.7 μm, respectively. A decrease of 2.7 % and 6.8 % in mean particle size for 2000 and 800 grit abrasive particles is confirmed. Therefore, more motion energy was consumed in abrasive broken for larger abrasive particles, and accordingly influences the polishing process. In addition, the larger size particle could act as a physical barrier on the specimen surface to avoid the impact of micro-jets induced by cavitation collapse and affect the material removal [21]. The diameters of the micro-jets are around 10-30 μm [33]. The mean particle size of 1200 and 800 grit abrasive particles are 13.8 μm and 19 μm, respectively, which would screen the micro-jets and inhibit material removal. Therefore, when using abrasives of 1200 and 800 grit sizes, both surface quality and machining efficiency are deteriorated. 0 0 10 20 Particle size μm 30 40 Relative distribution 15 100 Before polishing 10 0 50 5 0 0 20 40 Particle size μm 60 80 0 100 After polishing 10 50 5 0 0 10 20 Particle size μm (a) 30 40 15 0 100 After polishing 10 50 5 0 0 20 40 Particle size μm 60 80 0 (b) Fig. 9 Particle size distribution before and after polishing: (a) 2000 and (b) 800 grit sizes Advances in Production Engineering & Management 17(2) 2022 Cumulative distribution 5 Relative distribution 50 15 Relative distribution 10 Cumulative distribution 100 Before polishing Cumulative distribution Relative distribution 15 Cumulative distribution Abrasive grit size Fig. 8 Effects of abrasive size on surface roughness and MRR 201 Liu, Wang, Zhu, Liew, Li, Huang 4.4 Effects of abrasive concentration Fig. 10 shows the effects of abrasive concentration on surface roughness Ra and MRR. The abrasive concentration at 10 % resulted in minimum Ra and maximum MRR compared to 5 % and 15 %. The former studies [21, 25] also showed that the surface roughness is improved with the increase of abrasive concentration in a certain range, then the Ra value cannot get better with a further increase in abrasive concentration. And the MRR also showed the same tendency. When the abrasive concentration is too high, the interference between the abrasive particles increases. It is supposed that more motion energy of the abrasive particles would be consumed in the impact between the particles but not the material removal of the workpiece, which would accordingly affect the polishing performance. Furthermore, a large number of abrasive particles would act competing nucleation sites, which may inhibit the cavitation erosion against the workpiece, resulting in the reduction of material removal. 5. Conclusion Fig. 10 Effects of abrasive concentration on surface roughness and MRR Since ultrasonic process is cost effective and applicable to the manufacturing of micro-to macroscale structures, it may lead to new applications in specially designed surface treatment by controlling the process parameters appropriately. In this work, the machining capability of UAP which used ultrasonic cavitation in an abrasive slurry was studied. Polishing experiments on SLM manufactured IN625 alloy specimen were conducted using the orthogonal experimental design method with an L9(34) orthogonal array. Range analysis was performed on the experimental results to investigate the effects of ultrasonic power, machining time, abrasive size, and abrasive concentration on polishing performance. The work is useful for studying the influential process parameters involved in ultrasonic abrasive polishing and optimizing the process parameters. The following conclusions can be drawn: • When the ultrasonic power is too high, both abrasive wear and cavitation bubbles increase, which may play a screening role that inhibits cavitation erosion and abrasion of particles against the workpiece. Therefore, the surface quality and the machining efficiency would be deteriorated. • During polishing process, severe cavitation erosion can occur and create leftover pits on the workpiece surface, which has a large influence on Ra. • The AM surface is significantly modified in the initial polishing stage because the partially melted powders and some peak irregular structures are removed. • Using too large abrasive particles is not helpful for material removal. The larger particles have larger surface areas to compete for bubble nucleation and act as physical barriers on the workpiece surface to inhibit the material removal of the workpiece. And the severe wear of large abrasive particles also influences the polishing performance. • Both the surface quality and the MRR were improved when the abrasive concentration increased within a certain range. While the abrasive concentration is too high, the interference between the abrasive particles increases, the material removal is suppressed, and the surface quality is also deteriorated. 202 Advances in Production Engineering & Management 17(2) 2022 Ultrasonic abrasive polishing of additive manufactured parts: An experimental study on the effects of process … • Based on the range analysis, the influence order of different process parameters on Ra was abrasive concentration > abrasive size > machining time > ultrasonic power, while the influence order of the parameters on MRR was abrasive size > machining time > abrasive concentration > ultrasonic power in this study. When the ultrasonic power, machining time, grit size and abrasive concentration are 900 W, 10 min, 2000 grit size, and 10 %, respectively, the analysis results show smallest Ra value and highest MRR. Funding This work is supported by China Postdoctoral Science Foundation [Grant no. 2019M651093], the Natural Science Foundation of Liaoning Province (China) [Grant no. 2021-MS-135], Dalian Science and Technology Development Funds of China [Grant no. 2020RQ092], the National Natural Science Foundation of China [Grant no. 51805067], Fundamental Research Funds for the Central Universities of China [Grant no. 3132019366]. Conflicts of Interest The authors declare no conflict of interest. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] ASTM International. (2015). ISO/ASTM52900-15 Standard terminology for additive manufacturing-general principles- terminology, West Conshohocken, PA: ASTM International. Mandić, M., Galeta, T., Raos, P., Jugović, V. (2016). 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Incubation pit analysis and calculation of the hydrodynamic impact pressure from the implosion of an acoustic cavitation bubble, Ultrasonics Sonochemistry, Vol. 21, No. 2, 866-878, doi: 10.1016/j.ultsonch.2013.10.003. 204 Advances in Production Engineering & Management 17(2) 2022 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 2 | June 2022 | pp 205–218 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.2.431 Original scientific paper Machinability analysis and multi-response optimization using NGSA-II algorithm for particle reinforced aluminum based metal matrix composites Umer, U.a,*, Mohammed, M.K.a, Abidi, M.H.a, Alkhalefah, H.a, Kishawy, H.A.b aAdvanced Manufacturing Institute, King Saud University, Riyadh, Saudi Arabia Research Laboratory, University of Ontario Institute of Technology, Oshawa, ON, Canada bMachining ABSTRACT ARTICLE INFO In this study the effects of reinforcement particle size and cutting parameters on machining performance variables like cutting force, maximum tool-chip interface temperature and surface roughness of the machined surface have been investigated while machining Aluminum based metal matrix composites (MMCs). MMC bars with silicon carbide reinforcement having 10 % volume fraction and particle sizes of 5 μm, 10 μm and 15 μm are machined with polycrystalline diamond (PCD) inserts. Experiments are performed using central composite design (CCD) having four parameters with three levels. Response surfaces for each performance variables are generated using polynomial models. Single variable and interaction effects have been investigated using principal component analysis and 3D response charts. Multi-response optimization has been performed to minimize surface roughness and maximum toolchip interface temperature using non-dominated sorting genetic algorithm II (NSGA-II). In addition, constraints have been applied to the optimization search to filter design points with high cutting forces and low material removal rate. Most of the optimal solutions are found to be with moderate cutting speeds, low feed rate and low depth of cuts. Keywords: Metal Matrix Composites (MMC); Machining; Reinforcement particle; Machinability; Multi-objective optimization; Non-dominated sorting genetic algorithm (NSGA-II) *Corresponding author: uumer@ksu.edu.sa (Umer, U.) Article history: Received 8 March 2022 Revised 31 August 2022 Accepted 31 August 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction 1.1 General Metal matrix composites (MMCs) are gaining popularity in different fields such as automotive, aerospace, biomedical and electronics. They are gradually replacing conventional metals and alloys owing to their superior properties e.g., strength to weight ratio and wear resistance. They are usually made by net-shape manufacturing techniques. However, to obtain the required accuracy and surface finish, secondary processes such as machining cannot be avoided. Machining of MMCs is different and quite challenging as compared to the traditional metals and alloys due to the presence of hard reinforcement particles. The interactions between reinforcement particles and cutting tools result in excessive tool wear. The debonding and fracture of these reinforcement particles leads to poor surface integrity of the machined surface. The choice of optimum cutting parameters becomes more complex and depends on several factors like shape, size, volume fraction and distribution of these reinforcement particles. 205 Umer, Mohammed, Abidi, Alkhalefah, Kishawy There have been many attempts to analyze machinability of particle reinforced MMCs with respect to cutting forces, chip morphology, surface finish, sub-surface damages and tool wear. The effect of reinforcement particle size on tool wear and surface finish was analyzed by Ciftci et al. [1] during machining of Aluminum based MMC with silicon carbide reinforcement (Al/SiCp). They utilized both coated and uncoated carbide tools. MMCs were made up of 30 μm, 45 μm and 110 μm particle sizes and volume fraction of 16 %. They reported that both tool wear and surface finish deteriorate with increasing particle size. Similar findings were reported by Kannan et al. [2] also while machining Al/Al2O3p MMC having different particle sizes and volume fractions. It was noted that high volume fraction of reinforcement particles also results in an increased tool wear that ultimately leads to poorer finish on the machined surface. High volume fraction of reinforcement particles leads to higher frequency of tool-particle interactions which result in accelerated tool wear. In another study Al/SiCp MMC were machined with 5 %, 10 % and 15 % volume fraction. They concluded that machinability of MMC was severely affected by the cutting speed and volume fraction of reinforcement particles [3]. The effects of cutting speed, feed rate, tool inclination angle and volume fraction of reinforcement particles for Al/SiCp MMC using carbide tool were investigated by Joshi et al. [4]. They developed a relationship between flank wear and cutting time and showed that the cutting speed and volume fraction of reinforcement particles are mainly responsible for increased tool wear. Rai et al. [5] performed machinability analysis for different reinforcement materials when cutting Aluminum based MMC with TiC, TiAl3 and Si particles. They evaluated cutting forces and surface roughness for each material and compared with the non-reinforced one. MMC with TiC reinforcement are found to be better and showed lowest cutting forces and reduced surface roughness. The authors reported absences of built-up-edge in case of Al/TiCp MMC which results in low tool wear by attrition as compared to other MMCs. The machinability of aluminum based MMC with B4C reinforcement particles was analyzed by Karakas et al. [6]. They investigated the formation of built-up-edge and tool wear while machining with coated and uncoated tungsten carbide tools. Flank wear and BUE formation was found to be significant for uncoated tools at all cutting speeds. Cheung et al. [7] studied the effect of volume fraction of reinforcement on the surface roughness of the machined surface. Tool marks and surface roughness are found to increase as volume fraction increases. They suggested that this might be due to the pronounced spring back effect of the tool cutting edge when it strikes to the hard reinforcement particles. The effect of reinforcement particle size was investigated by Chandrasekaran and Johansson [8] and found that for each particle size there is an optimum feed rate and volume fraction of the reinforcement particles. In another research conducted by Xiaoping and Seah [9] both particle size and volume fraction of reinforcement particles are found to be significant for tool life. They reported that there is a critical value of volume fraction for each particle size above which tool wear increases at a rapid rate. This critical volume found to decrease as particle size increases. According to researchers, surface integrity of the machined MMC is greatly dependent on the size, shape, volume fraction, bonding strength, and distribution pattern of the reinforcement particles. Lin et al. [10] reported that a good quality surface is not easier to achieve for MMCs as fractured and debonded reinforcement particles abrade the surface and cutting tool that leads to pits and tool marks on the machined surface. The effects of shape of the reinforcement (particles and whiskers) on the quality of the machined MMC were analyzed by Cheung et al. [7] when cutting Al/SiCp MMC using diamond tools. They examined the tool-particle interactions and reported that cut-through particles leave a good surface finish as compared to the debonded particles as later are mainly responsible for cracking and pits on the machined surface. It was noted that the cut-through mechanism is dominant in whiskers as compared to the particle based MMCs. Sub-surface damages and surface roughness examinations for machining with particle reinforced MMCs were done by El-Gallab and Sklad [11]. They plotted microhardness profiles for the sub-surface damages and showed that damage is mostly located 60 μm to 100 μm beneath the machined surface. Transmission electron microscopic (TEM) examinations revealed that subsurface damage is associated with piling up of dislocations in smaller grains areas. Dandekar and 206 Advances in Production Engineering & Management 17(2) 2022 Machinability analysis and multi-response optimization using NGSA-II algorithm for particle reinforced aluminum … Shin [12] developed a 3D finite element (FE) model with cohesive elements to predict subsurface damage due to particle debonding while machining Al/SiCp MMC. They calculated debonding energy for SiC particles and showed that the damage depth increases with feed rate which also results in higher cutting forces. Machinability analysis for MMCs with different tools was investigated by Hung et al. [13]. They measured the sub-surface damage by testing the microhardness of the plastically deformed machined surfaces. Microscopic examinations of the machined surfaces showed that CBN and PCD tools fractured the reinforced particles along their crystallographic planes resulting in low plastic deformation. In contrast machining with other tools resulted in particles debonding resulted in higher sub-surface damage. Pramanik et al. [14] compared residual stresses for the non-reinforced alloy and MMC. It was noted that longitudinal residual stresses for the non-reinforced alloys are tensile in nature and increases with both cutting speed and feed rate. For MMC the residual stresses are found to be compressive and showing very little dependency on the cutting parameters, i.e. almost constant by changing cutting speed and feed rate. As residual stresses in machining are mainly due to plastic deformation and temperature gradients inside the material, these phenomena are somewhat altered by the presence of hard reinforcement particles. From authors perspective this might be due to constrained matrix flow, hammering effect of the reinforcement particles and compression of the matrix between the cutting tool and hard ceramic particles. The effect of reinforcement particles during MMC machining was studied by Cheung et al. [7] using quick stop test. They observed