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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 Logotip Univerza - angleški- crni.wmf Chair of Production Engineering (CPE) Advances in Production Engineering & Management Volume 16 | Number 3 | September 2021 | pp 265–388 Contents Scope and topics 268 A new solution to distributed permutation flow shop scheduling problem based on 269 NASH Q-Learning Ren, J.F.; Ye, C.M.; Li, Y. Using the gradient boosting decision tree (GBDT) algorithm for a train delay prediction model 285 considering the delay propagation feature Zhang, Y.D.; Liao, L.; Yu, Q.; Ma, W.G.; Li, K.H. A smart Warehouse 4.0 approach for the pallet management using machine vision and 297 Internet of Things (IoT): A real industrial case study Vukicevic, A.; Mladineo, M.; Banduka, N.; Macužic, I. Increasing Sigma levels in productivity improvement and industrial sustainability with 307 Six Sigma methods in manufacturing industry: A systematic literature review Purba, H.H.; Nindiani, A.; Trimarjoko, A.; Jaqin, C.; Hasibuan, S.; Tampubolon, S. Modeling and optimization of finish diamond turning of spherical surfaces based on 326 response surface methodology and cuckoo search algorithm Kramar, D.; Cica, Dj. Tactical manufacturing capacity planning based on discrete event simulation and 335 throughput accounting: A case study of medium sized production enterprise Jurczyk-Bunkowska, M. Simulation-based optimization of coupled material–energy flow at ironmaking-steelmaking 348 interface using One-Ladle Technique Hu, Z.C.; Zheng, Z.; He, L.M.; Fan, J.P.; Li, F. Recharging and transportation scheduling for electric vehicle battery under the 359 swapping mode Huang, A.Q.; Zhang, Y.Q.; He, Z.F.; Hua, G.W.; Shi, X.L. A multi-objective selective maintenance optimization method for series-parallel systems 372 using NSGA-III and NSGA-II evolutionary algorithms Xu, E.B.; Yang, M.S.; Li, Y.; Gao, X.Q.; Wang, Z.Y.; Ren, L.J. Calendar of events 385 Notes for contributors 387 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 tobridge the gap between theory and practice, applications based on advanced theory and casestudies are particularly welcome. For theoretical papers, their originality and research contribu­tions are the main factors in the evaluation process. General approaches, formalisms, algorithmsor 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 ProcessesMachine Learning in ProductionAdvanced Production TechnologiesMachine-to-Machine EconomyArtificial Intelligence in ProductionMachine Tools Assembly SystemsMachining SystemsAutomation Manufacturing SystemsBig Data in ProductionMaterials Science, MultidisciplinaryBlock Chain in ManufacturingMechanical EngineeringComputer-Integrated ManufacturingMechatronics Cutting and Forming ProcessesMetrology in ProductionDecision Support SystemsModelling and SimulationDeep Learning in ManufacturingNumerical TechniquesDiscrete Systems and MethodologyOperations Researche-ManufacturingOperations Planning, Scheduling and ControlEvolutionary Computation in ProductionOptimisation TechniquesFuzzy SystemsProject ManagementHuman Factor Engineering, ErgonomicsQuality ManagementIndustrial EngineeringRisk and UncertaintyIndustrial Processes Self-Organizing SystemsIndustrial Robotics Smart ManufacturingIntelligent Manufacturing SystemsStatistical Methods Joining ProcessesSupply Chain ManagementKnowledge ManagementVirtual Reality in Production Logistics in Production A new solution to distributed permutation flow shop scheduling problem based on NASH Q-Learning Ren, J.F.a,b, Ye, C.M.a,*, Li, Y.a aSchool of Business, University of Shanghai for Science and Technology, Shanghai, P.R. China bSchool of Computer and Information Engineering, Henan University of Economics and Law, Zhengzhou, P.R. China ABSTRACT Aiming at Distributed Permutation Flow-shop Scheduling Problems (DPFSPs), this study took the minimization of the maximum completion time of the workpieces to be processed in all production tasks as the goal, and took the multi-agent Reinforcement Learning (RL) method as the main frame of thesolution model, then, combining with the NASH equilibrium theory and the RL method, it proposed a NASH Q-Learning algorithm for Distributed Flow-shopScheduling Problem (DFSP) based on Mean Field (MF). In the RL part, this study designed a two-layer online learning mode in which the sample collec­tion and the training improvement proceed alternately, the outer layer collects samples, when the collected samples meet the requirement of batch size, it enters to the inner layer loop, which uses the Q-learning model-free batchprocessing mode to proceed and adopts neural network to approximate the value function to adapt to large-scale problems. By comparing the Average Relative Percentage Deviation (ARPD) index of the benchmark test questions, the calculation results of the proposed algorithm outperformed other similar algorithms, which proved the feasibility and efficiency of the proposed algo­rithm. ARTICLE INFO Keywords: Flow shop scheduling;Distributed scheduling;Permutation flow shop;Reinforcement learning; NASH Q-learning; Mean field (MF) *Corresponding author:171910083@st.usst.edu.cn(Ye, C.M.) Article history: Received 29 July 2021 Revised 8 September 2021Accepted 26 September 2021 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 workmust maintain attribution to the author(s) and the title ofthe work, journal citation and DOI. 1. Introduction Under intelligent manufacturing mode, cross-product value chain integration has become anormal situation, for example, many parts of air conditioners and refrigerators are similar oreven the same, so to reduce costs, they can be produced and processed via distributed produc­tion. On this basis, this paper abstracted the problem of distributed production in different geo­graphical locations to a DFSP, and divided it into two sub-problems, the reasonable allocation ofworkpieces among factories, and the processing sequence arrangement within a factory. Field scholars have achieved various research results in terms of DFSP [1-3], for example,Wang et al. [4] analyzed the research status and development direction of DFSPs. Fernandez-Viagas and Framinan [5] proposed a new heuristic algorithm and obtained better upper bounda­ries. In terms of DPFSP, Gao et al. [6, 7] used heuristic algorithm to solve the problem, Naderi andRuiz [8] proposed a scatter search algorithm, Lin et al. [9] proposed an improved iterative greedyalgorithm, Fernandez-Viagas and Framinan [5] proposed a bounded search iterative greedy algo­rithm, Yang et al. [10] comprehensively optimized the assembly transport strategy, productionprocess, and production configuration of a reconfigurable flow shop, Wang et al. [11] proposed a distributed estimation algorithm, and they used their respective algorithm to solve the problem.Rifai et al. [12] proposed a multi-objective adaptive large neighborhood search algorithm basedon the Pareto front to study the distributed reentrant arrangement flow shop. Wang et al. [13]proposed a hybrid distributed estimation algorithm based on fuzzy logic to solve the productionscheduling problem with the maximum completion time criterion under machine failure condi­tions. Komaki and Malakooti [14] proposed a generalized variable neighborhood search meta-heuristic algorithm to solve the problem of minimizing the maximum completion time of thedistributed no-waiting flow shop scheduling problem. Chen et al. [15] proposed the non-dominated sorting genetic algorithm (NSGA) to the design of non-compact flow shop schedulingplan, and successfully solved the multi-objective optimization problem considering process con­nection, Lebbar et al. [16] proposed a computational evaluation of a new mixed integer linearprogramming (MILP) model developed for the multi-machine flowshop scheduling, Rathinam et al. [17] proposed heuristic based methodology to solve permutation flow shop scheduling. As the multi-agent Deep Reinforcement Learning (DRL) technology [18] is developing rapidly,the multi-agent application of the Q-learning algorithm has become more prominent [19-22],and scholars have successively applied this new technology to combinatorial optimization prob­lems such as workshop scheduling, and obtained a series of research results. For example, a fewstudies [23-26] explored deep into the communication and cooperation between the multipleagents of DRL. Omidshafiei et al. [27] studied multi-task and multi-agent RL problem, and pro­posed a method to upgrade single-task strategy to multi-task strategy. Sunehag et al. [28] used anew value decomposition network structure to train individual agents to solve the joint rewardproblem of multiple agents. Li et al. [29] proposed a workflow job scheduling algorithm based onload balancing, and the research results showed that the proposed algorithm can effectively uti­lize the cloud resources. Neary et al. [30] studied the interaction of collaborative multi-agent RLin a shared environment. Some scholars applied Nash equilibrium and multi-agent RL algorithmto optimal control problems [31, 32]. Shah et al. [33] studied the Nash equilibrium RL problem of the two-person zero-sum game. Feng et al. [34] proposed a polynomial time algorithm for dual-agent scheduling problem to find all Pareto optimal solutions. In summary, this paper took DFSP as the research object and proposed new NASH-Q DRL algo­rithm to solve DFSP based on existing multi-agent RL theory and algorithm results, and the prob­lem was solved by a data-driven method, which avoided the design of complex heuristic rules. 2. Problem description Distributed workshop scheduling can be divided into several types: distributed parallel machinescheduling, distributed flow shop scheduling, distributed job shop scheduling, distributed as­sembly scheduling, and distributed flexible workshop scheduling. This paper aims at the DPFSP,namely the distributed permutation flow shop scheduling problem, before solving the problem,it’s assumed that each factory has one flow production line, the production capacity of each fac­tory is the same, each factory has the same workshop layout, the same number of machines, andthe same processing ability for all workpieces. Phase 2 Fig. 1 Scheduling of distributed flow shop In DPFSP, the first thing to do is to solve the workpiece allocation problem in each workshop,that is, to allocate workpieces to be processed to each workshop according to certain initial con­ditions; the second is to solve the workpiece processing sequence on the production line in eachworkshop, that is, to arrange the processing sequence of the workpieces that have been allocatedto a same workshop, and use machines to process the sorted workpieces one by one. Due to mu­tual coupling, the problem shows high complexity, Fig. 1 gives a diagram of the scheduling ofdistributed flow shop. In problem solving, the goal is to minimize the maximum completion time of all workpieces.The maximum completion time of DPFSP means the total completion time of all the workpieces,which is determined by the workshop with the longest completion time, and this workshop iscalled the key workshop in this study. Assume: a processing task has a total of n workpieces that need to be processed in F workshops, each workshop has m machines, and each workpiece needs to go through m processing procedures, the processing procedures of all workpieces arethe same, once the workshop is decided for a workpiece, all procedures need to be completedwithin this workshop, the numbers of workpieces allocated to each workpiece are (....1, ....2,…, ........), the processing time of workpiece i on machine j in workshop f is denoted as ............ ,.... , the completion time of the k-th workpiece on machine j is denoted as ............ ,.... , the processing sequence of workpiec­es is denoted as ........, the overall scheduling scheme is denoted as .... =[....1, ....2,…, ........], then the objective function is: ................(....)= ............{ ................(........)