semi-continuous chips and believed that it is a result of reduction in ductility of the matrix due to hard reinforcement particles. It has also been observed that during cutting the reinforcement particles accumulate along the shear plane. The debonding of the particles and stress concentration accelerate the process of crack propagation resulting in serrated or semi-continuous chips [15]. Similar findings are reported in other studies while turning [11, 16] and drilling [17] Al/SiCp MMCs. Olivas et al. [18] reported that tensile residual stresses present on the surface of the ductile matrix generated during fabrication of MMC also facilitate this crack propagation/formation of semi-continuous chips. The relationships between thrust force, torque and tool wear were examined by Morin et al. [19] while drilling non-reinforced aluminum alloy and MMC. They reported almost equal thrust force and torque for aluminum alloy and MMC and concluded that it is the matrix which controls the forces and not the particles. Nonetheless, it was noted that the overall force signal profile over the entire cutting length is much dependent on the size, volume and bonding strength of the reinforcement particles. Sikder and Kishawy [20] developed an analytical force model when machining Aluminum based MMCs with different sizes and volume fractions of alumina (Al2O3) particles. They showed that debonding energy and hence cutting force increases with particle size due to increase in surface area of the debonding particle. In contrast Sun et al. [21] reported reduction in cutting forces while machining Al/SiCp MMC. However, their study focused on comparatively big particle sizes (15 μm to 60 μm) and large volume fractions (20 % to 50 %). Various optimization techniques have been used by researchers for machining MMCs and other metallic alloys. However evolutionary algorithms and heuristic optimizers are found to be dominant over gradient based methods. Muthukrishnan and Davim [27] did a surface roughness optimization study using analysis of variance(ANOVA) and artificial neural network (ANN). The study showed that feed rate is the dominant factor to control the surface roughness of the machined MMC in comparison to the depth of cut and cutting speed. They suggested the most optimal cutting parameters to minimize surface roughness. Regression model for tool wear was developed by Seeman et al. [28] while machining MMC. Built-up edge (BUE) formation was detected at low cutting speeds resulting in high tool wear. Microscopic examination revealed the presence of both abrasive and adhesive wear at low cutting speeds. Flank wear is found to be more dependent on the cutting speed and feed rate as compared to the depth of cut. Second order response surface models for cutting force, power and specific cutting force for machining Al/SiCp MMC were developed by Gaitonde et al. [29]. The developed models showed that variation of cutting force with respect to feed rate is almost same for any value of cutting speed. In addition, they found that an increase in cutting speed resulted in reduction of the cutting force. This is found to be more pronounced at higher feed rates in comparison to lower values. Antonio et al. Advances in Production Engineering & Management 17(2) 2022 207 Umer, Mohammed, Abidi, Alkhalefah, Kishawy [30] performed optimization using genetic algorithm (GA) considering multiple objectives while machining aluminum based MMC with 20 % volume of SiC reinforced particles. The output variables considered in the study were machining forces, tool wear and surface roughness. All forces are found to increase with the tool wear whilst cutting force showing marked increase. With other parameters kept constant, surface roughness is found to increase with decrease in cutting speed. The optimum cutting parameters reported with cutting speed of 350 m/min, feed rate of 0.1mm/rev and cutting time equals to 19 min. In view of the above it is evident that machinability studies in MMC involving temperature measurement are rare. In addition, the interaction effects of particle size with cutting parameters are not explicitly presented in the open literature. This study aims to perform machinability optimization for cutting temperatures and surface roughness while machining MMCs with different particle sizes. The interaction effects of particle size and cutting parameters on maximum tool-chip interface temperature, surface roughness of the machined surface and cutting force has been described in details and finally optimum parameters are suggested for each particle size’s MMC. 2. Materials and methods Aluminum based MMC bars of SupremEx® grade supplied by Materion, UK were utilized for turning operations. These composite bars were made using powder metallurgy and mechanical alloying process route and 100 % compaction is achieved using hot isostatic pressing. Reinforcement particles were made of silicon carbide (SiC) having an average size of 5 μm, 10 μm and 15 μm with 10 % volume fraction. A Kistler piezoelectric quartz dynamometer (9257B) was employed for measuring the cutting forces Fc during machining of MMCs. Before converting the analog force signals to digital ones, a dual mode charge amplifier (Kistler 5017B) was connected that converts low charge signals to proportional voltage signals. Dynoware® was used to acquire and save the data for further analysis. An Optris 640 thermal imaging camera was selected to capture maximum tool-chip interface temperature T during MMC machining. The camera was mounted on the tool-post as shown in the Fig. 1 and it was set to record maximum temperature during the cutting. The surface quality parameter Ra of the turned surfaces was measured using a Taylor Hobson Surtronics S100 tester at three locations after each experimental run and the average value was noted. For the design of experiment (DOE) study, a central composite design CCD-25 with four factors and 3 levels was selected for the study. The factors and their levels are shown in Table 1. Factors Fig. 1 Experimental setup for MMC turning with thermal imaging camera Particle size, p (µm) Cutting speed, v (m/min) Feed rate, f (mm/rev) Depth of cut, d (mm) 208 Table 1 Factors and their levels for the DOE Levels 0 1 5 10 60 120 0.1 0.15 1.0 1.5 2 15 180 0.2 2.0 Advances in Production Engineering & Management 17(2) 2022 Machinability analysis and multi-response optimization using NGSA-II algorithm for particle reinforced aluminum … Using DOE results response surfaces are generated based on 2nd degree polynomials for all the three input variables. These response surfaces are used by the optimization solver in order to predict output variables for the experimental runs not available in the DOE matrix. For optimization, Non-dominated Sorting Genetic Algorithm II (NSGA-II) has been utilized [31]. NGSA-II is a fast and elitist genetic algorithm for multi-response optimization. Elitism improves converges and avoids local optima and guides towards the real pareto optimal design points. There are no penalty parameters for constraints implementation. In fact, the method utilizes a modified dominance method to cater for constraint handling. Though other methods can also be utilized and compared with NGSA-II, the main goal of the study is to select and apply an efficient and robust optimization technique that can handle multiple objectives and constraint considering the population size. The optimization work and other statistical analysis are carried with the help of a general purpose optimization software modeFrontier® developed by Esteco [32]. The workflow involving all elements for the optimization problem is shown in Fig. 2. The optimization problem is set to minimize maximum tool-chip interface temperature and surface roughness on the machined surface with the consideration of constraints on cutting force and material removal rate. The optimization problem is illustrated in Table 2. Fig. 2 Optimization workflow with all inputs, outputs, objectives and constraints Table 2 Optimization problem’s objectives and constraints Minimize T Objectives Minimize Ra MRR ≥ 200 mm3/s Constraints Fc ≤ 800 N 3. Results and discussions The CCD-25 design matrix with the resulting output variables, i.e. cutting force Fc, maximum tool chip interface temperature T, and surface roughness Ra are shown in Table 3. Advances in Production Engineering & Management 17(2) 2022 209 Umer, Mohammed, Abidi, Alkhalefah, Kishawy Id 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 p (µm) 5 5 5 5 5 5 5 5 5 10 10 10 10 10 10 10 15 15 15 15 15 15 15 15 15 Table 3 The CCD-25 design matrix with output variables v f d Fc (m/min) (mm/rev) (mm) (N) 60 0.1 1 287 60 0.2 1 522 60 0.1 2 841 60 0.2 2 1092 180 0.1 1 262 180 0.2 1 489 180 0.1 2 816 180 0.2 2 1066 120 0.15 1.5 766 60 0.15 1.5 857 180 0.15 1.5 841 120 0.15 1 431 120 0.15 2 1028 120 0.1 1.5 691 120 0.2 1.5 967 120 0.15 1.5 854 60 0.1 1 357 60 0.2 1 621 60 0.1 2 904 60 0.2 2 1214 180 0.1 1 339 180 0.2 1 598 180 0.1 2 887 180 0.2 2 1196 120 0.15 1.5 864 T (°C) 323.5 393.2 435.2 466.5 530.3 538.4 610 698.1 543.3 407.7 638.2 492.9 581.8 529 572.4 569.2 302.5 392.7 428.5 537.2 560.1 608.2 732.4 781.2 543.1 Ra (µm) 2.12 1.62 1.91 1.52 0.76 1.69 0.83 1.69 1.18 2.53 1.53 1.56 2.04 1.03 1.97 2.17 1.57 2.53 2.49 3.07 1.33 2.4 1.9 2.39 2.16 To investigate relationships between input and output variables the spearman’s rank correlation coefficient is evaluated and depicted in Fig. 3. It is quite evident that maximum tool-chip interface temperature is highly dependent on cutting speed followed by depth of cut and feed rate. Particle size’s effect on temperature is comparatively low but cannot be ignored as tool’s crater wear is found to be highly sensitive with respect to maximum tool-chip interface temperature. Surface roughness is found to be severely affected by the size of particle, followed by cutting speed and feed rate. As discussed in the literature review, debonding of particles leave pits and cracks on the machined surface. With large reinforcement particles size of pits increases resulting in poor surface finish. The negative rank for cutting speed indicates reduction in surface roughness with higher cutting speed. This is a common observation in machining as this eliminates BUE resulting in low tool wear and good surface integrity. Finally, the coefficients for cutting force show that it is mainly controlled by depth of cut and feed rate. However the effect of particle size cannot be ignored and the cutting force is found to increase with particle size as observed by Sikder and Kishawy [20]. Cutting force is not much affected by the cutting speed as both strain hardening and thermal softening increases with the cutting speed. Hence both effects neutralize each other. The interaction effects of the input variables on surface roughness of the machined surface are shown in Fig. 4. The highest interaction effect is provided by feed rate and particle size followed by depth of cut and particle size. With the increase in feed rate, the tool marks on the machined surface becomes more pronounced and hence results in poor surface finish. Similarly due to fracture and debonding of large reinforcement particles, the waviness on the machined surface increases. In contrast the interaction effect of cutting speed and particle size has negligible effect due to their inverse effects on Ra when examining individually. 210 Advances in Production Engineering & Management 17(2) 2022 Machinability analysis and multi-response optimization using NGSA-II algorithm for particle reinforced aluminum … Fig. 3 Spearman’s rank correlation matrix Fig. 4 Interaction effects of input variables on surface roughness Fig. 5 highlights interaction effect of particle size and cutting parameters on maximum tool-chip interface temperature. The maximum tool-chip interface temperature is an important performance indicator in machining as it is strongly coupled with tool performance and surface integrity of the workpiece. It can be inferred from the figure that maximum interaction effect is provided by the combination of cutting speed and particle size followed by the combination of cutting speed and depth of cut. As it is well known fact in machining that temperatures are mostly affected by cutting speed due to increase in rate of plastic deformation. Hence temperature rises in the primary shear zone. With large reinforcement particles at higher cutting speed, the kinetic energy of the hard reinforcement particles increases [32].This escalates abrasive wear on the cutting tool resulting in higher frictional stresses at the tool-chip interface and hence, temperature rises at the secondary shear zone. The interaction effects of input variables on cutting force are depicted in Fig. 6. The interaction effect of depth of cut and feed rate is found to be highest followed by the interaction effect of depth of cut and particle size. With the increase in feed rate and depth of cut the chip cross sectional area or the chip load increases on the tool rake face which results in higher cutting and radial forces. In addition, the debonding energy required for the cutting action increases with big sized particles. Similarly, as discussed above tool wear accelerates with increase in particle size. Both phenomena give rise to higher cutting forces. Advances in Production Engineering & Management 17(2) 2022 211 Umer, Mohammed, Abidi, Alkhalefah, Kishawy Fig. 5 Interaction effects of input variables on maximum tool-chip interface temperature Fig. 6 Interaction effects of input variables on cutting force The relationships between all the input and output variables can be visualized by principal component analysis as shown in Fig. 7. In this method multidimensional data is reduced to 2 or 3 dimensions of maximum variability called principal components. Here the data is plotted against to principal components PC1 and PC2 as depicted in Fig. 7. PC1 corresponds to 37 % variation in the data whereas PC2 corresponds to 28.6 % variation in data. The arrows show the dependency of the input or output variables on the variability of the principal components. Those are collinear with PC1 show 100 % dependency and orthogonal ones show null dependency. In this way the relationship between variables could be analyzed by observing their directions or their components in principal directions. It can be seen that Fc and d have large components along PC1. Similarly, Ra, v and T are strongly dependent on PC2. As d is found to be closer to Fc as compared to f and p, this suggests a strong correlation between Fc and d. In this way, Ra is found to be more dependent on p as compared to f and d. Also, T shows a strong dependency on v in comparison to d and f. 212 Advances in Production Engineering & Management 17(2) 2022 Machinability analysis and multi-response optimization using NGSA-II algorithm for particle reinforced aluminum … Fig. 7 Principal component analysis (PCA) for all input and output variables The combined effect of feed rate and reinforcement particle size on surface roughness is shown in Fig. 8. The effect of reinforcement particle size on surface roughness at low feed rate is almost negligible and it increases gradually with feed rate. Similarly with small reinforcement the effect of feed rate on surface roughness is quite low. However, it is increasing with particle size and marked increase in surface roughness can be observed with particle size of 15 μm. Thus, maximum surface roughness is found to be with large reinforcement particles and higher feed rates. Feed marks parallel to the direction of the cutting velocity are more pronounced with increasing feed rate. Also, it has been observed that the reinforcement particles are partially or totally fractured or debonded from the machined surface during cutting. This aggravates further with large reinforcement particles, thus results in poor surface finish. Fig. 8 Effects of feed rate and particle size on surface roughness Advances in Production Engineering & Management 17(2) 2022 213 Umer, Mohammed, Abidi, Alkhalefah, Kishawy Fig. 9 shows the combined effect of depth of cut and reinforcement particle size on cutting force during MMC machining. The effect of reinforcement particle size on cutting force is marginally very low as compared to the depth of cut, though both factors contribute positively as shown in figure. Maximum cutting force is obtained at the top right corner, i.e. with large depth of cut and big reinforcement particles. As cutting force is proportional to the depth of cut due to increase in chip load, the debonding energy increases with particle size that leads to further escalation in cutting force as depicted in Fig. 9. The combined effect of feed rate and reinforcement particle size on maximum tool-chip interface temperature is shown in Fig. 10. It is depicted that maximum tool-chip interface temperature increases with both feed rate and reinforcement particle size. Increase in particle size at low feed rate results in approximately 5.6 % rise in temperature. Whereas a jump of 8.8 % is observed at higher feed rate as shown in figure. The plastic energy consumed at the primary shear zone is proportional to the uncut chip thickness, i.e. feed rate. Thus, higher feed rates result in high heat dissipation which escalates temperature at the tool-chip interface. Similarly large reinforcement particles give rise to rapid tool wear which increases friction and heat generation at the secondary shear zone, thus resulting in higher tool-chip interface temperature. Large reinforcement particles are also responsible for high abrasive wear on the tool flank face. This is due to increase in kinetic energy for the large particles which increases their rolling and sliding actions on the tool’s surface. Effects of particle size on tool’s flank wear can be analyzed in Fig. 11 (Scanning electrons photomicrographs) showing high abrasive wear on tool’s flank face with 15 μm MMC. Welded aluminum can be seen on the tool’s edges as it is a common problem when machining at dry conditions with higher speeds and low feed rates. Fig. 9 Effects of depth of cut and particle size on cutting force 214 Advances in Production Engineering & Management 17(2) 2022 Machinability analysis and multi-response optimization using NGSA-II algorithm for particle reinforced aluminum … Fig. 10 Effects feed rate and particle size on maximum tool-chip interface temperature (a) (b) (c) Fig. 11 Tool wear when machining MMC: (a) 5 μm, (b) 10 μm, (c) 15 μm v = 180 m/min, f = 0.10 mm/rev, d = 1.0 mm, cutting time = 10 min All the experimental runs obtained after optimization are shown in a 3D bubble chart as illustrated in Fig. 12. They are plotted against the two objectives, i.e. surface roughness Ra and maximum tool chip interface temperature T. The size of the bubble indicates reinforcement particle size. The design points with yellow colors are considered as unfeasible, i.e. violating at least one constraint in the optimization problem. The solid ones are said to be real as they are from the DOE matrix, whereas hollow bubbles represent virtual design point obtained via response surfaces. As the objective is to minimize both surface roughness and maximum tool-chip interface temperature, the optimal design points should be at the lower left corner of the diagram. A pareto-front can be drawn for each particle size to find out the optimal design points. Using the pareto front for 5 μm particle size three design points A5, B5 and C5 can be marked as candidates for optimal solution. Similarly, A10 and B10 can be marked as optimal for 10 μm particle size MMC. For 15 μm MMC, only one feasible design point is found in the optimal area and marked as A15 as shown in figure. The feasible design points marked with letter B are characterized by low feed rate, low depth of cut and moderate cutting speed. Similarly design point A5 have higher cutting speed and relatively higher MMR as compared to design points B5. The details of all the possible optimal solutions are shown in Table 4. The relationship between four variables at a time can be visualized by a 4D bubble chart as shown in Fig. 13. Similar to the 3D bubble chart as explained above, the design points are plotted against the two objectives Ra and T. Cutting speed v is represented by color of the bubble whereas feed rate f is represented by the size of the bubble. It can be seen that higher temperatures are mostly contributed by high cutting speed and high interactions effects of the remaining input variables, i.e. f · d, f · p and d · p. Similarly poor surface finish is found to be associated with low cutting speed, moderate and high feed rate or depth of cut and large reinforcement particles. Advances in Production Engineering & Management 17(2) 2022 215 Umer, Mohammed, Abidi, Alkhalefah, Kishawy Fig. 12 3D bubble charts showing design points against the two objectives Id A5 B5 C5 A10 B10 A15 216 p (μm) 5 5 5 10 10 15 Table 4 Details of optimal solutions v f d (m/min) (mm/rev) (mm) 180 0.1 1.0 120 0.1 1.0 60 0.2 1.0 120 0.1 1.5 120 0.1 1.0 120 0.1 1.0 Fc (N) 262 262 522 691 316 329 T (°C) 530.3 453.5 393.2 529.0 457.1 455.8 Ra (μm) 0.76 1.02 1.62 1.03 1.17 1.19 Fig. 13 4D bubble charts showing design points with four variables at a time Advances in Production Engineering & Management 17(2) 2022 Machinability analysis and multi-response optimization using NGSA-II algorithm for particle reinforced aluminum … 4. Conclusions Machinability analysis and multi-objective optimization for particle reinforced aluminium based MMC have been performed during machining with PCD inserts. Effects of particle size on cutting force, surface roughness and maximum tool-chip interface temperature have been investigated with some qualitative analysis for the flank wear on PCD inserts. Following conclusions can be drawn: • It has been noticed that particle size main and interaction effects contribute significantly towards the machinability of particle reinforced aluminium based MMCs. • Surface roughness of the machined MMCs is found to be highly affected by the size of the reinforcement particles. Large reinforcement particles lead to poorer surface finish. • As feed rates increase surface roughness more aggressively than other cutting parameters, the highest interaction effect is provided by the combination of particle size and feed rate. • Large reinforcement particles are also found responsible for higher cutting temperatures. The interaction effect of cutting speed and particle size is found to be significant in controlling the maximum tool-chip interface temperature. • Cutting force is found to be mainly influenced by depth of cut and feed rate. Particle size effect is found to be low for the volume fraction selected in the study. However, its effect cannot be ignored when other parameters are kept constant. • The interaction effect of depth of cut and particle size is found significant for the cutting force. The debonding energy of the reinforced particles increases with size during machining. Hence results in escalation of the cutting force. • Most of the optimal solutions are found to be with moderate cutting speed, low depth of cut and low feed rates. Acknowledgement This project was funded by the National Plan for Science, Technology, and Innovation (MAARIFAH), King Abdulaziz City for Science and Technology, Kingdom of Saudi Arabia, Award No. 13-ADV-971-02. 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On the role of reinforcements on tool performance during cutting of metal matrix composites, Journal of Manufacturing Processes, Vol. 8, No. 2, 67-75, doi: 10.1016/S1526-6125(07)00006-0. 218 Advances in Production Engineering & Management 17(2) 2022 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 2 | June 2022 | pp 219–230 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.2.432 Original scientific paper Supply chain coordination contract design: The case of farmer with capital constraints and behavioral preferences Wang, Y.L.a,b, Yin, X.M.b, Zheng, X.Y.b, Cai, J.R.a,b,*, Fang, X.c aResearch Center for Enterprise Management, Chongqing Technology and Business University, Chongqing, P.R. China of Business Administration, Chongqing Technology and Business University, Chongqing, P.R. China cSchool of Management Science and Engineering, Chongqing Technology and Business University, Chongqing, P.R. China bSchool ABSTRACT ARTICLE INFO Coordination mechanism design is an important issue in agricultural supply chain. This study investigates agricultural supply chain coordination contracts in the presence of output uncertainty. It considers a two-level supply chain comprising a farmer and a retailer, where the farmer faces capital constraints and shows stockout-averse (SA), waste-averse (WA), or stockout- and wasteaverse (SW) preferences. The results show that the retailer order, production input, and supply chain expected utility in the decentralized decision framework are lower than those realized under the centralized decision model; hence, the wholesale price contract cannot coordinate the supply chain. Nevertheless, the designed coordination contract mechanism coordinates the supply chain efficiently and realizes a flexible distribution of benefits between the farmer and the retailer. Furthermore, when the revenue-sharing coefficient meets specific conditions, both the farmer and the retailer achieve a win-win situation. Finally, we verify the coordination contract design using numerical simulations and analyze the effects of SA and WA preferences on decision-making and the supply chain expected utility. This study provides theoretical guidance for the coordination mechanism design of agricultural supply chain with capital constraints and behavioral preferences. Keywords: Supply chain; Supply chain coordination; Contract design; Capital constraints; Waste-averse preferences; Stockout-averse preferences; Behavioral preferences *Corresponding author: caijr@ctbu.edu.cn (Cai, J.R.) Article history: Received 9 February 2022 Revised 8 August 2022 Accepted 13 August 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction Agricultural production is influenced by uncertain environmental factors (such as the weather, war crisis, human factors, etc.). Hence, farmers are cautious regarding the amount of production input needed. Before the production season, retailers pre-order agricultural products from farmers based on the predicted market demand. Then, farmers organize the agricultural production according to the retailer's orders. However, uncertainty in the output may lead to a mismatch between agricultural output and retailer orders. Overproduction or underproduction generates losses to farmers; hence, they may become waste-averse (WA) or stockout-averse (SA) [1]. In addition, some farmers have limited funds; due to the long production cycle of agricultural products, they may face capital constraints. Therefore, designing an effective supply chain coordination contract mechanism is crucial for managing farmers' financial constraints and behavioral preferences. 219 Wang, Yin, Zheng, Cai, Fang When faced with capital constraints, farmers may seek financing from formal financial institutions or other legal channels [2], such as trade credit and bank credit [3-6], advance payment discounts (advance payment) [7-9], and purchase order financing [9]. Therefore, research has begun focusing on financing services and financing strategies [10-13]. However, a financing strategy may benefit the individual but may not the entire supply chain. Hence, a coordination contract mechanism is needed for achieving coordination in the supply chain and a "win-win" situation for all participants. The literatures indicate that the wholesale price contract [14], option contract [15], revenue-sharing contract and buyback contract [16-19], output penalty contract and cost-sharing contract [19], general contract based on risk compensation [20], and twoway revenue-sharing contract [21] may coordinate the supply chain efficiently. However, when addressing supply chain coordination problems in the presence of financial constraints, the above literatures assume that the output is determined, and participants are risk neutral. Therefore, this study’s original contribution lies in the following three aspects: • The output is assumed to be randomly determined owing to the uncertainty in the agricultural production. • Agricultural products may be in excess or insufficient; hence, we consider that the farmer may have behavioral preferences: stockout- and waste-averse (SW), WA, or SA preferences. • We design a supply chain coordination contract mechanism and analyze the influence of behavioral preferences on participants’ decision-making and the expected utility of the supply chain. The remainder of this paper is organized as follows. Section 2 describes the problems, assumptions, and notations. Section 3 presents the model. Section 4 introduces the design of the coordinated contract mechanism. Section 5 provides a numerical simulation analysis, and Section 6 provides our concluding remarks. 2. Model’s setup, assumptions, and notations 2.1 Problem description We address the case of a two-level supply chain comprising a financially constrained farmer and a retailer. According to the predicted market demand, the retailer books agricultural products 𝑄𝑄 to the farmer in advance. The farmer determines its production input 𝑞𝑞 according to the retailer's order. Since the output of agricultural products is randomly determined, the farmer's output is 𝑢𝑢𝑢𝑢, where 𝑢𝑢 is the random output factor, with 𝑢𝑢 ∈ (0, 𝐵𝐵) [22]. In the sales season, the farmer sells agricultural products to the retailer at the unit wholesale price 𝑤𝑤 agreed in the contract. The retailer resells them to consumers at unit price 𝑝𝑝, satisfying consumer demand. This mechanism is shown in Fig. 1. uq Min{uq,Q} Min{uq,Q} q w Farmer Retailer Market p Q 2.2 Model assumptions Fig. 1 Schematic diagram of the study structure Assumption 1: The market price of agricultural products 𝑝𝑝 is inversely proportional to the number of agricultural products min {𝑄𝑄, 𝑢𝑢𝑢𝑢}, namely, 𝑝𝑝 = 𝐴𝐴 − min {𝑄𝑄, 𝑢𝑢𝑢𝑢} [23]. 𝐴𝐴 is the highest price that consumers are willing to pay, and min {𝑄𝑄, 𝑢𝑢𝑢𝑢} is the transaction volume of the farmer and retailer, namely: 𝑄𝑄, 𝑄𝑄 ≤ 𝑢𝑢𝑢𝑢 𝑚𝑚𝑚𝑚𝑚𝑚{𝑄𝑄, 𝑢𝑢𝑢𝑢} = � 𝑢𝑢𝑢𝑢, 𝑄𝑄 > 𝑢𝑢𝑢𝑢 220 Advances in Production Engineering & Management 17(2) 2022 Supply chain coordination contract design: The case of farmer with capital constraints and behavioral preferences Assumption 2: The farmer has SA preferences when the production cannot meet the retailer's order, as 𝑄𝑄 > 𝑢𝑢𝑢𝑢. In the case of insufficient production, an additional penalty 𝜆𝜆(𝑄𝑄 − 𝑢𝑢𝑢𝑢)+ is generated; 𝜆𝜆 is the shortage aversion coefficient. On the other hand, the farmer has 𝑊𝑊𝑊𝑊 preferences when the output is in excess, namely, 𝑄𝑄 < 𝑢𝑢𝑢𝑢. In this case, an additional penalty 𝛽𝛽(𝑢𝑢𝑢𝑢 − 𝑄𝑄)+ is imposed on the excess production; 𝛽𝛽 is the 𝑊𝑊𝑊𝑊 coefficient. Similar assumptions are made in the literature [1]. Assumption 3: Since farmers may have different behavioral preferences, we consider situations where the farmer has 𝑊𝑊𝑊𝑊, 𝑆𝑆𝑆𝑆 and 𝑆𝑆𝑆𝑆 preferences. Assumption 4: We consider a scenario in which a farmer faces capital constraints, namely, 𝑐𝑐𝑐𝑐 > 𝑇𝑇. To supplement the insufficient funds (𝑐𝑐𝑐𝑐 − 𝑇𝑇)+ , the farmer obtains financing from a third party. The financing rate is 𝑟𝑟, and the financing cost is 𝑟𝑟(𝑐𝑐𝑐𝑐 − 𝑇𝑇)+ ; 𝑐𝑐 is the unit production cost of agricultural products, and 𝑇𝑇 indicates the funds held by the farmer. Assumption 5: 𝑝𝑝 > 𝑤𝑤 > 𝑐𝑐. Assumption 6: The farmer and the retailer have symmetrical information. 