} .... = 1,2, … , .... (1) 3. Used methods 3.1 Multi-agent DRL Multi-agent RL needs to be described by Markov game, because at a same moment, multipleagents respectively take independent actions, after the actions are performed, the reward re­ceived by each agent is not only related to itself, but also related to other agents, there’re mutual game relationships among agents, and the multi-agent RL system can be described in the follow­ing form: (...., ...., ...., ...., ...., ....) (2) where, N represents the number of multi-agents; S represents the state of the system; A repre­sents the set of actions of the agents, which is consisted of ....1, ....2,…, ........; T represents the state transition function, namely ....: ....× ....× .....[0,1], under state S, after action A is performed, the probability distribution of the next state is obtained; R represents the reward obtained by the agents, that is, ........(...., ...., ....') represents the reward obtained by agent i for performing action A and transforming from state S to state ....'; ....represents the learning rate. Each agent performs differ­ent actions, and all actions constitute systematic joint actions, which make the environment un­dergo changes and reach a new state, and each agent gets its own reward value, as shown in Fig. 2. Each agent in the multi-agent system needs to interact with the environment to obtain rewardvalues, thereby improving the strategy and obtaining the optimal strategy in the current envi­ronment. The process of the strategy learning is the multi-agent RL. The matrix game can be expressed as (...., ....1, ....2,…, ........, ....1, ....2,…, ........), where N is the number of agents in the system, An is the action set of the n-th agent, and Rn is the reward function of the n-th agent, apparently, the reward obtained by each agent is related to the joint actions of the sys­tem, ....1 × ....2 ×, … ,× ........ represents the space of joint actions. The strategy of each agent is theprobability distribution of the action space, and the goal of each agent is to get the maximum re­ward value. Assume ........ represents the strategy of agent n, (....1, ....2,…, ........) represents the joint strat­egy of the system, then the value function of agent n can be expressed as ........(....1, ....2,…, ........,…, ........). Fig. 2 Multi-agent RL system ** If there is ........ ......, ....= 1,2, … , ....in the joint strategy (....1 , ....2 ,…, ........*) of the matrix game, and it ** ** satisfies (....1 , ....2 ,…, ........,…, ........*) =(....1 , ....2 ,…, ........*), then it is a NASH equilibrium. In multi-agent RL algorithm, the NASH equilibrium can be described as: When the system performs joint actions [....1, ....2,…, ........], the expected reward obtained by agent n is ........[....1, ....2,…, ........], ........(........) represents the probability of agent n choosing action ........, then the NASH equilibrium can be defined as: . ........(....1, ....2,…, ........)....1*(....1)… ........(........)… ........*(........) ....1,…,.............1,…,........ = . ........(....1, ....2,…, ........)....1*(....1)… ........*(........)… ........*(........) ....1,…,.............1,…,........ wherein, .............., ....= 1,2, … , ..... The Minmax-Q algorithm is an earlier multi-agent method for random decision-making [35].The algorithm solves the zero-sum game of two agents, and theoretically proves the convergenceof the algorithm. However, due to the limitation in actual applications, the algorithm can hardlysolve general sum problems. Aiming at this shortcoming of the Minmax-Q algorithm, the NASH-Qalgorithm [36] extends to the multi-agent complete information general sum random game prob­lems, and it uses NASH equilibrium to define the value function. The random game is the random game process of N agents, it can be expressed as Eq. 3: (...., ...., ....1, ....2,…, ........, ...., ....1, ....2,…, ........, ....) (3) where, N represents the number of multi-agents, S represents the state of the system, An repre­sents the action space of agent n, T represents the state transition function, namely ....: ....× ....× .....[0,1], under state S, after performing action A, the probability distribution of the next state could be obtained, Rn represents the reward obtained by agent n, .represents the learning rate, the strategy of agent n is defined as ........: .........(........), which represents the probability distribution from the state to the agent action space, wherein ....(........) represents all possible sets of the action space probability distribution of agent n. The cumulative discount value function of agent n under the current strategy p can be de­scribed by Eq. 4 as: 8 ............(....)= ................. [............|.... = ....0, ....] (4) ....=0 The action value function can be described as Eq. 5: ............(...., ....)= ........(...., ....)+ ............'~....[............(....')] (5) The value function described by Eq. 5 is based on the condition of single agent, the action A in the formula is the joint action adopted by each agent, obviously, the action value function of theagents is based on the system state and the joint action space. Integrating Eq. 5, Eq. 4 can be rewritten as Eq. 6: ............(....)= ........~....(....)[............(...., ....)] (6) It represents that the state value function is obtained through the expectation of the action value function. Under the state that each agent performs discrete actions, the multi-agent RL is modeledthrough random games. Under the condition that each agent in the system doesn’t know the re­wards of other agents, still each agent can observe the previous behaviors of other agents, andrespond to the instant rewards generated. The MiniMax-Q learning algorithm is usually used to solve zero-sum game problems, its coreidea is that each agent maximizes the expected reward value in the worst case in the game withthe opponent, it solves the Nash equilibrium strategy of the game under specific state s by con­structing MiniMax linear programming method, and uses the time-series difference method toiteratively learn the state value function or the action value function. In the zero-sum game oftwo agents, for a given state s0, the state value function of the n-th agent can be defined as Eq. 7: * ........*(....0)= ............min . ........ (....0, ........, ....-....)........(....0, ........) ........(....0,·) ....-.........-.... (7) ................. where, the value of n is 1 or 2, and a-n represents actions other than an. This paper aims to use multi-agent method to solve the distributed production schedulingproblem, therefore, based on the MiniMax-Q learning algorithm, it extends to the general sumgame problem of multi-agents, namely the NASH Q-learning algorithm, which uses quadraticprogramming method to solve the NASH equilibrium point, in the game of each state, it couldfind out the global optimal point or the saddle point, so that the system can converge to theNASH equilibrium point in the cooperative equilibrium or the adversarial equilibrium. 3.2 Multi-agent MF-DRL algorithm Mean Field Theory is a method for studying complex multi-agent problems using machine learn­ing and physical field theories [37], it can simplify random models with huge scale or complexstructure. The overall goal of using multiple agents to solve distributed production scheduling problemsis to minimize the completion time. Each agent must learn the optimal strategy to cooperate withthe overall goal of the system, and the solution algorithm was improved based on the work ofRuiz et al. [38]. It’s assumed that, prepresents the joint strategy of the system, pi represents the strategy of agent i, vi represents the value function of agent i, N represents the number of agents; p* represents the joint strategy of the system under NASH equilibrium, and strategy p* is consist­ ** * ed of N agent strategies (....1 , ....2 ,…, ........*); the system state is s, then the strategy of agent i is ........ , * and the strategy of other agents except for agent i in the joint strategy p* is represented as ....-.... , ** ** namely ....-.... , ....2 ,…, ........-1 , ........+1 *), and the value function of agent i can be described by *.(....1 ,…, ........ Eq. 8: * ........(....; ....*)= ........(....; ........ , ....-*.... ) (8) According to the feature of NASH equilibrium, Eq. 9 could be obtained as: * ........(....; ........ , ....-*.... ) =........(....; ........, ....-*.... ) (9) The multi-agent system is in the optimal state at this moment, in the system, agent i executes tasks according to strategy ........*, and other agents execute tasks according to strategy ....-.... * , obvious­ly, .....{1,2, … , ....}, that is, any agent in the system has the opportunity to act as an independentagent, and each agent has the opportunity to act as a virtual agent and work with other agents toplay the game with independent agents in the system. The initial state of the system is s, then the value function of the system can be described by Eq. 10: ....*(....) .[....1(....), ....2(....), … , ........(....)]....* (10) The Q-value of the current state is initialized according to the definition of the NASH Q-learning algorithm, and is updated continuously through iterations, also, a NASH factor is addedduring Q-value update to ensure that the Q-value update can satisfy the compression mappingrequirements. At the same time, the relationship between the Q-value function and the state val­ue function can be known from Eq. 6, that is, the state value function can be updated synchro­nously and reach the NASH equilibrium. In a multi-agent system, it can be known from Eq. 3 that the dimension of the contact action isdetermined by the number of agents, for any agent i in the system, its action value function ........(...., ....) can be defined as: 1 ........(...., ....)= ....-1 . ........(...., ........, ........) (11) .........-1 This definition makes agent i have a connection with action Aj of other agents, and it simpli­fies the relationships among multiple agents and gives mathematical descriptions. The complexrelationships among multiple agents are simplified as pairwise correspondence between agent i and other agents, then by summing and averaging, the internal interactive relationships between agent i and other agents, and between other agents are retained; the pairwise approximation notonly reduces the complexity of the interaction between agents, but also implicitly preserves theglobal interaction between any pair of agents. In the workshop production scheduling problems, the sorting of workpieces within produc­tion line and the exchange of workpieces between production lines are both discrete actions.Assume: agent i has a total of .actions, the action space of Ai has a total of .components, and each component represents a selectable action. Ai is encoded by the One-Hot encoding method,the position code of the selected action is 1, and the position of other components is 0. In the algorithm, the distance or similarity between features is calculated by One-Hot encod­ing, the values of discrete actions are extended to the Euclidean space, and then a certain value of the discrete action can correspond to a certain point in the Euclidean space. At the same time,One-Hot encoding is also adopted for discrete features, which makes the calculation of distancesbetween actions more reasonable. After discrete actions are subject to One-Hot encoding, thefeatures of each dimension can be regarded as continuous features, and can be normalized usingthe normalization method of continuous features, for instance, they can be normalized to [-1,1]or to a mean of 0 and a variance of 1. The characteristics of One-Hot encoding provide conven­ience for calculating the mean action in the mean field theory, assuming ........ represents the meanaction, which is equivalent to the multinomial distribution of the actions of agents in the agentneighborhood, then it can be expressed by Eq. 12: ........ = ....1 -1 ......... (12) .... where, Aj represents the neighborhood agent action of agent i, and it can be expressed by Eq. 13: ........ = ........ + ............,.... (13) where, ............,....represents the distance between the neighborhood agent action of agent i and the mean action code. Then on this basis, the paired Q functions in Eq. 11 are analyzed, the first-order approxima­tion of the action value Qi of the agent is used to convert the interaction of multiple agents intothe interaction between two agents (as the number of neighborhood agents increases, the accu­racy increases, it’s because the average value of its high-order terms approaches 0), namely thevirtual agent that is composed of an agent and its neighborhood agents. Thus, Eq. 11 can be rewritten as Eq. 14: ........