2.3 Notations All the symbols used in this article are summarized in Table 1. Symbols 𝑐𝑐 𝑤𝑤 𝑝𝑝 𝑞𝑞 𝑄𝑄 𝑢𝑢 𝐹𝐹(𝑢𝑢) 𝑓𝑓(𝑢𝑢) 𝑇𝑇 𝑗𝑗 Π𝑅𝑅 𝑗𝑗 Π𝑖𝑖 Table 1 The listing of notations Descriptions Symbols Unit production cost 𝜆𝜆 Wholesale price 𝛽𝛽 Retail price 𝐶𝐶 (top right corner) Production input 𝐵𝐵 (top right corner) Order quantity 𝐻𝐻 (top right corner) Random output factor 𝑆𝑆𝑆𝑆 Cumulative distribution function of 𝑢𝑢 𝑊𝑊𝑊𝑊 Probability density function of 𝑢𝑢 𝑆𝑆𝑆𝑆 Funds held by the farmer 𝑟𝑟 Retailer’s expected profit * 𝑗𝑗 Supply chain expected utility U𝐹𝐹 𝑖𝑖 ∈ {𝑆𝑆𝑆𝑆, 𝑆𝑆𝑆𝑆, 𝑊𝑊𝑊𝑊}, 𝑗𝑗 ∈ {𝐶𝐶, 𝐵𝐵, 𝐻𝐻} Descriptions Stockout-aversion coefficient Waste-aversion coefficient Centralized decision model Decentralized decision model Coordination contract mechanism Stockout-aversion Waste-aversion Stockout- and waste-averse Financing rate Optimal value The farmer's expected utility 3. Alternative models 3.1 Centralized decision model In the centralized decision-making framework, the farmer and retailer belong to the same collective, and both aim to maximize the expected utility of the entire supply chain. When the farmer has SW preferences, the utility of the supply chain is: 𝐶𝐶 𝜋𝜋𝑆𝑆𝑆𝑆 = (𝐴𝐴 − min{𝑄𝑄, 𝑢𝑢𝑢𝑢}) min{𝑄𝑄, 𝑢𝑢𝑢𝑢} − 𝜆𝜆(𝑄𝑄 − 𝑢𝑢𝑢𝑢)+ − 𝛽𝛽(𝑢𝑢𝑢𝑢 − 𝑄𝑄)+ − 𝑐𝑐𝑐𝑐 − 𝑟𝑟(𝑐𝑐𝑐𝑐 − 𝑇𝑇)+ (1) In Eq. 1, (𝐴𝐴 − min{𝑄𝑄, 𝑢𝑢𝑢𝑢}) min{𝑄𝑄, 𝑢𝑢𝑢𝑢}represents sales revenue, and 𝜆𝜆(𝑄𝑄 − 𝑢𝑢𝑢𝑢)+ and 𝛽𝛽(𝑢𝑢𝑢𝑢 − 𝑄𝑄)+ are punishments for production shortage and overproduction, respectively; 𝑐𝑐𝑐𝑐 is the production cost, and 𝑟𝑟(𝑐𝑐𝑐𝑐 − 𝑇𝑇)+ is the financing interest cost. According to Eq. 1, the expected utility of the supply chain is: 𝐶𝐶 Π𝑆𝑆𝑆𝑆 𝑄𝑄 𝑞𝑞 𝑄𝑄 𝑞𝑞 = (𝐴𝐴 + 𝜆𝜆 + 𝛽𝛽) �𝑄𝑄 − 𝑞𝑞 � 𝐹𝐹(𝑢𝑢)𝑑𝑑𝑑𝑑� + 2𝑞𝑞 � 𝐹𝐹(𝑢𝑢)𝑑𝑑𝑑𝑑 − 𝑄𝑄 2 − 𝜆𝜆𝜆𝜆 − [𝛽𝛽𝛽𝛽 + (1 + 𝑟𝑟)𝑐𝑐]𝑞𝑞 + 𝑟𝑟𝑟𝑟 0 2 0 𝐶𝐶 The first partial derivatives of Π𝑆𝑆𝑆𝑆 with respect to 𝑄𝑄 and 𝑞𝑞 are, respectively: 𝜕𝜕Π𝐶𝐶 𝑆𝑆𝑆𝑆 𝜕𝜕𝜕𝜕 𝑄𝑄 𝑄𝑄 = (𝐴𝐴 + 𝜆𝜆 + 𝛽𝛽) �1 − 𝐹𝐹 � 𝑞𝑞 �� − 2 �𝑄𝑄 − 𝑞𝑞 � 𝑞𝑞 �� − 𝜆𝜆=0 Advances in Production Engineering & Management 17(2) 2022 (2) (3) 221 Wang, Yin, Zheng, Cai, Fang 𝑄𝑄 𝐶𝐶 (𝐴𝐴 + 𝜆𝜆 + 𝛽𝛽 − 2𝑞𝑞)𝑄𝑄 𝑄𝑄 𝜕𝜕Π𝑆𝑆𝑆𝑆 𝑞𝑞 = (4𝑞𝑞 − 𝐴𝐴 − 𝜆𝜆 − 𝛽𝛽) � 𝐹𝐹(𝑢𝑢)𝑑𝑑𝑑𝑑 + 𝐹𝐹 � � − 𝛽𝛽𝛽𝛽 − (1 + 𝑟𝑟)𝑐𝑐 = 0 𝜕𝜕𝜕𝜕 𝑞𝑞 𝑞𝑞 0 (4) 𝐶𝐶∗ By solving Eqs. 3 and 4 simultaneously, we obtain the optimal order quantity 𝑄𝑄𝑆𝑆𝑆𝑆 and pro𝐶𝐶∗ duction input quantity 𝑞𝑞𝑆𝑆𝑆𝑆 in the centralized decision framework: ⎧ ⎪ ⎪ (𝐴𝐴 + 𝜆𝜆 + 𝛽𝛽) �1 − 𝐹𝐹 � 𝐶𝐶∗ 𝑄𝑄𝑆𝑆𝑆𝑆 𝐶𝐶∗ 𝐶𝐶∗ 𝑄𝑄𝑆𝑆𝑆𝑆 𝑄𝑄𝑆𝑆𝑆𝑆 𝐶𝐶∗ 𝐶𝐶∗ �� − 2 �𝑄𝑄 − 𝑞𝑞 𝐹𝐹 � 𝑆𝑆𝑆𝑆 𝑆𝑆𝑆𝑆 𝐶𝐶∗ 𝐶𝐶∗ �� − 𝜆𝜆 = 0 𝑞𝑞𝑆𝑆𝑆𝑆 𝑞𝑞𝑆𝑆𝑆𝑆 𝐶𝐶∗ )𝑄𝑄 𝐶𝐶∗ 𝐶𝐶∗ 𝐶𝐶∗ (𝐴𝐴 + 𝜆𝜆 + 𝛽𝛽 − 2𝑞𝑞𝑆𝑆𝑆𝑆 𝑄𝑄𝑆𝑆𝑆𝑆 𝑆𝑆𝑆𝑆 ⎨(4𝑞𝑞𝐶𝐶∗ − 𝐴𝐴 − 𝜆𝜆 − 𝛽𝛽) �𝑞𝑞𝑆𝑆𝑆𝑆 𝐹𝐹(𝑢𝑢)𝑑𝑑𝑑𝑑 + 𝐹𝐹 � 𝐶𝐶∗ � − 𝛽𝛽𝛽𝛽 − (1 + 𝑟𝑟)𝑐𝑐 = 0 𝑆𝑆𝑆𝑆 𝐶𝐶∗ ⎪ 𝑞𝑞𝑆𝑆𝑆𝑆 𝑞𝑞𝑆𝑆𝑆𝑆 ⎪ 0 ⎩ We then obtain the optimal expected utility of the supply chain, as follows: 𝐶𝐶∗ 𝑄𝑄𝑆𝑆𝑆𝑆 𝐶𝐶∗ 𝑞𝑞𝑆𝑆𝑆𝑆 𝐶𝐶∗ 𝐶𝐶∗ 𝐶𝐶∗ Π𝑆𝑆𝑆𝑆 = (𝐴𝐴 + 𝜆𝜆 + 𝛽𝛽) �𝑄𝑄𝑆𝑆𝑆𝑆 − 𝑞𝑞𝑆𝑆𝑆𝑆 � 0 2 𝐶𝐶∗ 𝑄𝑄𝑆𝑆𝑆𝑆 𝐶𝐶∗ 𝑞𝑞𝑆𝑆𝑆𝑆 𝐶𝐶∗ 𝐹𝐹(𝑢𝑢)𝑑𝑑𝑑𝑑� + 2𝑞𝑞𝑆𝑆𝑆𝑆 � 𝐶𝐶∗ − [𝛽𝛽𝛽𝛽 + (1 + 𝑟𝑟)𝑐𝑐]𝑞𝑞𝑆𝑆𝑆𝑆 + 𝑟𝑟𝑟𝑟 0 2 𝐶𝐶∗ 𝐶𝐶∗ 𝐹𝐹(𝑢𝑢)𝑑𝑑𝑑𝑑 − 𝑄𝑄𝑆𝑆𝑆𝑆 − 𝜆𝜆𝑄𝑄𝑆𝑆𝑆𝑆 (5) (6) If the farmer only has SA preferences, 𝜆𝜆 > 0, and 𝛽𝛽 = 0; however, if the farmer only has 𝑊𝑊𝑊𝑊 preferences, 𝜆𝜆 = 0 and 𝛽𝛽 > 0. The optimal decision and the supply chain expected utility in the centralized decision framework may be obtained in the same way; this analysis step is, therefore, omitted. 3.2 Decentralized decision model In the decentralized decision framework, the farmer determines the amount of production input 𝑞𝑞 to maximize their expected utility, and the retailer determines the order quantity 𝑄𝑄 to maximize their expected profit. We assume that the farmer and retailer have the same decisional power; hence, they play a Cournot game. When the farmer has S𝑊𝑊preferences, the expected utility of the farmer and the expected profit of the retailer are as follows: 𝑈𝑈𝐹𝐹𝐵𝐵 = 𝐸𝐸[𝑤𝑤 min{𝑄𝑄, 𝑢𝑢𝑢𝑢} − 𝜆𝜆(𝑄𝑄 − 𝑢𝑢𝑢𝑢)+ − 𝛽𝛽(𝑢𝑢𝑢𝑢 − 𝑄𝑄)+ − 𝑐𝑐𝑐𝑐 − 𝑟𝑟(𝑐𝑐𝑐𝑐 − 𝑇𝑇)]=( 𝑤𝑤 + 𝛽𝛽)𝑄𝑄 − 𝑄𝑄 𝑞𝑞 𝛽𝛽𝛽𝛽𝛽𝛽 − 𝑞𝑞(𝑤𝑤 + 𝜆𝜆 + 𝛽𝛽) ∫0 𝐹𝐹(𝑢𝑢)𝑑𝑑𝑑𝑑 − 𝑐𝑐𝑐𝑐 − 𝑟𝑟(𝑐𝑐𝑐𝑐 − 𝑇𝑇) Π𝑅𝑅𝐵𝐵 = 𝐸𝐸[(𝐴𝐴 − min{𝑄𝑄, 𝑢𝑢𝑢𝑢}) min{𝑄𝑄, 𝑢𝑢𝑢𝑢} − 𝑤𝑤 min{𝑄𝑄, 𝑢𝑢𝑢𝑢}]=( 𝐴𝐴 − 𝑤𝑤 )𝑄𝑄 − 𝑄𝑄 2 − (𝐴𝐴 − 𝑄𝑄 𝑞𝑞 2 𝑄𝑄 𝑞𝑞 𝑤𝑤)𝑞𝑞 ∫0 𝐹𝐹(𝑢𝑢)𝑑𝑑𝑑𝑑 + 2𝑞𝑞 ∫0 𝐹𝐹(𝑢𝑢)𝑑𝑑𝑑𝑑 The first and second partial derivatives of 𝑈𝑈𝐹𝐹𝐵𝐵 with respect to 𝑞𝑞 are: 𝑄𝑄 𝜕𝜕𝑈𝑈𝐹𝐹𝐵𝐵 𝑄𝑄 𝑄𝑄 𝑞𝑞 = (𝑤𝑤 + 𝜆𝜆 + 𝛽𝛽) � 𝐹𝐹 � � − � 𝐹𝐹(𝑢𝑢)𝑑𝑑𝑑𝑑� − 𝛽𝛽𝛽𝛽 − (1 + 𝑟𝑟)𝑐𝑐 𝜕𝜕𝜕𝜕 𝑞𝑞 𝑞𝑞 0 𝜕𝜕 2 𝑈𝑈𝐹𝐹𝐵𝐵 𝑄𝑄 2 𝑄𝑄 (𝑤𝑤 = − + 𝜆𝜆 + 𝛽𝛽)𝑓𝑓 � �<0 𝜕𝜕𝑞𝑞 2 𝑞𝑞 3 𝑞𝑞 The first and second partial derivatives of Π𝑅𝑅𝐵𝐵 with respect to 𝑄𝑄 are: 𝜕𝜕Π𝑅𝑅𝐵𝐵 𝑄𝑄 𝑄𝑄 = (𝐴𝐴 − 𝑤𝑤) �1 − 𝐹𝐹 � �� − 2 �𝑄𝑄 − 𝑞𝑞𝑞𝑞 � �� 𝜕𝜕𝜕𝜕 𝑞𝑞 𝑞𝑞 (𝐴𝐴 − 𝑤𝑤) 𝑄𝑄 𝜕𝜕 2 Π𝑅𝑅𝐵𝐵 𝑄𝑄 =− 𝑓𝑓 � � − 2 �1 − 𝑓𝑓 � �� < 0 2 𝜕𝜕𝑄𝑄 𝑞𝑞 𝑞𝑞 𝑞𝑞 222 (7) (8) (9) (10) (11) (12) Advances in Production Engineering & Management 17(2) 2022 Supply chain coordination contract design: The case of farmer with capital constraints and behavioral preferences Since 𝜕𝜕2 𝑈𝑈𝐹𝐹𝐵𝐵 𝜕𝜕𝑞𝑞2 < 0, and 𝜕𝜕2 Π𝐵𝐵 𝑅𝑅 𝜕𝜕𝑄𝑄 2 𝜕𝜕𝑈𝑈 𝐵𝐵 𝜕𝜕Π𝐵𝐵 < 0, when 𝜕𝜕𝜕𝜕𝐹𝐹 = 0, and 𝜕𝜕𝜕𝜕𝑅𝑅 = 0, in the decentralized decision frame- 𝐵𝐵∗ 𝐵𝐵∗ work, the optimal order quantity 𝑄𝑄𝑆𝑆𝑆𝑆 and production input quantity 𝑞𝑞𝑆𝑆𝑆𝑆 may be obtained as follows: 𝐵𝐵∗ 𝐵𝐵∗ 𝑄𝑄𝑆𝑆𝑆𝑆 𝑄𝑄𝑆𝑆𝑆𝑆 𝐵𝐵∗ 𝐵𝐵∗ ⎧ (𝐴𝐴 − 𝑤𝑤) �1 − 𝐹𝐹 � 𝐵𝐵∗ �� − 2 �𝑄𝑄𝑆𝑆𝑆𝑆 − 𝑞𝑞𝑆𝑆𝑆𝑆 𝐹𝐹 � 𝐵𝐵∗ �� = 0 𝑞𝑞𝑆𝑆𝑆𝑆 𝑞𝑞𝑆𝑆𝑆𝑆 ⎪ 𝐵𝐵∗ 𝑄𝑄𝑆𝑆𝑆𝑆 (13) 𝐵𝐵∗ 𝐵𝐵∗ 𝐵𝐵∗ 𝑄𝑄𝑆𝑆𝑆𝑆 𝑄𝑄𝑆𝑆𝑆𝑆 ⎨ 𝑞𝑞𝑆𝑆𝑆𝑆 𝐹𝐹(𝑢𝑢)𝑑𝑑𝑑𝑑� − 𝛽𝛽𝛽𝛽 − (1 + 𝑟𝑟)𝑐𝑐 = 0 ⎪(𝑤𝑤 + 𝜆𝜆 + 𝛽𝛽) � 𝑞𝑞 𝐵𝐵∗ 𝐹𝐹 � 𝑞𝑞 𝐵𝐵∗ � − � 0 𝑆𝑆𝑆𝑆 𝑆𝑆𝑊𝑊 ⎩ Under decentralized decisions, the optimal expected utility of the farmer, the optimal expected profit of the retailer, and the optimal expected utility of the supply chain are, respectively: 𝑄𝑄𝐵𝐵∗ 𝑆𝑆𝑆𝑆 𝑞𝑞𝐵𝐵∗ 𝑆𝑆𝑆𝑆 𝐵𝐵∗ 𝐵𝐵∗ 𝐵𝐵∗ (𝑤𝑤 𝑈𝑈𝐹𝐹𝐵𝐵∗ =( 𝑤𝑤 + 𝛽𝛽)𝑄𝑄𝑆𝑆𝑆𝑆 − 𝛽𝛽𝛽𝛽𝑞𝑞𝑆𝑆𝑆𝑆 − 𝑞𝑞𝑆𝑆𝑆𝑆 + 𝜆𝜆 + 𝛽𝛽) ∫0 𝐵𝐵∗ Π𝑅𝑅𝐵𝐵∗ =( 𝐴𝐴 − 𝑤𝑤 )𝑄𝑄𝑆𝑆𝑆𝑆 − 𝐵𝐵∗ 2 𝑄𝑄𝑆𝑆𝑆𝑆 𝑄𝑄𝐵𝐵∗ 𝑆𝑆𝑆𝑆 𝑞𝑞𝐵𝐵∗ 𝑆𝑆𝑆𝑆 𝐵𝐵∗ − (𝐴𝐴 − 𝑤𝑤)𝑞𝑞𝑆𝑆𝑆𝑆 ∫0 𝐵𝐵∗ 𝑄𝑄𝑆𝑆𝑆𝑆 𝐵𝐵∗ 𝑞𝑞𝑆𝑆𝑆𝑆 𝐵𝐵∗ 𝐵𝐵∗ 𝐵𝐵∗ Π𝑆𝑆𝑆𝑆 = (𝐴𝐴 + 𝜆𝜆 + 𝛽𝛽) �𝑄𝑄𝑆𝑆𝑆𝑆 − 𝑞𝑞𝑆𝑆𝑆𝑆 � 0 𝐵𝐵∗ 𝐹𝐹(𝑢𝑢)𝑑𝑑𝑑𝑑 − 𝑐𝑐(1 + 𝑟𝑟)𝑞𝑞𝑆𝑆𝑆𝑆 + 𝑟𝑟T 𝐹𝐹(𝑢𝑢)𝑑𝑑𝑑𝑑 + 2 𝐵𝐵∗ 𝑄𝑄𝑆𝑆𝑆𝑆 𝐵𝐵∗ 𝑞𝑞𝑆𝑆𝑆𝑆 𝐵𝐵∗ 𝐹𝐹(𝑢𝑢)𝑑𝑑𝑑𝑑� + 2𝑞𝑞𝑆𝑆𝑆𝑆 � 𝐵𝐵∗ − [𝛽𝛽𝛽𝛽 + (1 + 𝑟𝑟)𝑐𝑐]𝑞𝑞𝑆𝑆𝑆𝑆 + 𝑟𝑟𝑟𝑟 0 𝑄𝑄𝐵𝐵∗ 𝑆𝑆𝑆𝑆 𝐵𝐵∗ 𝐵𝐵∗ 2 𝑞𝑞𝑆𝑆𝑆𝑆 2𝑞𝑞𝑆𝑆𝑆𝑆 ∫0 𝐹𝐹(𝑢𝑢)𝑑𝑑𝑑𝑑 2 𝐵𝐵∗ 𝐵𝐵∗ 𝐹𝐹(𝑢𝑢)𝑑𝑑𝑑𝑑 − 𝑄𝑄𝑆𝑆𝑆𝑆 − 𝜆𝜆𝑄𝑄𝑆𝑆𝑆𝑆 (14) (15) (16) If the farmer only has SA preferences, 𝜆𝜆 > 0, and 𝛽𝛽 = 0; however, if the farmer has WA preferences, 𝜆𝜆 = 0, and 𝛽𝛽 > 0. The optimal decision behavior and supply chain expected utility under decentralized decision may be obtained using the above procedure; hence, this analysis step is omitted. The above model analysis suggests the following proposition: Proposition 1: Supply chain coordination under decentralized decisions cannot be realized. 𝐶𝐶∗ 𝐵𝐵∗ Proof: Under decentralized decisions, if the supply chain realizes coordination, 𝑄𝑄𝑆𝑆𝑆𝑆 = 𝑄𝑄𝑆𝑆𝑆𝑆 , and 𝐶𝐶∗ 𝐵𝐵∗ 𝑞𝑞𝑆𝑆𝑆𝑆 = 𝑞𝑞𝑆𝑆𝑆𝑆 . A comparison between Eqs. 5 and 13 indicates that supply chain coordination may only be realized when both 𝑤𝑤 = −𝛽𝛽 and 𝑤𝑤 = −(𝜆𝜆 + 𝛽𝛽) are satisfied, which contradicts 𝑤𝑤 > 0; thus, supply chain coordination cannot be realized in this context. 4. Coordination contract mechanism design In the decentralized decision-making framework, both the farmer and the retailer aim to maximize their interests, ignoring the best interests of the entire supply chain. Therefore, to maximize the expected utility of the supply chain, an effective coordination contract mechanism is needed, so that both the farmer and the retailer are willing to participate in the mechanism. Inspired by the literature [16, 19, 24], we design a coordination contract mechanism in which the retailer gives Φ(0 ≤ Φ ≤ 1) times of their sales income to farmers, and the retailer shares ∆(0 ≤ ∆≤ 1) times of the shortage punishment, θ (0 ≤ θ ≤ 1) times the overproduction punishment, and 𝑘𝑘(0 ≤ 𝑘𝑘 ≤ 1) times the financing interest costs of the farmer. Under the proposed coordination contract mechanism, if the farmer has 𝑆𝑆𝑆𝑆 and 𝑊𝑊𝑊𝑊 preferences, the farmer's expected utility and the retailer's expected profit are, respectively: 𝑈𝑈𝐹𝐹𝐻𝐻 = 𝐸𝐸[𝑤𝑤 min{𝑄𝑄, 𝑢𝑢𝑢𝑢} + Φ(𝐴𝐴 − min{𝑄𝑄, 𝑢𝑢𝑢𝑢}) min{𝑄𝑄, 𝑢𝑢𝑢𝑢} − (1 − ∆)𝜆𝜆(𝑄𝑄 − 𝑢𝑢𝑢𝑢)+ − (1 − 𝜃𝜃)𝛽𝛽(𝑢𝑢𝑢𝑢 − 𝑄𝑄)+ − 𝑐𝑐𝑐𝑐 − (1 − 𝑘𝑘)𝑟𝑟(𝑐𝑐𝑐𝑐 − 𝑇𝑇)] Π𝑅𝑅𝐻𝐻 = 𝐸𝐸[(1 − Φ)(𝐴𝐴 − min{𝑄𝑄, 𝑢𝑢𝑢𝑢}) min{𝑄𝑄, 𝑢𝑢𝑢𝑢} − 𝑤𝑤 min{𝑄𝑄, 𝑢𝑢𝑢𝑢} − 𝑘𝑘𝑘𝑘(𝑐𝑐𝑐𝑐 − 𝑇𝑇) − ∆𝜆𝜆(𝑄𝑄 − 𝑢𝑢𝑢𝑢)+ − 𝜃𝜃𝛽𝛽(𝑢𝑢𝑢𝑢 − 𝑄𝑄)+ ] Advances in Production Engineering & Management 17(2) 2022 (17) (18) 223 Wang, Yin, Zheng, Cai, Fang Hence, we obtain the following proposition: Proposition 2: • Under the proposed coordination contract mechanism, if the coefficient satisfies Eq. 19, the supply chain may be coordinated; • the farmer's behavioral preferences do not affect the coordination contract mechanism design: 𝑤𝑤 𝜃𝜃 = 1 + − Φ ⎧ 𝛽𝛽 ⎪ (19) ∆= 1 − Φ ⎨ 𝑤𝑤𝑤𝑤 + (1 − Φ)(1 + 𝑟𝑟) ⎪𝑘𝑘 = ⎩ 𝑟𝑟𝑟𝑟 Proof: Substituting Eq. 19 into Eqs. 17 and 18, we obtain: (𝑤𝑤𝑤𝑤 + Φ𝑐𝑐 − 𝑐𝑐)𝑇𝑇 𝑐𝑐 � (𝑤𝑤𝑤𝑤 + Φ𝑐𝑐 − 𝑐𝑐)𝑇𝑇 𝐶𝐶 Π𝑅𝑅𝐻𝐻 = (1 − Φ)Π𝑆𝑆𝑆𝑆 − 𝑐𝑐 𝐶𝐶 𝑈𝑈𝐹𝐹𝐻𝐻 = ΦΠ𝑆𝑆𝑆𝑆 + Eq. 20 indicates that 𝜕𝜕𝜕𝜕𝐹𝐹𝐻𝐻 𝜕𝜕𝜕𝜕 = 𝜕𝜕Π𝐶𝐶 𝑆𝑆𝑆𝑆 𝜕𝜕𝜕𝜕 = 0 and 𝜕𝜕Π𝐻𝐻 𝑅𝑅 𝜕𝜕𝜕𝜕 = 𝜕𝜕Π𝐶𝐶 𝑆𝑆𝑆𝑆 𝜕𝜕𝜕𝜕 (20) 𝐶𝐶∗ 𝐻𝐻∗ = 0 are both valid; hence, 𝑄𝑄𝑆𝑆𝑆𝑆 = 𝑄𝑄𝑆𝑆𝑆𝑆 𝐶𝐶∗ 𝐻𝐻∗ and 𝑞𝑞𝑆𝑆𝑆𝑆 = 𝑞𝑞𝑆𝑆𝑆𝑆 , achieving coordination in the supply chain. In addition, Eq. 19 also shows that 𝜃𝜃, ∆, 𝑘𝑘 are independent of 𝜆𝜆 and 𝛽𝛽; in other words, the behavioral preferences of the farmer do not affect the design of the coordination contract mechanism. The premise that the farmer and retailer are willing to participate in the coordination contract mechanism is a Pareto improvement of benefits; we, thus, derive Eq. 21, and we obtain the following proposition: (𝑤𝑤𝑤𝑤 + Φ𝑐𝑐 − 𝑐𝑐)𝑇𝑇 𝐶𝐶 𝑈𝑈𝐹𝐹𝐻𝐻 = ΦΠ𝑆𝑆𝑆𝑆 + > 𝑈𝑈𝐹𝐹𝐵𝐵∗ 𝑐𝑐 � (21) (𝑤𝑤𝑤𝑤 + Φ𝑐𝑐 − 𝑐𝑐)𝑇𝑇 𝐶𝐶 𝐻𝐻 𝐵𝐵∗ (1 Π𝑅𝑅 = − Φ)Π𝑆𝑆𝑆𝑆 − > Π𝑅𝑅 𝑐𝑐 Proposition 3: If the revenue-sharing coefficient Φ meets Φ1 ≤ Φ ≤ Φ2 , , both the farmer and retailer are willing to participate in the coordination contract mechanism, and both achieve a win-win situation, where Φ1 and Φ2 satisfy Eqs. 22 and 23: 𝑐𝑐(𝑇𝑇 + 𝑈𝑈𝐹𝐹𝐵𝐵∗ ) − 𝑇𝑇𝑇𝑇𝑇𝑇 Φ1 = 𝐶𝐶∗ 𝑐𝑐(𝑇𝑇 + Π𝑆𝑆𝑆𝑆 ) 𝐶𝐶∗ 𝐵𝐵∗ 𝑐𝑐�𝑇𝑇 + Π𝑆𝑆𝑆𝑆 − Π𝑅𝑅 � − 𝑇𝑇𝑇𝑇𝑇𝑇 ⎨ ⎪Φ2 = 𝐶𝐶∗ 𝑐𝑐(𝑇𝑇 + Π𝑆𝑆𝑆𝑆 ) ⎩ ⎧ ⎪ Φ1 − Φ2 = 𝐶𝐶∗ 𝑈𝑈𝐹𝐹𝐵𝐵∗ + Π𝑅𝑅𝐵𝐵∗ − Π𝑆𝑆𝑆𝑆 <0 𝐶𝐶∗ 𝑇𝑇 + Π𝑆𝑆𝑆𝑆 (22) (23) 5. Results and discussion: numerical simulation We resort to the numerical simulation method to further verify the correctness of the above conclusions and obtain more robust findings. Without loss of generality, the parameters are set as follows: 𝐴𝐴 = 100, r = 0.1, B = 2, c = 1, w = 3, T = 5, 𝜆𝜆 = 𝛽𝛽 =1. 224 Advances in Production Engineering & Management 17(2) 2022 Supply chain coordination contract design: The case of farmer with capital constraints and behavioral preferences Model Centralized decision model Decentralized decision model Coordination contract mechanism Φ Table 2 Calculation results under different models 𝑄𝑄 𝑞𝑞 Farmer's expected utility Retailer's expected profit Expected utility of supply chain 34.17 26.43 1655.64 1682.07 — 86.36 300.95 0 0.1 0.2 0.4 0.8 86.36 86.36 86.36 86.36 86.36 300.95 300.95 300.95 300.95 300.95 — 26.34 — 10 383.49 756.98 1503.96 2997.93 — 3719.91 3346.42 2972.93 2225.95 731.98 3729.91 3729.91 3729.91 3729.91 3729.91 3729.91 Fig. 2 Effect of Φ on farmer's expected utility and retailer's expected profit 5.1 Analysis of the coordination contract Table 2 and Fig. 2 indicate that the optimal order, production input, and expected supply chain utility in the decentralized decision framework are lower than those realized under the centralized decision model. The designed coordination contract mechanism coordinates the supply chain and realizes a flexible distribution of benefits between the farmer and retailer. In particular, when the revenue-sharing coefficient is 0.0044 < Φ < 0.5527，the farmer and retailer achieve a win-win situation. 5.2 Sensitivity analysis To further understand the impact of farmers’ behavior preferences on decision-making and the expected utility of the supply chain, we separately analyze three different scenarios. Analysis of SW preferences If the farmer has 𝑆𝑆𝑆𝑆 preferences, namely, 𝜆𝜆>0 and 𝛽𝛽 > 0, we obtain the findings reported in Figs. 3-7. The following five conclusions may be drawn: • In the centralized decision model, the optimal order, production input, and expected supply chain utility are greater than those realized under the decentralized decision model. • The optimal order in the centralized and decentralized decision models decreases with 𝑊𝑊𝑊𝑊 coefficient 𝛽𝛽. • The optimal order in the centralized decision model decreases with 𝑆𝑆𝐴𝐴 coefficient 𝜆𝜆, while the retailer order in the decentralized decision framework increases with 𝑆𝑆𝐴𝐴 coefficient 𝜆𝜆. • Whether in a centralized or decentralized decision model, the optimal production input is an increasing and decreasing function of 𝑆𝑆𝐴𝐴 coefficient 𝜆𝜆 and 𝑊𝑊𝑊𝑊 coefficient 𝛽𝛽, respectively. • Whether in a centralized decision model or decentralized decision model, the expected utility of the supply chain is an increasing and decreasing function of 𝑆𝑆𝐴𝐴 coefficient 𝜆𝜆 and 𝑊𝑊𝑊𝑊 coefficient 𝛽𝛽, respectively. Advances in Production Engineering & Management 17(2) 2022 225 Wang, Yin, Zheng, Cai, Fang Fig. 3 Effect of 𝜆𝜆 and 𝛽𝛽 on retailer's order and farmer's production input Fig. 4 Effect of 𝜆𝜆 and 𝛽𝛽 on retailer's order under centralized decision and decentralized decision model Fig. 5 Effect of 𝜆𝜆 and 𝛽𝛽 on expected utility of supply chain under centralized decision and decentralized decision model 226 Fig. 6 Effect of 𝜆𝜆 and 𝛽𝛽 on farmer's production input under centralized decision and decentralized decision model Advances in Production Engineering & Management 17(2) 2022 Supply chain coordination contract design: The case of farmer with capital constraints and behavioral preferences Fig. 7 Effect of 𝜆𝜆 and 𝛽𝛽 on expected utility of supply chain under centralized decision and decentralized decision model Analysis of SA preferences If the farmer has 𝑆𝑆𝐴𝐴 preferences, that is, 𝜆𝜆 > 0 and 𝛽𝛽 = 0, we obtain the results reported in Figs. 8 and 9. Therefore, the following three conclusions can be drawn: • The optimal order (expected supply chain utility) in the decentralized decision model increases with 𝑆𝑆𝑆𝑆 coefficient 𝜆𝜆, while the opposite result is obtained in the centralized decision model. • Whether in the centralized or decentralized decision model, the optimal production input increases with the 𝑆𝑆𝑆𝑆 coefficient 𝜆𝜆. • The optimal order, production input, and expected supply chain utility in the centralized decision model are greater than those realized under the decentralized decision framework. Fig. 8 Effect of 𝜆𝜆 on retailer's order and farmer's production input under centralized decision and decentralized decision model Fig. 9 Effect of 𝜆𝜆 on expected utility of supply chain under centralized decision and decentralized decision model Advances in Production Engineering & Management 17(2) 2022 227 Wang, Yin, Zheng, Cai, Fang Analysis of WA preferences If the farmer only 𝑊𝑊𝑊𝑊 preferences, that is, 𝜆𝜆 = 0 and 𝛽𝛽 > 0, we obtain the results reported in Figs. 10 and 11. The following two conclusions can be drawn: • Whether in the centralized or decentralized decision model, the optimal order, production input, and expected utility of supply chain decrease with 𝑊𝑊𝑊𝑊 coefficient 𝛽𝛽. • The optimal order, production input, and expected supply chain utility in the centralized decision model are greater than those realized under the decentralized decision framework. Fig. 10 Effect of 𝛽𝛽 on retailer's order and farmer's production input under centralized decision and decentralized decision model Fig. 11 Effect of 𝛽𝛽 on expected utility of supply chain under centralized decision and decentralized decision model 6. Conclusion This study examines the design of supply chain coordination contracts in the presence of farmer’s capital constraints and behavioral preferences. It addresses the case of a two-level supply chain comprising a farmer and a retailer. The farmer faces capital constraints, seeks financing from a third party, and may have S𝑊𝑊, 𝑆𝑆𝑆𝑆, and 𝑊𝑊𝑊𝑊 preferences. The full-text analysis suggests the following conclusions: • In the decentralized decision framework, the supply chain cannot be coordinated. However, the designed coordination contract mechanism coordinates the supply chain efficiently and realizes a flexible distribution of benefits between the farmer and the retailer. Furthermore, when the revenue-sharing coefficient is small (0.0044 < Φ < 0.5527), both the farmer and the retailer achieve a win-win situation. • In the centralized decision model, regardless of the behavioral preferences of the farmer, the optimal order, production input, and expected utility of the supply chain are always greater than those realized under the decentralized decision scheme. 228 Advances in Production Engineering & Management 17(2) 2022 Supply chain coordination contract design: The case of farmer with capital constraints and behavioral preferences • The farmer's optimal production input is always an increasing and decreasing function of 𝑆𝑆𝑆𝑆 coefficient 𝜆𝜆 and 𝑊𝑊𝑊𝑊 coefficient 𝛽𝛽, respectively. • In the centralized decision model, the retailer's optimal order always decreases with 𝑆𝑆𝑆𝑆 coefficient 𝜆𝜆, but the opposite result holds in the decentralized decision framework. The retailer's order always decreases with 𝑊𝑊𝑊𝑊 coefficient 𝛽𝛽. • The expected utility of the supply chain is always an increasing and decreasing function of 𝑆𝑆𝑆𝑆 coefficient 𝜆𝜆 and 𝑊𝑊𝑊𝑊 coefficient 𝛽𝛽, respectively. The coordination method proposed in this paper can be applied in other industries with similar backgrounds. However, it may not be applicable in the cases of random demand, supply chain competition, and information asymmetry. These are all future research directions. Acknowledgement This work was supported by the Humanities and Social Science Research Project of Ministry of Education of China (20XJC630007), the Humanities and Social Sciences Foundation of Chongqing Education Commission of China (22SKJD103), the Project of Science and Technology Research Program of Chongqing Education Commission of China (KJQN202000809), and the Open Project of Research Center for Enterprise Management of Chongqing Technology and Business University in 2021. 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Supply chain information coordination based on blockchain technology: A comparative study with the traditional approach, Advances in Production Engineering & Management, Vol. 17, No. 1, 5-15, doi: 10.14743/apem2022.1.417. 