(...., ....)= ........(...., ........, ........) (14) Therefore, the multi-agent interaction is converted into two-agent interaction, that is, themean field theory is applied to simplify the pairwise interaction between an agent i and its neighborhood agents to the interaction between the agent i and the mean value of its neighbor­hood agents. After the agent system performs action Ai, the system state transits from s to s', and an instant reward Ri is obtained, then the mean field action value function update formula of the system canbe described by Eq. 15 as: ............+1(...., ........, ........)= ............(...., ........, ........)+ ....[........ + ................(....') -............(...., ........, ........)] (15) where, .represents the learning rate, .represents the discount factor. In Eq. 15, the mean field value function is used to replace the commonly used maximum valuefunction to iteratively solve the action value function. The reason is that if the maximum valuefunction is adopted, the cooperation of neighborhood agent strategies is required, and the cen­tral agent cannot directly change the strategies of neighborhood agents. Besides, if each agent isgreedy to obtain actions, then eventually the algorithm will fail to converge due to the dynamicinstability of the environment. The definition of the state value function is extended to the mean field state value function, which can be expresses by Eq. 16: .... )[........ ............(....)= .............(........|...., ........)............(....-....~....-.... ....(...., ........, ........)] (16) ........ In the staged game at each moment, ........ is obtained via strategy ............ of neighborhood agent j at the previous moment, and strategy ............ is also described using parameters of the mean action ............-1 of the previous moment, its update process is shown as Eq. 17: ....-1) ........ = 1 ............. and ........~............(·|...., ........ (17) ....-1 The strategy pin Eqs. 16 and 17 can also be regarded as the probability distribution of ac­tions taken by an agent. Obviously, the probability that an agent i takes the action Ai at time mo­ment t depends on the current state and the mean field action ........, and it can be described as Eq. 18. The agent strategy is a random behavior in which the action obeys a certain probability dis­tribution. The agent influences itself by observing the history behaviors of other agents in theneighborhood. Under a new state, an agent can determine its own best response action based onthe history behaviors of other agents. The strategies of other agents in the neighborhood alsoobey certain probability distribution rules, and the probability distribution can be determinedbased on prior knowledge and observed values, that is, to determine the strategy. Therefore, byobserving the history behaviors of other agents in the learning process, an agent can learn thestrategies of other agents and its influence on the system could be obtained. exp.-....................., ........, .......... ............(........|...., ....¯....)= (18) .............. exp .-....................., ........', .......... Eqs. 17 and 18 are continuously and interactively updated, which can continuously improvethe performance of the strategy and obtain the largest cumulative reward value. In addition, anexploratory factor .is added to Eq. 18 to try different behaviors by sacrificing some short-termbenefits, that is, for each current state, with a certain probability, behaviors that have not beentried before in the current state are tried to collect more information so that the agent couldreach the optimal strategy in the macroscopic scale. After the agent takes corresponding actionsin the current state, it will observe the new state of the system after the joint action is executed,and timely correct the credibility of other agents in the current state. In a multi-agent system, the learning of any agent should continuously interact with the learn­ing of other agents and continuously modify parameters to achieve the maximum cumulative reward value of the system, and the relationships among agents should be established throughcertain methods. The actions taken when the system transits from the current state to the nextstate should be jointly determined by the joint actions of the agents, which indirectly realizes thecommunication between agents. To ensure the flow of workpieces between different production lines, the action value functionof each agent is fitted by the deep neural network, and the loss function is constructed as Eq. 19: ....(............)=[........-................(...., ........, ........)]2 (19) where, ............ represents the parameters of the agent, ................(...., ........, ........) represents the action value func­tion fitted by the deep neural network, yi represents the target value of the mean field value func­tion and is calculated by Eq. 20: ........ = ........ + ............-........ (....') (20) where, Ri is the reward of agent i, ....-.... .... represents the calculation parameter of the mean field val­ue function. By taking the derivative of Eq. 19, the gradient direction of the parameter could be obtainedas shown in Eq. 21: ....................(............)=[........-................(...., ........, ........)]................................(...., ........, ........) (21) The parameters can be updated by solving the gradient descent method. During application, each agent represents a production line. Within the production lines, for any agent i, the action value function under parameters ........ .... are initialized and the corre- .... and ....-.... sponding mean action ........ of the agent is calculated. The outer loop for sample collection and the inner loop for training are designed. When thecollected samples meet the batch size requirement, it enters the inner loop and realizes moreefficient learning through the limited samples collected via the interaction between the agentsand the environment, as shown in Fig. 3. Fig. 3 Algorithm framework Through the alternation of the two stages: sample collection and storage, and using state ac­tion value function to approximate the deep neural network, in the inner loop of the algorithm,the learning algorithm is strengthened through the Q-learning model-free batch processingmode, and it is extended in the multi-agent RL system and iterated by fitting Q. The purpose is tocalculate the optimal strategy, and approximate the value function corresponding to the inputstate and action. Construct a quintuple as Eq. 22: ........................= {(........, ........, ........ , ........, ....'....)|....= 1,2,…,|........................|} (22) where, s represents the current state, A represents the action performed by the agent, ....repre­sents the mean action, R represents the instantaneous reward value, and ....'....represents the new state after performing the action. In the outer loop, the algorithm continuously collects andstores samples according to the element information determined by the quintuple, that is: ............= {(............, ................)|....= 1,2,…,|........................| (23) where, ............ =(........, ........, ........) (24) ................ = ........ + ....max ................................-1(....'.... , ....', ....') (25) where, counter represents the counter constant. The information of the quintuple is taken as the input, in each loop, after the value functionand the counter are initialized as 0, the approximate value of ................................ is calculated through thetraining set and the regression algorithm. On this basis, a deep neural network is built as the value function approximator to achieve efficient interaction with the environment, each agentcalculates and improves via the defined value function to generate high-quality strategies. When the discrete action space is very large or it is a continuous action space, the deep neuralnetwork is taken as the value function approximator to calculate the value function of the stateand action .....(...., ........, ........), at the same time, the Bellman equation is used to calculate ....+ ....max ....(....', ....', ....'), and an error function is introduced to calculate the deviation between thetwo. The back propagation algorithm is used to calculate the connection weight of the deep neu­ral network, so that the error function value is minimized. 2 ......(...., ....) -(....+ .........................(....).....(....', .....)).(26) . In a multi-agent system, each agent must go through two stages of individual learning and col­laborative improvement. For each agent, the specific state, action, mean action are taken as theinputs of the deep neural network, the estimated corresponding state action value function istaken as the output, then the agent will select the subsequent action according to the instructionof the output value. Under the batch processing mode, in each sampling stage, the RL methodinitializes the state action value function, in the t sampling steps, if the final state ........................ is not achieved, then the collected sample is stored into set Tuples; if it is the final state and the number of samples meets the requirement of |Tuples|, then the value function is updated; otherwise, if the number of samples doesn’t meet the requirement of |Tuples|, then executes the greedy strat­egy to choose action, and proceed the sampling. The outer loop in Fig. 3 describes the interaction between the system and the agent whoselearning is reinforced under batch processing mode based on the value function. In the algo­rithm, the orderly dependency between the action set and state is updated, then, it describes thespecific realization process of the outer loop of RL framework under the batch processing mode.By constructing the number of tuples that meets the threshold requirement, after sample collec­tion and storage is completed, the algorithm determines whether to enter the inner loop or not,and then executes the value function update of the batch processing mode. Samples are used to train the deep neural network value function approximator and calculate the ................of the current mode, the deviation under the batch learning mode can be expressed by Eq. 27: |........................| . (....(........, ........, ........) -................)2 (27) ....=1 Obviously, the optimization goal of the connection parameters of the deep neural network is: |........................| ....*............. min . (....(........, ........, ........) -................)2 (28) ....=1 In the process of neural network training, the RMSProp algorithm is adopted, this algorithm can well solve the change range of the parameters after update in the optimization, namely the swing amplitude problem. The RMSProp algorithm uses differential squared weighted averagesthrough the gradients of weights and biases, which is conductive to eliminating the directionwith large swing amplitude, and correcting the swing amplitude so that the swing amplitude ofeach dimension is smaller and the network converges faster. At the same time, the RMSProp al­gorithm can be built on batch processing training data naturally, and it is easier to be integratedinto a batch-processing mode RL algorithm. In this way, the approximator can not only be usedfor the RL of a single agent, through the RMSProp neural network training algorithm, it also real­izes high-quality neural network approximation value function, and it is the key link for the algo­rithm to be extended to the multi-agent system. 4. Results and discussion of case studies 4.1 Experiment setup In this study, the experiment constructed 9 states and 10 actions, the features of the states weredescribed by the processing status of the processing machines and the completion status of theworkpieces, such as the workload of the processing machines, the estimated earliest possiblecompletion time, and the estimated maximum completion time, etc. This paper took the minimization of the maximum completion time as the goal to research theworkshop scheduling problem, and the global reward was expressed as the sum of local rewards,in this way, the learning system was regarded as a multi-agent learning system with independentrewards, further, in the algorithm, attentions were first paid to the local rewards of each agentobtained according to local scheduling strategies, and then to the global reward. To intuitivelyunderstand the characteristics of the distributed scheduling problem, first, the sorting insideeach production line should be completed, if the equilibrium condition is not reached, then exe­cute the step of workpiece reallocation between production lines and other steps. In workshop scheduling, the processing machines were not allowed to perform two opera­tions within a discrete time step. Once a machine starts to perform a certain procedure on theworkpiece, it will be in the working state until the end of the procedure. Therefore, for an agent i, its value function was calculated according to the machine state at the decision time point t and the next decision time point t + .t. In the sample collection stage of the agent, the batch size was set to be 100, which means toenter the inner loop of the algorithm when the sample size reaches 100. About the supervisedlearning part, in theexperiment,for the relevant parametersof the RMSProp algorithm, themulti-factor varianceanalysis program was employed to analyze the obtained experimental results anddetermine the relationships among parameters and generate the best parameter combination. The parameters were respectively set as ........= (0.75,0.85,0.95,0.99), ........ = (10-4, 10-5, 10-6),........ = (10-4, 10-5, 10-6), ................h=(600,800,1000,1200), ........= ([-0.06,0.06], [-0.08,0.08], [-0.10,0.10]), and the 5 groups of parameters had a total of 4×3×3×4×3=432 combinations. After analyz­ing the experimental results using the variance analysis method, the p-values of the 5 groups of parameters were all lower than the 0.05 confidence interval, indicating that the algorithm wassensitive to these parameters, and finally it’s determined that the decay rate of RMSProp algo­rithm was 0.95, the learning rate lr was 10-5, the small constant sc was 10-6, the epoch of the neu­ral network algorithm was 1000, and the initial weight iw was a random number that is uniform­ly distributed between [-0.08, 0.08]. The influence of parameters on algorithm performance is shown in Fig. 4. lr sc epoch iw dr 0.8 0.7 0.6 0.5 0.4 -4 -5 -6 -4 -5 -6 0.75 0.85 0.95 0.99 10 10 10 10 10 10 600 800 1000 1200 [-0.06, 0.06] [-0.08, 0.08] [-0.10, 0.10] Fig. 4 Influence of parameters on algorithm performance 4.2 Comparison and analysis of results Based on the benchmark test set Taillard, the performance of the multi-agent RL algorithm wastested, and the results were compared with the results of the iterative greedy algorithm and thebenchmark results. In addition, Python was adopted to implement offline training of deep RLand the iterative greedy algorithm was implemented in a Matlab environment. By calculating theaverage relative percentage deviation (ARPD) index of each test question, the results were com­pared, as shown in Eq. 29: ........ * 1 ........ . ................ -................ ................ = × 100 (29) * ................ ........=1 where, NR represents the number of test runs, Cmax represents the minimum completion time * obtained in the nr-th experiment, and ................ represents the known optimal completion time. The smaller the value of ARPD, the better the performance of the algorithm. In the experiment, thenumber of agents was respectively set as 2, 3, 4, 5, 6, 7, 8, 9, 10 for testing, and the time level wasrespectively set as 20, 40, and 60. The ARPD comparison results are shown in Tables 1-3. The calculation results of iterative greedy algorithm (IG), multi-agent RL algorithm (MARL),IG1S, and IG2S [39] were compared. In the small-scale benchmark test, a total of 60 benchmarkquestions (20 × 5,20 × 10,20 × 20,50 × 5,50 × 10, 50 × 20) in the test set Taillard were selected, and three time levels T = 20, T = 40, and T = 60 were set in the experiment. When T = 60, theaverage value of ARPD of the MARL algorithm was the smallest among the four algorithms, fol­lowed by IG2S, the average ARPD of the IG algorithm designed in this paper was between thoseof the IG2S and the IG1S, the average ARPD values of the four algorithms were close, and theaverage ARPD of the IG2S algorithm was 12 % higher than that of the MARL algorithm. When T = 40, the average ARPD values of the four algorithms declined to varying degrees, indicating thatwithin a longer computation time, the algorithms could obtain better experimental results; theaverage ARPD values of the four algorithms respectively decreased by 5 %, 9 %, 6 %, and 7 %;the IG2S algorithm had the largest average ARPD decrement, followed by the MARL algorithm,whose overall average ARPD still kept the lowest. When T = 60, compared with the results then T = 40, the average ARPD of the algorithms showed no obvious increase, in actual industrial appli­cations, considering the real-time response requirements of the algorithm for the production environment, choosing T = 40 for the algorithm is more appropriate. Table 1 ARPD comparison (T = 20) Number of IG1S IG2S IG MARL production lines 2 0.68 0.52 0.64 0.53 3 0.69 0.60 0.66 0.55 4 0.68 0.63 0.67 0.56 5 0.70 0.64 0.69 0.56 6 0.72 0.66 0.68 0.58 7 0.72 0.68 0.72 0.58 8 0.93 0.79 0.89 0.59 9 0.99 0.89 0.89 0.60 10 1.21 1.05 1.01 0.64 Mean 0.81 0.72 0.76 0.58 Table 2 ARPD comparison (T = 40) Number of IG1S IG2S IG MARL production lines 2 0.62 0.48 0.54 0.46 3 0.63 0.49 0.54 0.48 4 0.65 0.52 0.59 0.50 5 0.65 0.52 0.69 0.49 6 0.68 0.66 0.60 0.51 7 0.73 0.68 0.68 0.53 8 0.90 0.73 0.79 0.54 9 0.92 0.83 0.86 0.54 10 1.19 0.92 0.98 0.60 Mean 0.77 0.65 0.70 0.52 Table 3 ARPD comparison (T = 60) Number of IG1S IG2S IG MARL production lines 2 0.60 0.46 0.54 0.45 3 0.62 0.46 0.53 0.46 4 0.65 0.50 0.58 0.50 5 0.63 0.50 0.66 0.49 6 0.66 0.65 0.70 0.50 7 0.71 0.66 0.67 0.53 8 0.90 0.73 0.73 0.53 9 0.91 0.81 0.81 0.54 10 1.17 0.91 0.95 0.60 Mean 0.76 0.63 0.69 0.51 The comparison of average ARPD values of the four algorithms at different time levels in thesmall-scale test is shown in Fig. 5. In the experiment of large-scale calculation examples, five types of scales (100 × 5,100 × 10,100 × 20,200 × 20,500 × 20) and a total of 50 calculation examples were chosen for the tests. Similarly, three time levels T = 20, T = 40, and T = 60 were set in the experiment, and the resultsof the ARPD values of the four algorithms are shown in Tables 4-6. T=20 T=40 T=60 Fig. 5 Comparison of average ARPD of small-scale calculation examples Table 4 ARPD comparison (T = 20) Number of productionlines IG1S IG2S IG MARL 2 1.42 1.02 1.37 0.83 3 1.76 1.32 1.66 0.95 4 1.78 1.53 1.79 1.13 5 1.90 1.74 1.94 1.35 6 2.54 2.34 2.44 1.67 7 2.98 2.58 2.68 1.68 8 3.55 2.87 3.34 1.89 9 3.89 3.01 3.90 1.90 10 4.34 3.05 4.39 2.21 Mean 2.68 2.16 2.61 1.51 Table 5 ARPD comparison (T = 40) Number of IG1S IG2S IG MARL production lines 2 1.40 1.00 1.35 0.73 3 1.74 1.30 1.64 0.84 4 1.72 1.51 1.77 1.12 5 1.90 1.70 1.94 1.34 6 2.51 2.33 2.43 1.62 7 2.96 2.57 2.67 1.63 8 3.59 2.84 3.33 1.80 9 3.89 3.00 3.90 1.90 10 4.32 3.02 4.38 2.19 Mean 2.67 2.14 2.60 1.46 Number of production lines Table IG1S 6 ARPD comparison (T IG2S = 60) IG MARL 2 1.40 1.00 1.34 0.69 3 1.73 1.27 1.64 0.80 4 1.72 1.49 1.77 1.07 5 1.90 1.70 1.92 1.31 6 2.50 2.31 2.43 1.62 7 2.96 2.53 2.67 1.62 8 3.58 2.84 3.31 1.80 9 3.89 3.00 3.90 1.88 10 4.31 3.02 4.36 2.16 Mean 2.67 2.13 2.59 1.44 In the three large-scale experiments, the workpieces and processing machines increased sig­nificantly, and the ARPD values of the algorithms had been improved greatly, indicating thatwhen dealing with large-scale problems, the algorithms’ problem-solving abilities had reduced.Taking T = 40 as an example, by comparing the ARPD values of the algorithms in small-scale andlarge-scale scenarios, the MARL algorithm had the smallest increment, followed by the IG2S al­gorithm, which indicated that when dealing with large-scale problems, the multi-agent RL algo­rithm designed in this paper also showed obvious superiority. In the experiment of large-scale calculation examples, the comparison of average ARPD valuesof the four algorithms at different time levels is shown in Fig. 6, obviously, the ARPD of the MARLalgorithm was the smallest. In order to further test the performance of the algorithm to solve a larger scale and keep oth­er conditions unchanged, when the number of production lines increases to 15 and 20, it can befound that the performance of the proposed algorithm decreases significantly and loses its lead­ing edge compared with other algorithms. This shows that the algorithm has great limitations insolving large-scale problems. How to further improve the algorithm and improve the perfor­mance of the algorithm in solving large-scale problems is a problem we are currently exploring. T=20 T=40 T=60 MARL IG IG2S IG1S 3 2,5 2 1,5 IG1S 1 IG2S 0,5 IG MARL 0 Fig. 6 Comparison of mean ARPD in large-scale computation examples This paper designed a multi-agent RL method to solve DPFSPs. Based on the NASH equilibri­um theory and the NASH Q-learning method, a multi-agent MF-DRL algorithm had been pro­posed in the study, and global perspective algorithm elements such as joint state and joint ac­tions were constructed. The experimental results showed that, the proposed multi-agent RLmethod was effective in solving DPFSPs, and it outperformed other algorithms in case of large-scale problems. The RL method proposed in this paper was mainly based on the value functionmethod, it hadn’t involved the strategy-based RL method, and now the effect of the strategy-based RL method on the solution of distributed production scheduling hasn’t been explored yet, studies of this aspect will be carried out in the subsequent research. 5. Conclusion This paper designed a multi-agent RL method to solve DPFSPs. Based on the NASH equilibriumtheory and the NASH Q-learning method, a multi-agent MF-DRL algorithm had been proposed inthe study, and global perspective algorithm elements such as joint state and joint actions wereconstructed. The experimental results showed that, the proposed multi-agent RL method waseffective in solving DPFSPs, and it outperformed other algorithms in case of large-scale prob­lems. The RL method proposed in this paper was mainly based on the value function method, ithadn’t involved the strategy-based RL method, and now the effect of the strategy-based RLmethod on the solution of distributed production scheduling hasn’t been explored yet, studies ofthis aspect will be carried out in the subsequent research. Acknowledgment Project supported by the Key Soft Science Project of "Science and Technology Innovation Action Plan of ShanghaiScience and Technology Commission, China (No. 20692104300). 