230 Advances in Production Engineering & Management 17(2) 2022 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 2 | June 2022 | pp 231–242 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.2.433 Original scientific paper Numerical study of racking resistance of timber-made double-skin façade elements Kozem Šilih, E.a, Premrov, M.a,* a University of Maribor, Faculty of Civil Engineering, Transportation Engineering and Architecture, Maribor, Slovenia ABSTRACT ARTICLE INFO The use of a double-skin façade (DSF) is a quite new approach in the building renovation process, complementing conventional renovation strategies. A double-skin façade is an envelope wall construction that consists of two transparent surfaces separated by a cavity and can essentially improve the thermal and acoustic resistance of the building envelope. The main double-skin wall components are usually composed of a hardened external single glazing pane and a double or triple thermal insulating internal glass pane, which are connected to the frame structure. Recently, many studies have analysed the thermal and acoustic performance of DSF elements, but almost none in terms of structural behaviour, especially in terms of determining the racking resistance of such wall elements. Moreover, with a view to reduce the global warming potential, an eco-friendly timber frame instead of a commonly used steel, aluminium or plastic frame is studied in this analysis. However, structurally combining timber and glass to develop an appropriate load-bearing structural element is a very complex process involving a combination of two materials with different material properties, where the type of bonding can be selected as a crucial parameter affecting the racking resistance range. Since the costs of experiments performed on such full-scale DSF elements are very high and such experiments are time-consuming, it is crucial to develop special mathematical models for analysing the influence of the most important parameters. Therefore, the main goal of this paper is to develop the finite element mathematical model of the studied DSF structural elements with a highly ecological solution by using a timber frame. In the second step, the developed model is further implemented in the numerical analysis of racking stiffness and followed by a comprehensive parametric numerical study on different parameters influencing the horizontal load-bearing capacity of such DSF timber elements. The obtained results indicate that the new approach of the developed load-bearing prefabricated timber DSF elements can essentially improve racking resistance and stiffness compared with the widely studied timber-glass single-skin wall elements and can thus be fully recommended especially in the structural renovation process of old buildings. Keywords: Timber; Glass; Double-skin façades; Racking resistance; Mathematical modelling; Numerical analysis; Finite Elements Methods (FEM) *Corresponding author: miroslav.premrov@um.si (Premrov, M.) Article history: Received 2 December 2021 Revised 12 August 2022 Accepted 19 August 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction In the past few decades, climate change has prompted experts to urgently call for action to remove the causes and alleviate the consequences of climate change that affect the environment, and design new buildings primarily with eco-friendly materials. Therefore, the field of energy consumption is witnessing a global trend aiming is to reduce greenhouse gas emissions. Consequently, a new strategy to design buildings with net zero emissions has to be adopted not only for new buildings, but also for building renovations, [1-4]. Since most energy flux is transmitted through 231 Kozem Šilih, Premrov building envelope elements [5, 6], the façade upgrade with essential thermal transmittance decrease can be one of the most effective interventions to improve the thermal efficiency and aesthetic appeal of existing buildings, [4]. In this sense, the advantages of wood and glass have led to the development of so-called timber-glass wall elements, in which single-layer outer and thermal insulated inner double or triple glass panes are rigidly connected to the timber frame with a bonding line, [2, 4, 5]. Since such DSF wall elements were developed primarily as external building envelope elements to enhance solar heat gains of the building during the heating period, they are usually placed on the south façade of the building. The proper orientation of such transparent façade elements enables the utilisation of solar energy for heating and internal illumination of the building [7-11]. However, the consequent asymmetrical layout of such transparent wall elements can result in many problems with the horizontal stability of the whole building. Their asymmetrical position can cause a serious plan irregularity problem, which may result in high torsional actions caused by heavy seismic or wind loads. The contribution of such DSF wall elements to the horizontal carrying capacity of the whole building is usually neglected and has not yet been implemented in any standards. Moreover, the hybrid steel-glass or timber-glass shear wall system can be created to realise hybrid structures with glass as the main stabilising material. Various hybrid glass component solutions are currently being studied mainly in the academic context, [12]. It was demonstrated in many experimental [4, 13, 14] and numerical studies [15] performed on full-scale single-skin timber-glass load-bearing structural wall elements that triple insulating glazing can foster higher racking resistance and stiffness compared with the single glazing. However, the racking stiffness is not in a range with the timber-framed walls with conventional sheathing boards, such as OSB or fibre-plaster boards, which are prescribed as primary load-bearing racking structural wall elements by standards. However, the goal of the design process in the comprehensive renovation of old buildings is also to improve the thermal standard of the building, and the sound and the racking resistance of the load-bearing envelope façade elements. Consequently, the concept of a specially developed double-skin façade (DSF) elements with an additional single-layer outer glass pane added to the commonly used triple insulating inner glazing rigidly connected to the frame structure and separated by a cavity could be a good and useful approach [16-18]. Such a solution can significantly decrease the U-value of such transparent envelope wall elements, and considerably improve the sound resistance. Combining timber and glass to make an appropriate load-bearing structural element is a very complex process involving a combination of two materials with different material properties, where the bonding line can be selected as a crucial parameter affecting the obtained load-bearing range [14], [19-26]. It is important to point out that only the load-bearing approach to the racking resistance and stiffness of such timber DSF elements will be numerically analysed in this paper as an upgrade of the already published experimental [5, 13, 14] and numerical studies [15, 27] performed on full-scale timber-glass wall elements with double and triple insulating glazing, but only as a concept of single-skin façade (SSF) elements. No energy, LCA or acoustic studies on DSF elements will be performed in the presented study. It should be emphasised that, to our knowledge, no special studies have been published on the topic of the racking resistance of timber DSF elements. In the broader study in [18], the structural approach to timber DSF was studied, but only for the vertical load impact. In [28], an experimental analysis of the racking resistance and stiffness of DSF elements was carried out as part of a national research project in two different specially selected full-scale test groups, varying the type of the adhesive connecting the insulating inner glazing to the timber frame (polyurethane and epoxy). As mentioned before, there are many different parameters which significantly influence the racking resistance and stiffness of timber DSF elements, especially the type of the bonding line between the glass pane and the timber frame, and the type and thickness of the glass panes. Since the experiments performed on such full-scale DSF elements are very time-consuming and also the costs are very high, it is crucial to develop special mathematical models to be used to further analyse the influence of most important parameters, and based on these results, to develop special simple final expressions for the racking resistance and stiffness of timber DSF elements to be suitable also for simple engineering usage. 232 Advances in Production Engineering & Management 17(2) 2022 Numerical study of racking resistance of timber-made double-skin façade elements The main goal of this paper is to develop a mathematical model of the studied DSF structural elements with a highly ecological solution by using a timber frame (Section 3). The developed finite element model can be further implemented in the numerical analysis of the racking resistance and stiffness (Section 4) and followed by a broad parametric numerical study on different most important parameters influencing the horizontal load-bearing capacity of such DSF elements (Section 5). Special attention will be dedicated to analysing the influence of the thickness ta and width wa of the bonding line, and to the thickness of the outer and inner glass pane tgl. Based on our previous experimental [5, 13, 14, 25, 26] and numerical studies [15, 27] performed on conventional single-skin façade (SSF) timber-glass wall elements and certain findings from experiments performed on full-scale DSF elements [28], only a case with a polyurethane adhesive in the bonding line between the insulating inner glazing and the timber frame is analysed in the presented study as the most appropriate and useful bonding solution (Fig. 1). 2. Main concept of timber double-skin façade wall elements According to [16], a double-skin façade (DSF) is an envelope element that consists of two transparent surfaces rigidly connected to a frame structure and separated by a cavity. The cavity is used as an air channel and can be naturally or mechanically ventilated and thus it does not offer an occupied space. The width of the cavity can vary from 200 mm to over 2 m. Solar shading systems can be integrated within the cavity. The insulating glazing is usually placed on the inner side of the façade, while the extra skin is placed on the external side to significantly improve the thermal transmittance of the wall element, and reduce the energy demand for heating and cooling, [16-18], [29-36]. The extra skin can reduce the cooling demand in the summer and the heating demand in the winter. Therefore, DSF elements have been proposed as a promising passive building technology to enhance energy efficiency and improve indoor thermal comfort [29]. Simulations of different envelope scenarios in the Mediterranean climate [36] have shown that the most energy efficient DSF is with low-e glazing as the outer layer. It is concluded in [17], however, that in warm climates its benefit in the summer is limited. Such a constructed envelope element also demonstrates better sound resistance [29, 35, 36] in comparison with widely used SSF elements and can, therefore, be suitable for high noise areas where a high level of sound insulation is required. The exterior glazing primarily consists of a hardened fully tampered single glass pane, while ordinary annealed glass is usually used for the thermal-insulating double or triple inner glazing, as schematically presented in Fig. 1. As already mentioned in the introduction, the type of the bonding line with appropriate adhesive dimensions was the crucial parameter in the structural behaviour of experimentally and numerically tested single-skin timber-glass façade wall elements against a horizontal load impact. Additionally, there are many types of adhesives to choose from, such as silicone, polyurethane, acrylate and epoxy. Fig. 1 Schematic presentation of the timber DSF wall element Advances in Production Engineering & Management 17(2) 2022 233 Kozem Šilih, Premrov Basically, the frame structure can be made from many different materials, but it is mainly made from steel, aluminium or plastic. However, it is obvious that, for this specific building typology to reach the zero energy building targets, mere energy conserving strategies involving decreases with the DSF elements energy demand for heating and cooling, as stated before, may not suffice. Renewable energy sources and technologies should be additionally considered as integral parts of the building envelope and systems [36]. Bearing in mind an eco-friendly renovation approach, the use of low-carbon materials is one of the most acknowledged mitigation measures for carbon reduction. Therefore, the adoption of timber as the main structural frame material can potentially further reduce the overall embodied carbon, [18]. Consequently, our study will be limited to the approach using a timber frame. In addition to the foreseen structural advantages, the DSF envelope wall elements improve the sound insulation of the building envelope and energy performance compared to the regular triple insulating glazing [17, 18, 29], therefore they can be very useful especially in renovation process by upgrading of the envelope elements in old existing buildings, compared also with commonly used single-skin façade solutions. However, most studies do not address structural solutions, instead focusing on energy analyses and their impact on the LCA results or analyses of sound insulation compared to single façade transparent elements. The numerical study in [18] is focused only on the vertical load impact but does not address the racking resistance range as the most important if the DSF elements are considered bracing structural elements. 3. Mathematical model The studied DSF wall elements have been modelled and analysed by using the commercial finite element model (FEM) computer program SAP2000 Nonlinear v 17.0.0 [37]. In the computational model, the timber frame was modelled by 1-dimensional (beam) finite elements, while the glazing boards were modelled using 2-dimensional finite elements of the “composite shell” type, which allows for the simulating of composite multi-layer shells. The adhesive bonding of the glazing panes to the timber frame was modelled using linear link elements (springs). As in reality, the adhesive bonding is provided continuously over the whole perimeter, the stiffness properties of the discrete spring elements were defined based on the spacing of the springs in the computational model using Eqs. 1 and 2 [15, 22, 38] for the inner and outer type of the bonding line: 𝐾𝐾1 = 𝐾𝐾2 = 𝐸𝐸𝑎𝑎 ∙𝐴𝐴𝑎𝑎 𝑡𝑡𝑎𝑎 𝐺𝐺𝑎𝑎 ∙𝐴𝐴𝑎𝑎 𝑡𝑡𝑎𝑎 = = 𝐸𝐸𝑎𝑎 ∙(𝑤𝑤𝑎𝑎 ∙𝑙𝑙𝑎𝑎 ) 𝑡𝑡𝑎𝑎 𝐺𝐺𝑎𝑎 ∙(𝑤𝑤𝑎𝑎 ∙𝑙𝑙𝑎𝑎 ) 𝑡𝑡𝑎𝑎 (1) (2) where K1 is the stiffness in the direction normal to the connected plane, while K2 is the shear stiffness in the two perpendicular directions in the connected plane. Ea and Ga are the modulus of elasticity and the shear modulus of the adhesive material, respectively, ta and wa designate the thickness and the width of the adhesive layer, respectively, while la is the impact length for a single spring element and is equal to the spacing between the springs. According to the scheme in Fig. 2b in our study, the bonding line between the inner glazing and the timber frame is marked with ta,inn and wa,inn variable parameters for the springs in Eqs. 1 and 2, while the parameters ta,out and wa,out are used for the outer bonding in the modelling process. The present study was performed for the case of the double-skin timber-glass wall system DSFP (double-skin façade) with full-scale dimensions of 1.25 m × 2.34 m (Fig. 2a), taken from the experimental analysis performed in [28]. The geometry and the typical cross-section of the DSF wall element with all adhesive types are shown in Fig. 2. As stated, two different types of adhesives were used, i.e. polyurethane (Ködiglaze P, [39]) for the inner triple insulation glazing, and silicone (Ködiglaze S, [40]) for the outer single glazing. The timber frame is composed of glue-laminated timber GL24h according to the EN 1194 classification [41]. For the inner triple insulating glazing, float glass (44.2) is used [42], i.e. glass panes 2, 3 and 4 in Fig. 2b, while a thermally toughened soda lime silicate safety glass (TVG 55.4) is used for the single outer glazing [43], i.e. glass pane 1 in Fig. 2b. It is important to point out that only the linear-elastic behaviour of all material components will be considered at this stage of modelling. 