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Appendix The abbreviations used in the article: RL Reinforcement Learning MF Mean Field DFSP Distributed Flow-Shop Scheduling Problem DPFSP Distributed Permutation Flow-shop Scheduling Problem DRL Deep Reinforcement Learning MF-DRL Mean Field Deep Reinforcement Learning ARPD Average Relative Percentage Deviation MARL Multi agent Reinforcement Learning RMSProp Root Mean Square Prop IG Iterative Greedy IG1S The single stage Iterative Greedy IG2S The two stage Iterative Greedy Using the gradient boosting decision tree (GBDT) algorithm for a train delay prediction model considering the delay propagation feature Zhang, Y.D.a,*, Liao, L.a, Yu, Q.a, Ma, W.G.a, Li, K.H.b aSchool of Information Science and Technology, Southwest Jiaotong University, Chengdu, P.R. China bSchool of management, Xihua University, Chengdu, P.R. China A B S T R A C T Accurate prediction of train delay is an important basis for the intelligentadjustment of train operation plans. This paper proposes a train delay predic­tion model that considers the delay propagation feature. The model consistsof two parts. The first part is the extraction of delay propagation feature. Thebest delay classification scheme is determined through the clustering methodof delay types for historical data based on the density-based spatial clustering of applications with noise algorithm (DBSCAN), and combining the best delay classification scheme and the k-nearest neighbor (KNN) algorithm to designthe classification method of delay type for online data. The delay propagationfactor is used to quantify the delay propagation relationship, and on this basis,the horizontal and vertical delay propagation feature are constructed. The second part is the delay prediction, which takes the train operation statusfeature and delay propagation feature as input feature, and use the gradientboosting decision tree (GBDT) algorithm to complete the prediction. Themodel was tested and simulated using the actual train operation data, andcompared with random forest (RF), support vector regression (SVR) andmultilayer perceptron (MLP). The results show that considering the delaypropagation feature in the train delay prediction model can further improve the accuracy of train delay prediction. The delay prediction model proposedin this paper can provide a theoretical basis for the intelligentization of rail­way dispatching, enabling dispatchers to control delays more reasonably, and improve the quality of railway transportation services. A R T I C L E I N F O Keywords: Train delay prediction; Actual train operation data; Delay type identification; Delay propagation feature extrac­tion;Density-based spatial clustering of applications with noise (DBSCAN);k-nearest neighbor (KNN);Gradient boosting decision tree (GBDT);Random forest (RF);Support vector regression (SVR);Multilayer perceptron (MLP) *Corresponding author:ydzhang@swjtu.edu.cn(Zhang, Y.D.) Article history: Received 24 July 2021 Revised 25 October 2021 Accepted 28 October 2021 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 ofthe work, journal citation and DOI. 1.Introduction With the development of railway network and the growth of passenger travel demand, the utili­zation rate of railway lines is getting higher and higher. Under the premise of ensuring the safetyof train operation, ensuring the punctuality is the key of railway transportation to improve thequality of service. Once the train is delayed, the dispatchers must use dispatch adjustment meth­ods reasonably and scientifically [1]. The accurate prediction of train delays can assist dispatch­ers to make scientific decisions, and even realize the intelligent dynamic adjustment of trainoperation plans. The traditional train delay prediction mainly relies on the work experience and operatingskills of dispatchers. Due to the uncertainty of train delays, this method is difficult to reasonablypredict the delay before it occurs. On the other hand, the primary delay caused by the interfer­ence of external factors will produce a domino effect-like delay propagation effect on the line,which will lead to the secondary delay. However, it is very limited to rely on the experience ofdispatchers to predict the secondary delay. With the development of railway informatization, on the basis that the actual operation data of trains can be fully collected and fully processed, theapplication of big data and machine learning to train delay prediction has important referencevalue for the development of intelligent dispatching and command work [2]. The machine learn­ing method is based on the actual train operation data and do not require relevant details withinthe system. The actual data can reflect the relevant factors and their interactions of delays. Thismethod is conducive to revealing the occurrence and propagation of train delays. This paper proposes a train delay prediction model that considers the delay propagation fea­ture. When the model uses machine learning methods for delay prediction, the delay propaga­tion feature is added to improve the prediction accuracy. The main contributions of this paperinclude: (1) Design the clustering method of delay types for historical data based on density-based spatial clustering of applications with noise (DBSCAN) and the classification method ofdelay types for online data based on k-nearest neighbor (KNN); (2) According to the determineddelay type, the delay propagation factor is used to quantify the delay propagation relationshipand construct as the horizontal and vertical delay propagation feature; (3) Construct a gradientboosting decision tree (GBDT) model to complete the prediction of train delays according to thetrain operation status feature and the delay propagation feature. This paper is organized as follows. Section 2 summarizes the current research on train delayprediction. Section 3 describes the problems to be solved. Section 4 describes the overall struc­ture of the train delay prediction model proposed in this paper and describes the design princi­ples of each part in detail. In Section 5, an example is analyzed based on the actual data of trainoperation. Section 6 summarizes the work of this paper. 2. Related work The input feature set of the machine learning model will affect the performance of the model. Sothe selected input feature should have the greatest impact on the output results. It is a routine consideration to use information related to train characteristics and train status as the input feature set of the prediction model, because these are factors that directly affecttrain delays. Oneto et al. [3] took the section running time, working day/non-working day fea­ture as the input feature set. Wang and Zhang [4] identified the number of delayed trains at eachstation, the total value of delays of each station and the total value of each train's delays as fac­tors affecting train delays. Shi et al. [5] considered the current station and train codes when es­tablishing the feature set. The related historical value of train operation is also related to thedelay prediction. Nair et al. [6] considered the historical delay value and historical running timeof the train at the station as the input feature of model. But the train runs according to the pre-designed train operation diagram, therefore, the planned values related to the operation dia­gram such as the planned running time [7], the planned stopping time of trains and the plannedrunning interval between trains [8, 9] should also be taken into consideration. To improve the quality of prediction, some studies have begun to consider other factors be­sides the feature of train operation status. Tang et al. [10] used the primary delay time, the num­ber of affected trains and the delay causes as independent variables. Zhang et al. [11] based onthe secondary delay data, considered the impact of the preceding train on the current train andconstructed a model input feature set. Hu et al. [12] used a hierarchical clustering algorithm toanalyze the delayed trains and based on the results of 4 types of delayed train sequences madesubsequent delay time predictions. Zeng et al. [13] used cause analysis to infer the delay propa­gation chain, integrated the train event information with the primary delay and secondary delayinformation contained in prediction model. The above literature review shows that when establishing the input feature of prediction model, most studies consider the train operating status information, and also the factors relatedto the data characteristics and the predicted output. But few studies consider the delay propaga­tion relationship in the delay prediction. In terms of prediction models, using machine learningmodels to predict delays has a better fitting effect than traditional statistical models [14, 15].The machine learning model can realize the prediction of delay more accurately and quickly, andat the same time, the output can be stabilized in the case of a large amount of data. Decision treemodel [16], random forest model [6, 7, 9, 13], neural network model [8, 17] and SVR model [10]are now widely used in train delay prediction research. Therefore, this article will establish a GBDT-PF model considers the delay propagation be­tween trains and the delay propagation of the train itself. The model can identify the delay typesand obtain the delay propagation relationship. The delay classification scheme can enable dis­patchers to understand the law of the occurrence of primary delays, and the delay propagationrelationship has a direct impact on the subsequent train delays, so the prediction model thatconsiders the delay propagation relationship can obtain higher accuracy. 3.Problem statement The train operation process in the railway network can be expressed as a collection of a series ofevents and processes [18]. The dependency between events and processes can be representedby timed event graphs. Fig. 1 is the use of time event graph to show the operation status of eachtrain. According to the time of day, each train is arranged vertically (1,2,3, ., ....) and each station is arranged horizontally (1,2,3, ., ....). In Fig. 1, the node ........,.... represents the arrival or departure event of train ....at station ...., the weight of the node ........,.... represents the delay value of train ....at station ...., the directed arc .....................,...., ........+1,.....represents the operation process that train ....and train ....+1 run to station ..... the weight of the directed arc .............,...., ........+1,.....represents the running interval between train ....and train ....+1 at station ..... When ........,.... represents the departure event, the directed arc .....................,...., ........,....+1.rep­resents the running process of train ....from station s to station ....+1, the weight of the directed arc .............,...., ........,....+1.represents the running time of the corresponding train ....from station ....to the station ....+1. When ........,.... represents the arrival event, the directed arc .....................,...., ........,....+1.represents the stopping process of train ....at station ...., and the weight of the directed arc .............,...., ........,....+1.repre­sents the stop time of train ....at station ..... According to Fig. 1, when ........,.... is primary delay, the horizontal propagation of the delay occurs through the directed arc .....................,...., ........+1,....., and it affects the next train. Vertical propagation of the delay occurs through the directed arc .....................,...., ........,....+1., and it affects the train itself. Train i -1 Train i Train i+1 Station s-1 Station s Station s+1 Fig. 1 Time event graph of train operation status (when ........,.... represents a departure event) The delay value of the train should be related to the historical value and has nothing to dowith whether the train will be delayed in the future. For the node ........,...., there are only two nodes directly related to it, the node ........-1,.... in the horizontal direction and the node ........,....-1 in the vertical direction. These two nodes also represent the delay propagation between trains and the delaypropagation of the train itself. Therefore, given the train ....and the station ...., considering the train operating state factors ........, the delay propagation factor of the train itself ........,....-1 and the delay propagation factor between the trains ........-1,...., a nonlinear function is learned to complete the prediction of .........,....: .........,.... = ............., ........,....-1, ........-1,..... (1) Among them, .........,.... is the delay time of the arrival or departure of train ....at station ..... ........ is a fea­ture set related to ........,.... based on historical data, ........,....-1is a feature set related to the vertical prop­agation of delays, ........-1,.... is a feature set related to the horizontal propagation of delays, and ....is the establishment machine learning model. 4. Methodology Fig. 2 shows the structure of the GBDT-PF model. The feature extraction part is to complete theconstruction of the input feature set. Then the GBDT model is trained to realize the prediction of.........,..... For the value .........,...., it is necessary to confirm the type of the two nodes ........,....-1 and ........-1,...., but since the original data set has no related records for the type of delay, before constructing thefeature set, the first task is to classify the delay types in the historical data, then construct a dataset that can be used for delay type identification, so as to carry out the subsequent delay predic­tion. Fig. 2 The GBDT-PF model 4.1 Cluster analysis of delay types for historical data based on DBSCAN Using DBSCAN algorithm to complete the cluster analysis of delay types for historical data isshown in Fig. 3. For ........,...., according to the characteristics of the primary delay and the secondarydelay, the input feature set of the cluster analysis is determined as shown in Table 1. Fig. 3 The process of cluster analysis of delay types for historical data based on DBSCAN Table 1 The input feature set of the cluster analysis Feature Symbol Meaning Input fea­ture set of cluster analysis ............................,.... ................................,....