234 Advances in Production Engineering & Management 17(2) 2022 Numerical study of racking resistance of timber-made double-skin façade elements a) 1. Laminated outer glass (5 + 5 mm) 2. Float glass (6 mm) 3. Float glass (6 mm) 4. Laminated glass (4 + 4 mm) b) Fig. 2 External dimensions of the wall samples and dimensions of the timber frame elements (a), and the system cross-section with installation details (b) Table 1 Material properties of the adhesives [39, 40] Silicone (Ködiglaze S) Polyurethane (Ködiglaze P) Poisson's ratio ν 0.5 0.49 Shear modulus Gs (MPa) 0.351 0.454 Elastic modulus E0 (MPa) 1,053 1,354 Decay time td (s) 100 290 Decay constant β 0.0026 0.0016 The input data for two types of adhesives, and the material properties of the glass and timber are listed in Tables 1 and 2, respectively. Advances in Production Engineering & Management 17(2) 2022 235 Kozem Šilih, Premrov Standard E (MPa) ν (-) G (MPa) ft (MPa) fc (MPa) ρ (kg/m3) Table 2 Material properties of the timber [41] and glass components [42, 43] Timber frame GL24h [41] EN 1194 II 11,600 Ʇ 720 II 0.25 Ʇ 0.45 II 720 Ʇ 35 II 14 Ʇ 0.5 II 14 Ʇ 0.5 380 Float glass [42] EN 12150 70,000 0.23 0.45 45 500 2,500 Thermally toughened glass [43] EN 12150 70,000 0.23 0.45 120 500 2,500 The developed numerical finite element model of the whole composite DSF wall element as established in SAP 2000 [37] is shown in Fig. 3a. The timber material was considered as an isotropic elastic material (with the modulus of elasticity E0,mean) and the elements of the timber frame were modelled as the simple plane-stress elements. Both glass panes were modelled using the linear shell elements offered by the SAP2000 software. While glass is a very brittle material it was therefore modelled as acting linearly elastic in tension and compression. The schematic presentation of the detail bonding line modelling simulating the adhesive bonding between the timber frame and both glazings by using discrete two-dimensional spring elements with perpendicular stiffness properties K1 and K2 is presented in Fig. 3b. It is important to point out that the bonding lines for the outer and inner glazing are modelled and simulated separately with different values of K1 and K2 according to Eqs. 1 and 2. The tensile (left bottom) support was arranged using three M16 bolts and two steel plates (one on each side of the wall element). The steel plates were connected to a rigid steel frame. In the numerical model, the bolts were considered as linear elastic spring supports with the stiffness equal to the slip modulus Kser for bolts. It should be noted that the steel plates were not included in the numerical model. The compressive (right bottom) support was modelled using rigid point supports. a) b) Fig. 3 a) DSF-P finite element model, and b) the presentation of the spring/link elements 4. Numerical analysis and discussion of results In the numerical analysis, the model was loaded with a vertical load in the first phase, followed by the second phase with a gradual increase of the horizontal load (“step by step analysis”). Based on the ratio between the horizontal force and the calculated displacement, the racking stiffness R was determined. Subsequently, the results were compared with the results of the experimental tests performed in [28]. 236 Advances in Production Engineering & Management 17(2) 2022 Numerical study of racking resistance of timber-made double-skin façade elements Fig. 4 shows a comparison between the results of the experimental tests [28] performed on three full-scale test samples with the polyurethane adhesive for the inner glazing (DSF-P1, DSFP2 and DSF-P3) and the numerical analysis performed on the test samples with exactly the same all dimensions presented in Fig. 2 and all material properties listed in Tables 1 and 2. The diagram shows a very good agreement between the numerical and experimental results of three full- scale test samples regarding the behaviour of the structure in the elastic range until irreversible non-linear deformations appear. However, it should be mentioned that the test samples in [28] were experimentally tested pending the total failure of the element and the yielding of both adhesives occurred by the forces of approximately F1 = 28 kN. This yielding stage of the adhesive was not modelled with our developed mathematical model, as in the first phase of the developed new structural DSF elements, it is assumed to be used only as a bracing element for buildings, where the wind load is decisive as the horizontal load impact and the structure thus has to be dimensioned only in the linear-elastic range. The horizontal displacement u1 at a force of F1 = 10 kN and the calculated racking stiffness R for both experimental test and the numerical simulation are presented in Table 3. For the experimental results, the average value of all three test samples is calculated [28]. It is obvious from the presented results that the numerical results exhibit a very good agreement with the experimental ones. Therefore, it can be concluded that the developed FE model can be used for further parametrical studies with different parameters, which can significantly affect the racking resistance of DSF wall elements. 35 30 25 [kN] 20 Force 15 10 DSF-P1 DSF-P2 5 0 DSF-P3 NUMERICAL ANALYSIS 0 10 20 30 40 50 Displacement [mm] 60 70 80 Fig. 4 Experimental and numerical force-displacement diagrams for the DSF-P wall element Table 3 Experimental and numerical displacements at an acting force of F1 = 10 kN and racking stiffness R Model type Displacement u1 (mm) at F1 = 10 kN – numerical Displacement u1 (mm) at F1 = 10 kN – experimental [28] Numerical stiffness: R = F1 / u1 (N/mm) Experimental stiffness [28]: R = F1 / u1 (N/mm) Advances in Production Engineering & Management 17(2) 2022 DSF-P 11.67 11.00 857 909 237 Kozem Šilih, Premrov 5. Parametric numerical analysis of the horizontal load-bearing capacity and stiffness of DSF-P wall elements The parametric analysis was performed on the DSF-P model, in which the polyurethane adhesive thickness of the inner insulating glazing ta,inn was varied first, while the other parameters, such as silicone adhesive thickness of the outer glazing, glass thickness tgl and the width of the adhesive layer wa, remained unchanged. The thickness of the outer single glass (Glass 1) and the thickness of the triple inner insulating glass (Glass 2, 3, 4) according to Fig. 2b were further varied. In this case, the widths of the adhesive layer changed depending on the thickness of Glasses 2 and 3. 5.1 Analysis of the influence of the adhesive thickness on the horizontal load-bearing capacity of DSF wall panels In the first parametric study, the thickness of the polyurethane adhesive bonding the triple insulating glazing to the timber frame was parametrically changed (ta,inn = 3 mm, 5 mm, 7 mm, 9 mm), while the thickness of the silicone bonding the outer glass pane to the timber frame was constant ta,out = 3 mm in all cases. Table 4 and Fig. 5 show the results of displacements at an acting horizontal force of F1 = 10 kN and the calculated racking stiffness as a function of the thickness of the variable polyurethane adhesive. As expected, the racking stiffness of the wall element almost hyperbolically decreases with the increasing thickness of the polyurethane adhesive, since a greater thickness of adhesive represents a greater yielding of the joint between the timber frame and the glass. Very similar conclusions on the influence of the adhesive thickness were also obtained in the numerical study in [15] performed on single-skin façade elements with only triple or double insulating glazing. Table 4 Displacements u and stiffnesses R at different thicknesses of the polyurethane adhesive ta,inn ta,inn u at F1 = 10 kN R (mm) (mm) (N/mm) 3 6.40 1,563 5 9.26 1,080 7 11.67 857 9 13.07 765 Fig. 5 Racking stiffness values for the parametrical selected adhesive thicknesses ta,inn 238 Advances in Production Engineering & Management 17(2) 2022 Numerical study of racking resistance of timber-made double-skin façade elements 5.2 Analysis of the influence of the glass thickness on the horizontal load-bearing capacity of DSF wall elements Parametric analyses were also carried out, varying the thickness of the outer Glass 1 tgl,out and of the inner glasses 2, 3, 4 tgl,inn and taking into account the respective constant width of the polyurethane adhesive layer wa = 28 mm for the inner glazing. The layout of the glasses is shown in Fig. 6. Table 5 shows the results for different thicknesses of the outer single Glass 1 tgl,out at an acting horizontal force of F1 = 10 kN with a constant adhesive thickness of ta,inn = 7 mm and width wa,out = 20 mm for the fixing of the triple inner insulating glass to the timber frame. The silicone adhesive of the constant thickness of ta,out = 3 mm was used to fix the single outer insulating glass to the timber frame. The thicknesses of the inner triple glazing (Glasses 2, 3, 4) are constant and the same as used in the experimental analysis [28]. It is evident from the listed results that the glass thickness tgl,out has almost no impact on the racking resistance if the width of the bonding line wa,out is not adequately changed. Therefore, the width of the adhesive in the bonding line wa will be systemically changed with the increasing thickness of the glass panes tgl in our further analysis. 1. Laminated glass 2. Float glass 3. Float glass 4. Laminated glass Fig. 6 Illustration of the glass layout and thickness of the DSF-P wall element Table 5 Calculated displacements u and stiffness R for different glass thicknesses of outer Glass 1 tgl,out Glass pane 1 – outer wa,out (mm) 2 – inner 3 – inner 4 – inner u (mm) at F1 = 10 kN R (N/mm) Thicknesses of the outer glass tgl,out and inner glass tgl,inn (mm) Example 1 4+4 20 6 6 4+4 11.68 856.16 Example 2 5+5 20 6 6 4+4 11.67 856.90 Example 3 6+6 20 6 6 4+4 11.66 857.63 Example 4 7+7 20 6 6 4+4 11.64 859.11 5.3 Analysis of the influence of the adhesive layer width on the horizontal load-bearing capacity of DSF wall elements Table 6 shows the obtained numerical results for different parametrically selected thicknesses of the triple inner insulating glass (glasses 2, 3, 4) at an acting force of F1 = 10 kN. The inner glazing is bonded to the timber frame with a polyurethane adhesive with a constant thickness of ta,inn = 7 mm. The thickness of the silicone adhesive fixing of the outer single glass (Glass 1) to the timber frame remained unchanged ta,out = 3 mm and the thickness of the outer Glass 1 tgl,out remained constant (5 + 5 mm) as used in the experimental study [28]. The calculation of the spring stiffness takes into account the influence of the adhesive layer width wa and varies according to the thickness of glasses 2, 3 and 4. Consequently, the values wa,inn systematically increase from 24 mm in Example 1 to 36 mm in Example 4. The calculated results are graphically presented in Fig. 7. The linear approximation is marked with the dashed line. Advances in Production Engineering & Management 17(2) 2022 239 Kozem Šilih, Premrov Table 6 Displacements u and stiffness R for different glass thicknesses 2, 3, 4 Thicknesses of the outer glass tgl,out and inner glass tgl,inn (mm) Glass pane Example 1 Example 2 Example 3 Example 4 1 – outer 5+5 5+5 5+5 5+5 2 – inner 4 6 8 10 3 – inner 4 6 8 10 4 – inner 3+3 4+4 5+5 6+6 wa,inn (mm) 24 28 32 36 u (mm) at F1 = 10 kN 12.62 11.67 10.90 10.25 R (N/mm) 792 857 917 976 Fig. 7 Stiffness for different cases of the considered width of the adhesive The results evidently demonstrate that the thickness of the outer single Glass 1 has practically no influence on the racking stiffness of the wall element if the corresponding width of the adhesive is not changed. On the other hand, increasing the thickness of the inner insulating glasses 2, 3 and 4, but considering the corresponding increasing width of the adhesive layer wa in Eqs. 1 and 2, increases the overall DSF racking stiffness in an almost linear way, and has an important positive effect on the horizontal load-bearing capacity of the wall element. 6. Conclusion The paper presents the finite element model developed and used for the numerical analysis of the resistance and stiffness of double-skin façade (DSF) elements. Respecting the known facts from different experimental and numerical analyses performed on single-skin timber-glass wall elements, there are many various parameters which significantly affect the racking resistance of such elements and can be further implemented to double-skin timber glass façade elements. Considering that the costs of the experiments performed on such full-scale DSF elements are very high and such experiments are time-consuming, an extensive parametric numerical study of various main parameters influencing the horizontal load carrying capacity of such DSF elements was performed. Particular attention was paid to the analysis of the influence of the adhesive thickness and the width of the bonding line as well as the thickness of the outer and inner glazing panel. The computational analyses carried out on individual load-bearing DSF wall elements have shown a considerable influence of the adhesive layer width bonding the glass pane to the timber frame with almost linear behaviour approximation (Fig. 7), while the second important parameter, i.e. the adhesive thickness, exhibited almost hyperbolical influence (Fig. 5). On the other hand, the glass thickness was found to be a less important parameter, which becomes relevant only if the width of the adhesive layer increased simultaneously and adequately with the glass thickness. The obtained results indicate that the new approach of the developed load-bearing prefabricated timber DSF elements can essentially improve racking resistance and stiffness compared 240 Advances in Production Engineering & Management 17(2) 2022 Numerical study of racking resistance of timber-made double-skin façade elements with the widely studied timber-glass single-skin wall elements and can thus be fully recommended especially in the structural renovation process of old buildings. However, the presented spring FE model is maybe still complex for practical engineering usage, but very useful for parametrical research studies. 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EN 12150-1:2000: Glass in building – Thermally toughened soda lime silicate safety glass – Part 1: Definition and description, Brussels. 242 Advances in Production Engineering & Management 17(2) 2022 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 2 | June 2022 | pp 243–255 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.2.434 Original scientific paper A Plant Simulation approach for optimal resource utilization: A case study in the tire manufacturing industry Butrat, A.a, Supsomboon, S.b,* a,bThe Sirindhorn International Thai-German Graduate School of Engineering, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand ABSTRACT ARTICLE INFO In this study, the resource allocation and vital manufacturing processes in the tire manufacturing industry was comprehensively optimized. The paper deals in detail with the Banbury mixing process, which produces homogeneous rubber materials for tire components. In addition, the mixing process models were established by the Plant Simulation software to validate and compare scenarios and experiments with realistic production constraints. Discrete empirical distribution (dEmp) was proposed for population data. Various scenarios were created for different resource and process. Experiments were set as different group of compound set. Experiment manager was used as a tool to set up scenarios and the experiments to provide alternative results. The study results display the production time and machine utilization. The shortest production time of experiment results represents the best group of each scenario. As results, the scenario, which BB1 is changed from nonproductive Banbury mixer to special Banbury mixer along with the normal process is combined with second special process, provides the suitable production volume which can reduce of total production time for 8.06 %. Our study provides a variety of the resource utilization of a Banbury mixing process and suggests an efficient optimization method for production performance improvement. Keywords: Manufacturing; Resource utilization; Bottleneck; Optimization; Simulation modelling; Discrete-event simulation (DES); Discrete empirical distribution; Tires; Rubber; Banbury mixer; Tecnomatix Plant Simulation *Corresponding author: Srisawat.s@tggs.kmutnb.ac.th (Supsomboon, S.) Article history: Received 22 November 2021 Revised 1 March 2022 Accepted 13 June 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction Many companies face problems of the production capacity, bottleneck analysis is widely used to solve such problem. Bottleneck is a capacity constraint resource (CCR) whose available capacity limits the ability to meet the product volume of the system. The bottleneck identification is performed to find the bottleneck process which provides the highest machine utilization because of unbalance amount of batch [1, 2]. The production process is analysed according to the time operations. After the bottleneck process is defined, the technique to reduce the processing time of the bottleneck process and balance the processing time in a line process called Line balancing is applied. This technique assigns the work to stations in a line process in order to achieve the desired output rate with the smallest number of workstations [3]. 243 Butrat, Supsomboon Recently, many companies apply digital manufacturing program to optimize their production system with respect to time, cost and quality [4]. These programs can be used to increase productivity and optimize production systems by applying visual commissioning to manufacturing process and increasing production flexibility [5]. The simulation processes model is created to test new ideas and propose options in various scenarios before actual implementation. Simulation models are created to explicitly visualize how an existing operation might perform under varied inputs and how a new or proposed operations might behave under the same or different situation: material flows and plant layouts [6]. Moreover, to increase the production rate, the optimization of production lines using line balance and discrete event simulation approach can be considered [7]. A software named Plant simulation is performed using discrete event simulation tools. This software allows the use of simulation techniques to identify and minimize various problems related to production systems [8-10]. For production planners, the use of dynamic production system simulations can improve the productivity of existing resources and reduce the cost of planning for new production resources. They can also optimize system variables under complicated constraints [11-16]. In this study, the case studied company is the tire company. Their products include Truck and Bus Radial Tire (TBR) and Private Car Radial Tire (PCR). Due to the increase of demand, the company production capacity had reached its limit. The basic analysis of the company showed that the bottleneck of the production system was Banbury mixing process. This mixing process is the process combining carbon black, natural and synthetic rubber and other various types of chemicals which are used to produce a homogeneous rubber material for tire components called Productive compound (Pro). Productive compound is produced by 1-4 steps of Banbury mixing process. The outcome of each Banbury mixing process in each step which cannot use to produce tire components is called Non-productive compound (Non-pro). The Banbury mixer can be divided into 3 types: Non-pro BB, Pro BB and Special BB. Non-pro BB is used to produce Nonproductive compound. Pro BB is used to produce Productive compound. Special BB can be used to produce less step of Non-productive compound and produce Productive compound in 1 step (some compound). There are 6 Banbury mixer in the production lines shown in Fig. 1. BB1, BB3 and BB4 are Non-pro BB. BB5 and BB6 are Pro BB. BB2 is Special BB. Fig. 1 Banbury mixing process flow chart and layout 244 Advances in Production Engineering & Management 17(2) 2022 A Plant Simulation approach for optimal resource utilization: A case study in the tire manufacturing industry Fig. 2 Banbury mixing processes, (a) normal process, (b) first special process, (c) second special process, (d) third special process The normal Banbury mixing process is usually done in five steps. The first four steps of mixing provide non-productive compounds and the last step provides productive compounds. However, there are some special Banbury mixing processes which can provide productive compounds in less numbers of steps. The Banbury mixing processes are described as follows. Normal Banbury mixing process (N) is to assign Non-pro BB to mix 1 to 4 steps, depending on each compound, and Pro BB to mix 1 step as shown in Fig. 2(a). The first special Banbury mixing process (1st) is to assign Special BB to mix 2 steps as shown in Fig. 2(b). The second special Banbury mixing process (2nd) is to assign Special BB to mix 1 step and Pro BB to mix 1 step as shown in Fig. 2(c). The third special Banbury mixing process (3rd) is to assign Special BB to mix 1 step as shown in Fig. 2(d). Because productive compounds are usually the last step in all Banbury mixing processes, the numbers of productive compound steps can be defined to a specific number. For example, if 5 compounds are needed and each compound requires 10 batches, the number of steps for productive compounds is 50 steps. However, for the same 5 compounds, the number of steps for non-productive compounds is different. Its number of steps can be 0 to 4 based on the mixing process. For example, if the normal process is chosen, 4 steps for non-productive compound and 1 step for productive compound can be performed. However, by the same compound, if the second special process is chosen, 1 step for non-productive compound and 1 step for productive compound can be performed. In addition, each compound could not be applied to all Banbury mixing processes. There were 11 compounds from 31 compounds which could be produced by special process. To simplify sets of compounds, it was defined into 5 sets based on Banbury mixing processes. First set was the 20 compounds which could only be produced by normal process. Second set was the 1 compound which could be produced by normal or first special process. Third set was the 4 compounds which could be produced by normal or second special process. Fourth set was the 5 compounds which could be produced by normal or third special process. Fifth set was the 1 compound which could be produced by normal, first or second special process. Moreover, the compound in the first set was called normal type (20 compounds) and the rest of compound was called special type (11 compounds). Due to the above factors, workload balance between each Banbury mixer was the critical issue when a production planner needed to design the production volume to meet the demand. This study presents the optimization of manufacturing operations by balancing production line. The concept of balancing the production line is to design the best group of Banbury mixing processes. With simulation technique, all the types of the production process data were analysed. The input data included processing time, setting-up time, batch size, time between batch and total demand. The output data included machine utilization, total setting-up time proportion, total time between batch proportion and total production time. The simulation scenarios were created as different plans for resource allocation. The simulation experiments were set as various of total production planning of pro, non-pro and special compounds. This part of the process is Advances in Production Engineering & Management 17(2) 2022 245 Butrat, Supsomboon important for every simulation model because it involves various sources of system randomness. Moreover, the simulation study performed discreate empirical distribution because a standard theoretical distribution could not be found. It provided a good representation of our data while population data had been used [17, 18]. In this study, a Plant Simulation approach for optimal resource utilization: a case study in the tire manufacturing industry is presented. The outline is organized as follows. Section 2 illustrates the current performance of Banbury mixing process. Section 3 illustrates the simulation scenarios and experiments, the scenario results comparisons and estimation of production cost saving. Section 4 summarizes the conclusions and provides suggestions for future work, respectively. 2. Current performance of Banbury mixing process After the problem was defined, the current production system was carefully analysed. The Banbury mixing process 3D simulation model was created in the Tecnomatix Plant Simulation as shown in Fig. 3. This model was called “Current capacity”, described the existing state of the production capacity of each Banbury mixer. It was created with the help of tables containing recorded data concerning the time in the current production plan. The special milling method of Special BB created in simulation model is presented in Fig. 4(b). The special method was used to order queue of the special mill machines (MM) shown in Fig. 4(a). This method was coded to check whether which MM was empty before transferring WIP to the empty MM. Fig. 5 shows that the WIP compound which is transferred from BB waits for its destination. The destination of WIP compound receives from the first row of “QrderQueue” list. After that, a MM is set as the destination of the WIP compound, then the MM is deleted from the QrderQueue list. The MM is returned after it is already empty and waits for the next WIP compound. Fig. 3 The Banbury mixing process 3D simulation model Fig. 4 (a) Special milling order queue, (b) Special milling in Special BB control 246 Advances in Production Engineering & Management 17(2) 2022 A Plant Simulation approach for optimal resource utilization: A case study in the tire manufacturing industry Fig. 5 Special milling operation method The Banbury operation time including size change time (SC), processing time (PT) and time between batch (BwB) was considered. The sequence of mixing process is described in Fig. 6. The size change time starts when a worker setting up the Banbury mixer. Then, the processing time starts when the front gate of Banbury mixer opens to feed raw materials in and finishes when the back gate of Banbury mixer opens to feed a work-in-process out. The time between batch is the waiting time between feeding the work-in-process out and feeding the next raw materials in. Batch size is the number of batches between 2 size changes. Total production volume is the total number of batches in a month. Fig. 6 Mixing process sequence According to the described above, the system is the Banbury mixing process with the 3 types of the time consumption in the mixers. The simulation models are proposed under these 4 assumptions: 1) The system will not break down and is completely reliable. 2) Due to automation record of time, the input time is population data, the statistic theory will be Discrete empirical distribution. 3) The model will finish after passing 31 days without any break. 4) The number of areas to place the finished product (Non-pro, Pro compound) is unlimited. Table 1 Banbury mixing process time and production volume data Banbury mixer Data BB1 BB2 BB3 BB4 Mode (s) 125 180 113 133 Mode frequency (times) 531 407 482 294 Processing time (PT) Max (s) 467 482 288 340 Min (s) 83 131 94 91 Mode (s) 22 23 150 32 Mode frequency (times) 1083 807 829 521 Time between batch (BwB) Max (s) 1093 4306 186 4898 Min (s) 16 18 41 21 Mode (s) 1017 1845 1296 1544 Mode frequency (times) 3 3 3 3 Size change time (SC) Max (s) 4544 4779 4743 3442 Min (s) 122 175 112 111 Average batch size (batch) 38 47 46 35 Total production volume (batch) 6042 6800 7242 6906 Advances in Production Engineering & Management 17(2) 2022 BB5 107 1166 380 63 24 1103 4923 12 521 3 4409 208 34 8935 BB6 131 471 232 68 30 2175 3980 13 1729 3 4332 110 48 8469 247 Butrat, Supsomboon Banbury mixer BB1 BB2 BB3 BB4 BB5 BB6 Table 2 The machine utilization and the production time Machine utilization Processing time (PT) Set-up time (SC) Recovery time (BwB) (%) (%) (%) 42.83 10.04 10.76 45.48 9.22 26.29 39.15 7.64 39.99 40.55 8.56 24.84 32.61 10.77 35.00 37.75 7.48 24.29 Total (%) 63.62 81.00 86.77 73.96 78.38 69.52 Production time (days) 31 The Banbury operation time, batch size and total production volume data are summarized in Table 1. According to the assumptions mentioned above, we calculated machine utilization to define current capacity. The results of each machine utilization and the production time were shown in Table 2. The initial model, which only the properties of current production capacity were entered, provided the information about the behaviour of the current system. Processing time, Size change time (Set-up time) and Time between batch (Recovery time) were set as dEmp as illustrated in Fig. 7. After a model was run for 31 days of the simulation time, the machine utilization results were obtained as shown in Table 3. Fig. 7 Simulation setting window Model validation was performed to validate data and information. The model output for an existing system was compared with the corresponding output for the system itself. Hypothesis testing given in Table 3 illustrates the difference values of machine utilization in the real system and the simulation model. Number of machines (n) is 6 and degree of freedom (n–1) is 5. Significant level at 0.05. After testing, the t-value is greater than –2.101 and less than 2.101 with 95 percent of confident interval. Therefore, H0 is accepted. It can be concluded that there is no statistically significant difference between the real system and the simulation model. After the model was validated, the production time was changed to be dynamic. This model was ended up after all production volumes were produced. The production volumes were separated into each Banbury mixing process including non-pro, pro and special. The machine utilizations were also separated including Non-pro BB, Pro BB and Special BB. The simulation results of this situation were obtained as shown in Fig. 8(b). Machine utilization was averaged for each BB type as shown in Fig. 8(a). The summary of the current performance is presented in Table 4. Machine BB1 BB2 BB3 BB4 BB5 BB6 248 Table 3 Hypothesis testing, real and simulation machine utilization (%) Utilization (%) 𝒅𝒅𝒊𝒊 = 𝒙𝒙𝒓𝒓 −𝒙𝒙𝒔𝒔 Hypothesis Real (𝑥𝑥𝑟𝑟 ) Sim (𝑥𝑥𝑠𝑠 ) 63.62 63.34 0.28 Null hypothesis (H0): 𝑋𝑋�𝑟𝑟 − 𝑋𝑋�𝑠𝑠 = 0 81.00 81.64 -0.64 Alternative (H1): 𝑋𝑋�𝑟𝑟 − 𝑋𝑋�𝑠𝑠 ≠ 0 86.77 88.45 -1.67 73.96 74.34 -0.38 The test statistic 𝑡𝑡 78.38 77.61 0.77 69.52 69.08 0.43 0.1547 -0.20 𝑑𝑑̅ S.D. 0.81 −2.101 ≤ 𝑡𝑡 ≤ 2.101 Advances in Production Engineering & Management 17(2) 2022 A Plant Simulation approach for optimal resource utilization: A case study in the tire manufacturing industry Table 4 The summary results of the current performance Production volume (batch) Machine utilization (%) Time (days) Non-pro Pro Special Non-pro BB Pro BB Special BB 20,190 17,404 6,800 25.11 91.50 89.85 100 Avg 93.69 Fig. 8 (a) Average machine utilization of each BB type, (b) Machine utilization of each BB 3. Results and discussion 3.1 Simulation scenarios and experiments Since the result of the current capacity was found that the average machine utilization of Special BB was full (100 %), the proposed idea to increase capacity was to change BB1 to Special BB in order to reduce the Special BB workload as presented in Fig. 9(a). After this idea was created and run in the Plant simulation, it was found that the workload of Special BB was reduced to 35.30 % but the machine utilization of Non-pro BB was increased to 100 % as illustrated Fig. 9(b). After changing BB1 to Special BB, the production time increased from 25.11 days to 36.20 days and the total average machine utilization reduced from 93.69 % to 65.84 % as presented in Table 5. Therefore, it was implied that this concept was not valid. The reason would probably because of the unsuitable amount of the production volume for Non-pro BB. Fig. 9 (a) Changing BB1 from normal BB to Special BB, (b) The result that BB1 changing Production volume (batch) Non-pro Pro Special 20,190 17,404 6,800 Table 5 The summary results of Changing BB1 Machine utilization (%) Time Machine BB1 (days) Non-pro BB Pro BB Special BB 36.20 Special BB 99.40 62.82 35.30 Avg 65.84 Due to the invalid scenario above, we decided to reduce the workload from Non-pro BB by reducing numbers of steps. The numbers of steps were reduced by combining the normal process with the