-1 ................................-1,.... ................................,....-1 ................................-1,.... ............................,....-1 ............................,....-1 The delay value of train ....at station ...., a positive value means delay, a negative valuemeans early, on time means the value is 0 The delay value of train ....at station ....-1, a positive value means delay, a negative value means early, on time means the value is 0 The delay value of train ....-1 at station ...., a positive value means delay, a negativevalue means early, on time means the value is 0 The delay sign of train ....at station ....-1 The delay sign of train ....-1 at station .... The deviation of running time of train ....from station ....-1 to station .... The deviation of running interval between train ....and train ....-1 at station .... The best delay classification scheme is an important basis for the classification of online datadelay categories and has a direct impact on the subsequent prediction accuracy. Therefore, dif­ferent classification schemes need to be compared to select the best scheme. For the DBSCANalgorithm, it is necessary to confirm the optimal classification number and the optimal combina­tion of parameters (radius and minimum sample size). Table 2 shows the internal indicators thatcan complete the evaluation of the classification number. Table 2 Cluster evaluation indicators Index Variable symbol Correlation Silhouette Coefficient Calinski Harabasz Score Davies-Bouldin Index ....1.... ....2.... ....3.... Positive correlation Positive correlation Negative correlation In order to compare the effectiveness of different delay classification schemes, each evalua- ' tion index is standardized. ............ represents the standardized result of the nth index. The range of ' the standardized indicators ............ is 0-1. For further comparison, the final weighted evaluationindex is calculated by Eq. 2, the final weighted evaluation index is a negative correlation index. 3' ........ = .....=1 ........·............ (2) Herein: ........ is the final weighted index, ........ is the weight of the nth index, and .....=1 3........ =1, 0 =........=1. The best parameter combination will be determined by cross validation. Establish the clus­tering model under the corresponding parameter combination, and output the number of classi­fications, the number of abnormal points, and the number of sample points in each category.There are two principles for determining the optimal parameter combination. First, select a pa­rameter combination with a small number of abnormal points. Second, choose a parametercombination with a relatively reasonable distribution of the number of sample points in eachcategory. 4.2Classification of delay types for online data based on KNN After obtaining the best delay classification scheme, construct a data set containing delay typelabels and complete the training of the delay classification model. The delay classification modelwill be completed using KNN algorithm. In KNN classification model, the K value has impact onthe accuracy of prediction. Therefore, this paper uses the 10-fold cross validation method to determine the best K value. Fig. 4 shows the process of the classification method of delay type for online data. Fig. 4 The process of the classification of delay types for online data based on KNN 4.3 Feature extraction The train operation status feature ........ are variables related to the node ........,..... First, the station in­formation and arrival/departure information of the node should be considered. Secondly, varia­bles related to ........,....-1 and ........-1,.... should be considered, including the delay value, the running in­terval between trains, and the train running time between stations, etc. In order to better characterize the delay propagation relationship, this paper defines the de­lay propagation factor of each node. The calculation method is as shown in Eq. 3, where ............................,.... is delay propagation factor of the node ........,...., ............ ,....is the delay value of nth node in the delay propa­gation chain. In particular, for nodes that are early or punctual, the delay propagation factor is 0,and for nodes that are primary delay, the delay propagation factor is 1. ............ ,................................,.... = ........ (3) . ........,.... ....=1 In the time event graph, each node has horizontal delay propagation and vertical delay prop­agation, the delay propagation factor is also different in the two directions, so there should bedelay propagation factor in both horizontal and vertical directions corresponding to each node.The vertical delay propagation feature ........,....-1 is related to the delay propagation of the train it­self, so it should be related to the vertical delay propagation factor of ........,....-1. The horizontal delay propagation feature ........-1,.... is related to the delay propagation between trains, so it should be related to the horizontal delay propagation factor of ........-1,..... Finally, the three type of input fea­tures of the GBDT model are shown in Table 3. Table 3 Input feature set of GBDT model Feature Symbol Meaning ................ Station number of the sth station ........ ........,....-1 ........-1,.... ...._....................,.... ................................,....-1 ............................,....-1 ................................-1,.... ............................,....-1 ............................,....-1 ............................-1,.... Arrival/departure sign of train ....at station .... The delay value of train ....at station ....-1, a positive value means delay, a negative value means early, on time means the value is 0 The planned running time of the train i from station ....-1 to station .... The delay value of the train ....-1 at station ...., a positive value means delay, a nega­tive value means early, on time means the value is 0 The planned running interval between the train ....and train ....-1 at station .... Delay propagation factor of ........,....-1(vertical) Delay spread factor of ........-1,.... (horizontal) 5. Experiment and simulation 5.1Data description This paper uses the actual operation data of the 1H passenger express of the West Coast Main Line (WCML) railway in the United Kingdom. There are 37 stations on the route, and the timespan is from June 1, 2017 to June 30, 2017, with a total of 47,693 records. The original data rec­ords information such as the train number, station number, actual or planned operating time,etc. Data from 75 % of the original data for model training and remaining 25 % of the originaldata for model testing. 5.2Determine the type of delay Use the weighted evaluation index ........ to determine the optimal classification number within therange of the classification number 2-10. The evaluation indicators under different classification numbers are shown in Table 4. When classification number is 9, ........ has a minimum value, so thebest classification number is 9. In the range where the radius value is 0.05-3 and the minimumsample size value is 2-20, the DBSCAN model is constructed by cross validation, and get 21 groups of parameter combination results with the classification number of 9. According to the principle of selecting parameter combinations in section 4.1, the radius is 2.15, and the mini­mum sample size is 4. According to the classification scheme, the delay type of each category is determined in a vis­ual form. In the visual analysis, the analysis is carried out from the vertical and horizontal direc­tions of the train delay propagation. Fig. 5 to Fig. 8 are the visual analysis diagrams of category 0-3, ............................,.... is represented by the color of the point in the scatter diagram. The visualization of category 0 is shown in Fig. 5. In the vertical direction, the value of ............................,....-1 is greater than or equal to the value of ................................,....-1. In the horizontal direction, the value of ............................,....-1 is greater than or equal to the value of ................................-1,..... So the train was not affected by the delay propagation in both directions. The train was delayed during operation or was delayed at this station, so it was primary delay. Table 4 The weighted evaluation index values under different classification numbers Classification number .... 2 3 4 ........ 0.682 0.839 0.315 Classification number .... 5 6 7 ........ 0.257 0.274 0.209 Classification number .... 8 9 10 ........ 0.195 0.015 0.046 a) Scatter diagram of LTdelayisand LTdiff - b) Scatter diagram of TTdelayis- and TTdiffii- ,1 - ss ,11,,1 Fig. 5 Visualization of Category 0 The visualization of category 1 is shown in Fig. 6. The delay of this train was affected by the delay propagation in both the horizontal and vertical directions, so it was secondary delay. The visual analysis results of categories 4, 5, 7, and 8 are the same as category 1. The visualization of the category 2 is shown in Fig. 7. The delay propagation occurred in the vertical direction, and the delay of the train at the previous station had an impact on this station, but there was no de­lay propagation in the horizontal direction, so it was secondary delay. The visual analysis results of the category 6 are the same as category 2. The visualization of category 3 is shown in Fig. 8. Contrary to category 2, category 3 is related to delays in horizontal directions, so it was second­ary delay. Finally, according to the characteristics of various types of delays in different directions, all data can be finally integrated into 4 types. The characteristics of the 4 types of delays are shown in Table 5, where delay type 1 is the primary delay, and the other three types are secondary de­lay. According to Table 5, the calculation methods of the delay propagation factors of the four types are different. Delay type 1 starts to propagate from the current node in the horizontal and vertical directions, and should be regarded as the primary delay in both directions. Delay type 2 are affected by the front nodes in both directions and should be calculated as secondary delay in both directions. Delay type 3 and delay type 4 are only affected by the front nodes in one direc­tion, so it is regarded as secondary delay in one direction and the primary delay in the other di­rection. Advances in Production Engineering & Management 16(3) 2021 a) Scatter diagram of ................................,....-1 and ............................,....-1 b) Scatter diagram of ................................-1,.... and ............................,....-1 Fig. 6 Visualization of Category 1 a) Scatter diagram of ................................,....-1 and ............................,....-1 b) Scatter diagram of ................................-1,.... and ............................,....-1 Fig. 7 Visualization of Category 2 a) Scatter diagram of ................................,....-1 and ............................,....-1 b) Scatter diagram of ................................-1,.... and ............................,....-1 Fig. 8 Visualization of Category 3 Table 5 Results of four types of delays Delay type Category Horizontal direction Vertical direction Result 1 0 No delay propagation No delay propagation Primary delay 2 1, 4, 5, 7,8 Delay spread horizontally Delay spread vertically 3 2,6 No delay propagation Delay spread vertically Secondary delay 4 3 Delay spread horizontally No delay propagation 5.3Model performance On the basis of determining the delay type, construct a training set containing the label of thedelay type, and determine the K value of the KNN classification model to be 4. In order to verifythe performance of GBDT-PF model, this paper will compare the random forest (RF), supportvector regression (SVR) and multilayer perceptron (MLP) that are widely used in train delayprediction, and will also verify the importance of the delay propagation feature. The optimalparameter combination of four models is shown in Table 6. This paper uses three evaluationindicators include root mean square error (RMSE), mean absolute error (MAE) and coefficient ofdetermination (R2) to evaluate the parameter combination. Table 7 shows the RMSE, MAE andR2 of each model. Table 6 The optimal parameter combination of four models The value under different feature combinations Model Parameter ........ ........,........,....-1,........-1,.... learning_rate 0.49 0.06 n_estimators 96 91 GBDT min_samples_split min_samples_leaf 300 2 284 3 max_depth 5 17 max_feature 5 3 n_estimators 80 90 RF max_features 4 6 max_depth 7 9 SVR .... loss 3.2 epsilon_insensitive 2.1 epsilon_insensitive MLP hidden_layer_sizes (20,20,20) (80,80,80) Table 7 The index values of each model under different feature combinations Model Input feature RMSE MAE R2 1.53354 0.51600 0.94404 ........ RF ........,........,....-1,........-1,.... 1.44952 0.44150 0.95000 ........ 1.67973 0.79100 0.93286 SVR ........,........,....-1,........-1,.... 1.58231 0.62100 0.94042 ........ 1.69797 0.64000 0.93140 MLP ........,........,....-1,........-1,.... 1.66474 0.60150 0.93405 ........ 1.40097 0.40600 0.95330 GBDT ........,........,....-1,........-1,.... 1.35860 0.37400 0.95608 After adding the delay propagation feature, the index value of each model is optimized.Therefore, considering the impact of the delay propagation in the delay prediction can improvethe prediction accuracy. Among the four models, the GBDT model with delay propagation fea­ture performs better on three indicators. Fig. 9 shows the distribution of the prediction errors ofeach model. Fig. 9 Error distribution of each models under different feature combinations It can be seen from Fig. 9 that the peak value of the model error distribution curve containingthe delay propagation feature is closer to the vertical axis, indicating that the overall error is smaller. The error distribution curve of the GBDT model with delay propagation feature is clos­est to the vertical axis in all models, so its overall error is the smallest and the prediction accura­cy is higher. 5.4Model simulation In order to display the prediction results of the delay prediction model more intuitively, thispaper uses the PYQT5 package to complete the simulation of the model on the Pycharm soft­ware. The simulation program design process completed by PYQT5 is shown in Fig. 10. There are two main functions of the simulation program: (1) It can display the train infor­mation, station information, departure or arrival time in real time. At the same time, differentcolors are used to indicate the current degree of delay. Green means the train is on time, bluemeans the train is early, yellow means the train is delayed within 5 minutes, orange means 5-15minutes delay, and red means more than 15 minutes delay; (2) According to train operation dataand prediction model, display the operation status of each train on the line dynamically. Accord­ing to the simulation interface, the prediction results can be viewed in real time, and the delaypropagation phenomenon can be observed. Fig. 11 shows the operation of the three delayedtrains on the line through simulation interface. 6. Conclusion This paper proposes a GBDT-PF model that considers the delay propagation feature. The effec­tiveness of the method is evaluated by taking the train operation data of the British WCML lineas an example, and the following conclusions are drawn: • Based on the characteristics of primary delay and secondary delay in the delay propaga­tion, using DBSCAN algorithm to design a clustering method of delay types for historicaldata, through this method, the delays can be finally divided into four categories. The fourtypes of delays have obvious characteristics in the vertical and horizontal direction. Andaccording to the best delay classification scheme, the KNN algorithm is used to design theclassification method for online data to identify the type of delay. • Based on the results of the identification of delay types, the delay propagation relationshipis quantified by the delay propagation factor and used as the input feature of the GBDTmodel. According to the experimental comparison results, when predicting train delays,considering the delay propagation feature can further improve the prediction accuracy. With the development of railway informatization, based on the comprehensive collection ofactual train operation data, the dispatching and commanding of railway trains will also be moreintelligent. The delay prediction model proposed in this paper can provide delay prediction datafor intelligent dispatch and make the dispatching and command work more efficient. Acknowledgement This work was supported by Sichuan Science and Technology Program (2021YJ0070). References [1] Huang, P., Peng, Q., Wen, C., Yang, Y. (2018). Random forest prediction model for Wuhan-Guangzhou HSR prima­ry train delays recovery, Journal of the China Railway Society, Vol. 40, No. 7, 1-9. [2] Wen, C., Li, Z., Huang, P., Tian, R., Mou, W., Li, L. (2019). 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Online train delay recognition and running time predic­tion, In: Proceedings of 13th International IEEE Conference on Intelligent Transportation Systems, Funchal, Portu­gal, 1783-1788, doi: 10.1109/ITSC.2010.5625081. A smart Warehouse 4.0 approach for the pallet management using machine vision and Internet of Things (IoT): A real industrial case study Vukicevic, A.a, Mladineo, M.b, Banduka, N.a,b, Macužic, I.a,* aFaculty of Engineering, University of Kragujevac, Kragujevac, Serbia bFaculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia A B S T R A C T Printing companies are commonly SMEs with high flow of materials, whichmanagement could be significantly improved through the digitalization. Inthis study we propose a smart Warehouse 4.0 solution by using QR code, open-source software tools for machine vision and conventional surveillance equipment. Although there have been concerns regarding the usage of QR inlogistics, it has shown to be suitable for the particular use-case as pallets are static in the inter-warehouse. The reliability of reading of QR codes wasachieved by using multiple IP cameras, so that sub-optimal view angle or light reflection is compensated with alternative views. Since surveillance technolo­gy and machine vision are constantly evolving and becoming more affordable, we report that more attention needs to be invested into their adaptation to fitthe needs and budgets of SMEs, which are the industrial cornerstone in themost developed countries. The demo of proposed solution is available on thepublic repository https://github.com/ArsoVukicevic/PalletManagement. A R T I C L E I N F O Keywords: Smart manufacturing;SME;Industry 4.0;Logistics 4.0;Warehousing 4.0;Pallet management;Machine vision;Internet of Things (IoT); QR code *Corresponding author:ivanm@kg.ac.rs (Macužic, I.) Article history: Received 30 May 2020 Revised 15 September 2021Accepted 17 September 2021 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 workmust maintain attribution to the author(s) and the title ofthe work, journal citation and DOI. 1. Introduction All manufacturing-oriented companies, both SMEs and large corporations, are on a daily basisfaced with the problem of managing a large number of different articles: which may vary fromvarious raw materials to components and parts. Thus, the success of each business depends onthe continuous and fluent flow of the parts in the supply chain [1]. However, the real-world situ­ation is usually opposite, since there are huge problems in establishing of the reliable supplychain, leading to increase on inventory levels to fight against fluctuations and other disturb­ances. Modern management strategies, including Lean and World class manufacturing (WCM),define an unwanted level of inventory (raw material, work in progress, or finished products) aswaste since they occupy working capital [2]. So, if there is no successful warehouse managementin every company in the supply chain, all these issues cannot be properly addressed. The new industrial platform – Industry 4.0 [3-6], aims to ease and automate the tracking andmanagement of material flow, thus improving it on the global level (supply chain management)and on the local level (warehouse management). New Warehousing 4.0 solutions are based onthe Smart Products. Therefore, they need to be identifiable at any time – which requires sophis­ticated technology [3]. The new approaches are based on the application of QR (Quick Response)code and RFID (radio-frequency identification) tags, and other I4.0 technologies such as IoT,cloud and data mining [7, 8]. Tracking of unique products allows lifecycle management of single-item customized products and optimization of their production flow [9]. In general, solutions based on QR and RFID have been the most widely used since they are af­fordable and easy to use. These are important aspects, since the companies in many countriesare lagging behind with Industry 4.0 technology adoption [10]. Although there are concerns re­garding the security of QR code, it has been widely used in marketing (opening web-page URLwritten in QR code) and/or product tracking [11]. On the other hand, RFID technology uses RFID tags for storing information, and corresponding antennas to read and write data to the tag [12]with possibility to use data encryption. Although the RFID technology is more attractive, sincemuch more data can be stored in the tag, there is a serious concern about bad influence of theRFID technology on the human body. It is a non-ionizing type of radiation, but some researchesshow that it could have a negative impact on the human body in a long-term period [13, 14].Therefore, the range of antennas used in the industrial RFID solutions has been limited to below 0.1 m, although the range could be more than 1 m [15]. It means that RFID tags cannot be readfrom the distance, but from the vicinity, like the classic one-dimensional barcode. The possibility to read QR code from the distance by using high-resolution cameras becomes the advantage ofthe QR code over the RFID technology. In 2012, Qian et al. investigated the possibilities of tracking two-dimensional QR codes in thefood industry, and compared them with the RFID technology [16]. Their evaluation found thatthe implementation of mentioned solutions increased overall cost for 17.2 % but increased effi­ciency and sales up to 32.5 %. Liang et al. proposed usage of QR code for automatic separationand identification of equipment [17]. In the recent study from 2020, Liu et al. proposed a systembased on IoT that enables remote reading of barcodes for the purpose of implementing “smartcities” concept [18]. Regarding the industry practice, QR codes are widely used for employeeauthentication1 – however, it is not widely used in the logistics. This is because the QR technolo­gy has not been shown as reliable in cases where it needs to frequently read moving objects (i.e.baggage check in airports, markets etc.). The leading manufacturer of industrial solutions for thebarcode-based tracking of pallets is the Cognex2 company, and their solutions are based on usingindustrial cameras and accompanying information systems. However, limited budgets and com­plexity of such solutions is the major obstacle for their wider usage among SMEs. On the otherside, development of dedicated solutions was limited with costs of professional industrial cam­eras, which are needed for ensuring high quality of images for reading QR codes from distance.The SME from the printing industry, a use-case in this study, was considered as the representa­tive case because there are literally hundreds of different variations (formats, weights, colors,origins, fiber orientations, surfaces, printing characteristics, etc.) of paper in the production pro­cess and supporting materials that are used daily [19]. Particularly, this study focuses on cover­ing the needs of SMEs since they generate the most workplaces and GDPs of developed countries-thus covering their needs may have considerable impact on the economy and society [20, 21]. The starting assumption of this study is that above-mentioned barriers for QR code applicationare vanishing with the technological progress, since even a standard IP camera delivers imageswith 8+ megapixels. And when it comes to the transport of materials within a company, it is im­portant to emphasize that forklifts and pallets still represent the gold standard [1], like in thisuse-case. However, to the best of our knowledge, there is no scientific study, nor publically avail­able solution, that assesses their potential and usability for a particular industrial purpose oftracking pallets in the inter-warehouse of a printing company. Accordingly, the aim of this studywas to investigate how QR code, machine vision and IP cameras could be adapted for improving pallet management in a representative SME printing company. 