second special process called the fourth special Banbury mixing process (4th) as shown in Fig. 10(a). The fourth special Banbury mixing process is to assign Non-pro BB to proAdvances in Production Engineering & Management 17(2) 2022 249 Butrat, Supsomboon duce 1 step, Special BB to produce 1 step and Pro BB to produce 1 step as illustrated in Fig. 10(b). However, all compounds were also not applied to the fourth special process. There were only 7 compounds which could be produced by the normal process or the fourth special process. Therefore, the amount of the normal type had been changed from 20 compounds to 13 compounds and the amount of the special type had been changed from 11 compounds to 18 compounds. The summary of compound sets and the numbers of compound in each type are shown in Table 7. The experiments were the grouping in all compound sets. For instance, as shown in Table 6, experiment 24 means that compound set 1 is assigned to be produced by normal process (N), compound set 3 and 5 are assigned to be produced by second special process (2nd), compound set 2 is assigned to be produced by first special process (1st) and compound set 4 is assigned to be produced by third special process (3rd). As presented in Table 7, the numbers of groups were calculated by multiplying all possible processes in each condition. The number of groups in the current condition is 24 groups. The number of groups in the combined process condition is 48 groups. Fig. 10 (a) Mixing the normal and the second special process, (b) The fourth special Banbury mixing process Ex. 1 2 3 4 5 6 7 8 9 10 11 12 Ex. 25 26 27 28 29 30 31 32 33 34 35 36 250 1 N N N N N N N N N N N N 1 N N N N N N N N N N N N 2 N N N N N N N N N N N N 2 N N N N N N N N N N N N Table 6 All experiments from grouping the compound sets Compound set Compound set Ex. 3 4 5 1 2 3 4 N N N 13 N 1st N N N N 1st 14 N 1st N N N N 2nd 15 N 1st N N N 3rd N 16 N 1st N 3rd N 3rd 1st 17 N 1st N 3rd N 3rd 2nd 18 N 1st N 3rd 2nd N N 19 N 1st 2nd N 2nd N 1st 20 N 1st 2nd N 2nd N 2nd 21 N 1st 2nd N 2nd 3rd N 22 N 1st 2nd 3rd 2nd 3rd 1st 23 N 1st 2nd 3rd 2nd 3rd 2nd 24 N 1st 2nd 3rd Compound set Compound set Ex. 3 4 5 6 1 2 3 4 N N N 4th 37 N 1st N N N N 1st 4th 38 N 1st N N N N 2nd 4th 39 N 1st N N N 3rd N 4th 40 N 1st N 3rd N 3rd 1st 4th 41 N 1st N 3rd N 3rd 2nd 4th 42 N 1st N 3rd 2nd N N 4th 43 N 1st 2nd N 2nd N 1st 4th 44 N 1st 2nd N 2nd N 2nd 4th 45 N 1st 2nd N 2nd 3rd N 4th 46 N 1st 2nd 3rd 2nd 3rd 1st 4th 47 N 1st 2nd 3rd 2nd 3rd 2nd 4th 48 N 1st 2nd 3rd 5 N 1st 2nd N 1st 2nd N 1st 2nd N 1st 2nd 5 N 1st 2nd N 1st 2nd N 1st 2nd N 1st 2nd 6 4th 4th 4th 4th 4th 4th 4th 4th 4th 4th 4th 4th Advances in Production Engineering & Management 17(2) 2022 A Plant Simulation approach for optimal resource utilization: A case study in the tire manufacturing industry No. 1 2 3 4 5 6 Table 7 The summary of Banbury process and compound groups Current condition Combined process condition Compound sets Possible Possible No. of comps. No. of comps. process process Only Normal 20 1 13 1 Normal/1st special 5 2 5 2 Normal/2nd special 4 2 4 2 Normal/3rd special 1 2 1 2 Normal/1st special/2nd special 1 3 1 3 Normal/4th special 0 0 7 2 Total 31 24 31 48 Each experiment contained 3 types of batch amount for each compound including non-pro, pro and special. For Banbury production planning, production volumes of each compound can be calculated by Eq. 1. Production volume(batch) = Productive compound demand(batch) × Process step (1) For example, considering a productive compound in the set 5, with 1 batch of demand, if the compound is produced by normal process, production volumes will be 4 batches of non-pro and 1 batch of pro. If it is produced by first special process, production volume will be 2 batches of special. If it is produced by second special process, production volumes will be 1 batch of special and 1 batch of pro. After the production volume were calculated, the batch amount for each compound was summarized for each experiment as shown in Table 8. Ex. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Table 8 The production volumes of the experiments Current condition Combined process condition Non-pro Pro Special Ex. Non-pro Pro Special Ex. Non-pro 29,665 20,175 0 1 29,665 20,175 0 25 25,625 29,356 20,175 150 2 29,356 20,175 150 26 25,316 29,356 20,014 293 3 29,356 20,014 293 27 25,316 27,376 18,994 1,956 4 27,376 18,994 1,956 28 23,027 27,067 18,994 2,106 5 27,067 18,994 2,106 29 23,027 27,067 18,833 2,249 6 27,067 18,833 2,249 30 23,027 25,593 20,175 2,300 7 25,296 20,175 2,480 31 21,256 25,284 20,175 2,450 8 24,987 20,175 2,630 32 20,947 25,284 20,014 2,593 9 24,987 20,014 2,773 33 20,947 23,304 18,994 4,256 10 23,007 18,994 4,436 34 18,967 22,995 18,994 4,406 11 22,698 18,994 4,586 35 18,658 22,995 18,833 4,549 12 22,698 18,833 4,729 36 18,658 23,276 15,011 4,639 13 21,302 13,538 5,946 37 17,262 22,967 15,011 4,789 14 20,993 13,538 6,096 38 16,953 22,967 14,850 4,932 15 20,993 13,377 6,239 39 16,953 20,987 13,830 6,595 16 19,013 12,357 7,902 40 14,973 20,678 13,830 6,745 17 18,704 12,357 8,052 41 14,664 20,678 13,669 6,888 18 18,704 12,196 8,195 42 14,664 19,204 15,011 6,939 19 16,933 13,538 8,426 43 12,893 18,895 15,011 7,089 20 16,624 13,538 8,576 44 12,584 18,895 14,850 7,232 21 16,624 13,377 8,719 45 12,584 16,915 13,830 8,895 22 14,644 12,357 10,382 46 10,604 16,606 13,830 9,045 23 14,335 12,357 10,532 47 10,295 16,606 13,669 9,188 24 14,335 12,196 10,675 48 10,295 Pro 20,175 20,175 20,014 18,994 18,994 18,833 20,175 20,175 20,014 18,994 18,994 18,833 13,538 13,538 13,377 12,357 12,357 12,196 13,538 13,538 13,377 12,357 12,357 12,196 Special 2,746 2,896 3,039 4,702 4,852 4,995 5,226 5,376 5,519 7,182 7,332 7,475 8,692 8,842 8,985 10,648 10,798 10,941 11,172 11,322 11,465 13,128 13,278 13,421 All resource allocation plans were set up in 4 simulation scenarios illustrated in Table 9. Scenario I is the current capacity which has 5 compound sets, 20 normal compounds and 11 special compounds. BB1 is set as Non-pro BB, and there are 24 experiments. Scenarios II is the changing BB1 which has 5 compound sets, 20 normal compounds and 11 special compounds. BB1 is set as Special BB, and there are 24 experiments. Scenario III is applying fourth special process which has 6 compound sets, 13 normal compounds and 18 special compounds. BB1 is set as Non-pro BB, and there are 48 experiments. Scenarios IV is changing BB1 and applying fourth special process which has 6 compound sets, 13 normal compounds and 18 special compounds. BB1 is set as Advances in Production Engineering & Management 17(2) 2022 251 Butrat, Supsomboon Special BB, and there are 48 experiments. All scenarios are set to run 5 replications per experiment. Simulation scenarios were created in the Plant simulation and the simulation tool named “Experiment Manager” was used to set experiments and replication as presented in Fig. 11(a). The output values were defined including working proportion, setting-up proportion, recovery proportion, total proportion, and production time of each experiment in Fig. 11(b). The input values were defined as the production volume in each type and experiments were defined as the current input or the adjusted input in Table 6. In addition, all experiments were designed to have 5 observations per experiment as shown in Fig. 11(c). The graphs of results from experiments were plotted to find the lowest point which represented the best production time. Fig. 12(a-d) illustrates the experiment results of scenario I, II, III and IV. These graphs provide the lowest point at experiment 16, 24, 15 and 45, respectively. Most of the production times were varied according to Special BB and Non-pro BB. At this lowest point, either Special BB or Non-pro BB would be the maximum utilization. Scenarios I II III IV Compound sets 5 6 Table 9 The simulation scenarios Types No. of exp. (based on Machine BB1 grouping) Normal Special Non-pro BB 20 11 24 Special BB Non-pro BB 13 18 48 Special BB No. of replications per experiment 5 Fig. 11 Plant simulation tool named “Experiment Manager”, (a) setting window, (b) experiment table, (c) result table Fig. 12 The simulation results in each experiment, (a) Scenario I, (b) Scenario II, (c) Scenario III, (d) Scenario IV 252 Advances in Production Engineering & Management 17(2) 2022 A Plant Simulation approach for optimal resource utilization: A case study in the tire manufacturing industry 3.2 Scenario results comparisons Five scenarios were proposed to compare various capacity levels. The best experiment result of each scenario presented Banbury mixer machine utilization and production time. The graph in Fig. 13 represents the best experiment results of Scenario C, I, II, II and IV. As Scenario I results, the shortest production time was 24.43 days at experiment 16 which decreased by 0.68 days from current capacity (-2.71 %). Machine utilization of Non-pro BB, Pro BB and Special BB were 98.94 %, 74 % and 100 %, respectively. As Scenario II results, the shortest production time was 29.76 days at experiment 24 which increased by 4.65 days from production time (+18.52 %). Machine utilization of Non-pro BB, Pro BB and Special BB were 99.34 %, 60.16 % and 58.01 %, respectively. As Scenario III results, the shortest production time was 24.31 days at experiment 15 which decreased by 0.8 days from production time (-3.19%). Machine utilization of Non-pro BB, Pro BB and Special BB were 99.63 %, 71.95 % and 95.81 %, respectively. As Scenario IV results, the shortest production time was 22.46 days at experiment 45 which decreased by 2.65 days from current capacity (-10.55 %). Machine utilization of Non-pro BB, Pro BB and Special BB were 99.58 %, 77.95 % and 95.27 %, respectively. The summary results are shown in Table 10. Fig. 13 The best result of each sceanrio comparison Sce. C I II III IV Exp. 16 24 15 45 Table 10 The summary results of each scenario at the best experiment Production volume (batch) Machine utilization (%) Time Diff Sets BB1 NonSpecial (days) (%) Non-pro Pro Special Pro BB Avg pro BB BB 20,190 17,404 6,800 5 Non-pro 25.11 91.50 89.85 100 93.69 20,987 13,830 6,595 5 Non-pro 24.43 -2.71 98.94 74.00 100 90.98 16,606 13,669 9,188 5 Pro 29.76 18.52 99.34 60.16 58.01 72.50 20,993 13,377 6,239 6 Non-pro 24.31 -3.19 99.63 71.95 95.81 89.13 12,584 13,377 11,465 6 Pro 22.46 -10.55 99.58 77.95 95.27 90.93 3.3 Estimation of production cost saving As mentioned earlier, it recommended that BB1 should be changed to Special BB and fourth special process should be applied in order to reduce production time and utilize machine capacity. If the case study company implement this solution, the labor cost can be saved by production time reduction. In the current situation, BB1 required 4 workers to run the process but BB2 required 5 workers. To implement the solution, an additional worker of BB1 was recommended. Therefore, the total worker in the Banbury mixing process would be increased from 33 to 34 workers per shift. The wage per person was 1.22 USD per hours. As a result, the production time was reduced from 25.11 to 22.46 days per month. The yearly production saving was 22,834.90 USD per year as shown in Table 11. Advances in Production Engineering & Management 17(2) 2022 253 Butrat, Supsomboon Cases Current Solution Table 11 The summary of production cost saving after implement the solution Production time per month Labor cost No. of workers Wage Month Days Hours Year 33 25.11 602.64 291,147.44 1.22 12 34 22.46 539.04 268,312.55 4. Conclusion Diff -22,834.90 In this study, a Plant Simulation approach for optimal resource utilization was proposed. Plant simulation was applied to create Banbury mixing process 3D models and simulate the production data. Those models applied discrete empirical distribution (dEmp) to population data. Experiment manager tool set up the scenarios with the experiments and provided results. Experiment results displayed the production time and machine utilization. The shortest production time of an experiment represented the best result of a scenario. Four scenarios were compared to determine the optimal group of compound sets and number of machines. The results showed that scenario IV at experiment 45, which BB1 was changed from non-productive Banbury mixer to special Banbury mixer along with the normal process were combined with the second special process to be fourth special process, provided the shortest production time. This scenario required investment in changing Banbury mixer machine BB1. This solution could save production cost by reducing the production time by 22,834.90 USD per year. This study provides the resource utilization for Banbury mixing process to solve the capacity limitation. The adjustment in numbers of machines and the grouping in the compound sets are the solutions to reduce the production time. Discrete empirical distribution is demonstrated to deal with population data. The suitable method for verifying and optimizing various scenarios using Plant simulation are illustrated. Software configuration for setting operation times and experiments is explained. The simulation results found the shortest production time in each experiment and used to compare the shortest production time in each scenario. Our work also estimates the production cost saving for the best scenario from simulations. 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Advances in Production Engineering & Management 17(2) 2022 255 Calendar of events • 16th International Conference on Micromachining Technology, October 17-18, 2022, Dubai, United Arab Emirates. • 36th Annual European Simulation and Modelling Conference, October 26-28, 2022, Porto, Portugal. • 33rd DAAAM International Symposium, Virtual Online Edition, hosted by Vienna University of Technology, October 27-28, 2022, Vienna, Austria. • 7th International Conference of Computational Methods in Engineering Science, November 24-26, 2022, Zamosc, Poland. • 14th International Conference on Mechatronics and Manufacturing, February 10-12, 2023, Royal Princess Larn Luang, Bangkok, Thailand. • 7th International Conference on Material Engineering and Manufacturing, April 7-10, 2023, Chiba University, Japan. • 51th North American Manufacturing Research Conference, June 12-16, 2023, Rutgers University, New Brunswick, New Jersey, USA. 256 Advances in Production Engineering & Management 17(2) 2022 Notes for contributors General Articles submitted to the APEM journal should be original and unpublished contributions and should not be under consideration for any other publication at the same time. 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APEM Advances in Production Engineering & Management journal Chair of Production Engineering (CPE) University of Maribor APEM homepage: apem-journal.org Volume 17 | Number 2 | June 2022 | pp 137-258 Contents Scope and topics 140 A method for prediction of S-N curve of spot-welded joints based on numerical simulation Yang, L.; Yang, B.; Yang, G.W.; Xiao, S.N.; Zhu, T.; Wang, F. 141 Sustainability and digitalisation: Using Means-End Chain Theory to determine the key elements of the digital maturity model for research and development organisations with the aspect of sustainability Kupilas, K.J.; Rodríguez Montequín, V.; Díaz Piloñeta, M.; Alonso Álvarez, C. 152 Supply chain coordination based on the probability optimization of target profit Jian, M.; Liu, T.; Hayrutdinov, S.; Fu, H. 169 A bi-objective optimization of airport ferry vehicle scheduling based on heuristic algorithm: A real data case study Han, X.; Zhao, P.X.; Kong, D.X. 183 Ultrasonic abrasive polishing of additive manufactured parts: An experimental study on the effects of process parameters on polishing performance Liu, X.; Wang, J.; Zhu, J.; Liew, P.J.; Li, C.; Huang, C. 193 Machinability analysis and multi-response optimization using NGSA-II algorithm for particle reinforced aluminum based metal matrix composites Umer, U.; Mohammed, M.K.; Abidi, M.H.; Alkhalefah, H.; Kishawy, H.A. 205 Supply chain coordination contract design: The case of farmer with capital constraints and behavioral preferences Wang, Y.L.; Yin, X.M.; Zheng, X.Y.; Cai, J.R.; Fang, X. 219 Numerical study of racking resistance of timber-made double-skin façade elements Kozem Šilih, E.; Premrov, M. 231 A Plant Simulation approach for optimal resource utilization: A case study in the tire manufacturing industry Butrat, A.; Supsomboon, S. 243 Calendar of events 256 Notes for contributors 257 Published by CPE, University of Maribor ISSN 1854-6250 9 771854 625008 apem-journal.org