1 http://www.mytimestation.com [22] 2 https://www.cognex.com/ [23] 2.Materials and methods 2.1Machine vision Computer vision (CV) is an emerging scientific field that falls under the umbrella of Machinelearning (ML) and Artificial intelligence (AI). It groups algorithms that performs decision makingon the basis of observed visual inputs. CV is primarily focused on making higher-level decisionsby processing data that may not be only 2D images, but also point clouds, meshes, videos, etc. Onthe other side, Machine vision (MV) is nowadays identified as a subfield of CV that refers to theuse of CV and image processing techniques in industry setups (which means use of dedicated industry cameras, lenses, PCs, etc.) for making decisions (commonly real-time). Typical exam­ples of the use of MV in manufacturing industry are dimensional inspection [24] and defectsinspection [25]. 2.2 Internet of Things The term Internet of Things (IoT) refers to the use of devices connected to the internet, with thepurpose to measure and collect data, or control remote devices. Similarly, with the increase ofthe use of IoT, there is appearing Industrial IoT (IIoT) as a separate scientific topic. As two keyunderpinning technological pillars of the Industry 4.0, the use of CV and MV together with IoTshown a high potential for solving wide range of problems. Particularly, with the advances of networking and constant increase of IP cameras affordability and quality of images that can pro­vide in real-time. Accordingly, they have appearing as possible replacement for more expensiveindustrial cameras – especially for task such are reading QR code and tracking material flow inwarehouses. 2.3QR code technology Understanding the key concepts of QR technology is necessary for its successful application inindustry, since a developed solution needs to meet related industry standards3. The QR (Quick Response) was invented back in 1994. by Japanese company Denso Wave4, and it is composed ofparts shown in Fig. 1 The gray area indicates a clear zone with no data. Square elements in cor­ners (bottom left, top left and right) are used for detection of scale and orientation of the code.Different colors show specific zones that contain version, format, and QR code information.There are about forty versions of QR code, and the most commonly used are versions 1 and 2,which have 21 × 21 and 25 × 25 modules, respectively (dimensions determine amount of datathat could be written). The data zone also contains elements necessary for correcting errors onprinted codes, which enables reading damaged QR codes. There are four code correction levels5: L (7 %), M (15 %), Q (25 %), and H (30 %). In this study, we used version two with the M correc­tion level. Fig. 1 QR code composition as documented by the Denso company 3 https://www.iso.org/standard/62021.html (ISO/IEC 18004:2015) [26]. 4 It was initially invented for the purpose of tracking manufactured parts in the automotive industry. 5 It should be taken into account that error correction levels are related to the magnitude of the QR code (a greaterdegree of correction requires larger dimensions of the code). 2.4 Used equipment The development of the procedure was completely done in lab conditions, by using minimizedQR codes observed with multiple conventional USB web cameras. Particularly, this was possiblebecause technologies utilized in this study have robust interface for accessing various types ofcameras with minimal change of software code. The equipment used for the deployment into thereal-industry conditions included a conventional PC, network switch and NVR device connectedwith 8MP Dahua IP cameras that were mounted on the warehouse roof construction. 3. A case study: Proposed pallet management system in real industrial environment Photo from the use-case factory is shown in Fig. 2 The current practice for managing the materi­al flow in inter-warehouse is based on the standard principles of work orders in the printingindustry [19], [27-29]. Trained employees control material disposal and storage zones, and thespace is used in accordance with current needs and requirements determined by the weeklywork plan and customers’ requirements. Due to the dynamics of the business, and the companygrowth, there is an increasing need for a system able to ease the control of pallet flow and pre­vent frequent delays. Particularly, the continuous and increasing production often results inaccumulated inter-resources/products, significant space congestion and waste of time that em­ployees spent to search for missing pallets and parts necessary for the initiation of further man­ufacturing processes. Although the warehouse space is graphically coloured, it rarely easies em­ployees’ efforts because of the previously explained reasons. 3.1User requirements From the SME management standpoint, the disadvantages of the current practice are: • Due to the high frequency and overload, forklift drivers often do not comply FIFO rules –which results with misallocated pallets. • Pallets that are misallocated significantly increase the time needed to afterwards find andsort the pallets available in the warehouse. For the company, it is very important to beable to quickly identify complete work orders and the location of their pallets (tabs). • Failure to accurately and efficiently inventory all available pallets in the storage causes de­lays in subsequent manufacturing operations. Process engineers have reported that thedelay could be up to three hours -causing significant losses in the profit and productivity. • The solution needs to be easy to use and accessed by both management and employees on the site. It should be able to deliver a fast report, which contains documented current sta­tus and alignment of materials (pallets) through the production space. Fig. 2 A typical temporary or intra-warehouse of a printing SME. After finishing one operation, the tabs arestacked on pallets until they are requested by a following manufacturing process 3.2Pallet management by using QR code, machine vision and IP cameras Concept of the proposed solution is illustrated in Fig. 3. The solution was released as a series ofmodules, which do particular tasks: 1) Image acquisition, 2) QR codes detection, 3) User interac­tion (GUI), and 4) Reporting. The image acquisition was carried out with conventional IP cameras that were fixed on a roofconstruction (Fig. 4c). Key components of the surveillance6 system are IP cameras, network vid­eo recorder and central management software. The central PC-server runs the Python applica­ tion (the GUI was developed by using the Qt5 library), which processes incoming images on userrequest. Beside the standard Python libraries for data structures and numeric, OpenCV (imageacquisition and processing) and python-docx library (generation of MS Word documents) wereused, together with the QR code library for processing QR codes. Detailed architecture and UMLworkflow diagram of the solution are given in Fig. 4 In Fig. 5, we present the captures of our im­plementation in an SME that annually processes ~40 million tabs of paper. Fig. 3 Concept of the proposed solution Fig. 4 Software architecture and UML Workflow diagram of the proposed solution 6 For the purpose of this study, we used DAHUA IPC-HFW2831TP-ZS 8MP WDR IR Bullet IP Camera (4x), with DAHUAPFS3010-8ET-96 8 port Fast Ethernet PoE switch. Host PC had CPU 1151 INTEL Core i3-8100 3.6 GHz 6 MB BOX,results were visualized in HISENSE 40" H40B5100 LED Full HD digital LCD TV and printed on Printer HP LaserJet ProM102a. The starting point of the workflow is the moment when a manager assigns a work order to anemployee. Orders physically represent a series of tabs /sheets transported on pallets with fork­lifts (Fig. 4, right). For each incoming tab, one has to print an appropriate QR code by using theproposed software application. The generated QR code contains the following information thatdetermine one tab: 1) work order ID, 2) total tabs within the order, and 2) tab ID. The adaptedformat of the string data written in QR code is "XXXX ,YY/ZZ": the XXXX indicates the order ID(maximum is 9999 annually), YY indicates the total number of tabs in the work order (maximum 99)and ZZ indicates the tab ID. Below the QR code (which is not readable to humans), we printreadable information and time of the code generation, which are fused on a single file and print­ed on the printer connected to the local network (Fig. 5b). The sample QR code placed on thepallet is shown in Fig. 5d, while the print format is shown in Fig. 5e. The left side of the screen isreserved for user commands (printing QR, querying detected tabs etc.). Visualization of results isdone in the middle of the screen, while on the right side are lists of the inventory result. The useris allowed to query the inventory list with respect to orders (complete, incomplete) and tabs. Inorder to enable fast and intuitive inspection, we colored items found in the lists – so that the reditems/orders indicate error, yellow items indicate incomplete orders and green indicate com­plete orders. On this way, employees could easily spot complete orders, and initiate the accom­panying manufacturing process that waits for these pallets to be transported through the manu­facturing hall. Another supported functionality is the generation of MS Word reports, which in­clude a list of all orders and corresponding tabs (grouped on complete and incomplete). In thisway, the company could document and track the pallets flow and management through time ­with the aim to spot bottlenecks and make improvements. Fig. 5 Preview of the implemented solution: a) Large screen and server (including PC, switch and NVR device)placed in the protective box; b) Printer placed in the protective box; c) Dahua 8MP IP camera mounted onthe roof construction; d) QR code placed on the top of the palate; e) QR code format Fig. 6 Capture of the system usage in industry conditions. The upper left are commands for querying and printing ofQR codes, while the below are lists of tabs (a user is allowed to view all tabs or only tabs that belong to particularwork orders). In the middle are visualized positions of tabs that belong to a particular work order. On the right sideare a list of cameras and a list of tabs visible on the particular camera 4.Discussion Materials Management Systems (MMS), independently or as part of Enterprise Resources Plan­ning (ERP) systems have been one of the interesting and promising directions for the develop­ment of supported hardware/software supply chain platforms in recent years [30]. Although theavailable ERP solutions are numerous and varied (from complex to simple ones), there is still asignificant lack of ERP modules or independent systems that can enable (near) real-time moni­toring and monitoring of material status and flow at the store level (warehouses, warehousemonitoring and inventory tracking). For this reason, the need for research and practical work toaddress the problem identified is justified and it could lead to results that can make progress forboth the industry and the scientific community. Since the most of printing companies are SMEs,investment into complex or expensive commercial solution often represents a major obstacletowards their digitalization. Accordingly, the proposed solution was developed with aim to avoidthese obstacles (the overall hardware installation costs were about 2000 EUR), and it representsso-called “low-cost automation” [31, 32]. Particularly, we emphasize the needs of SMEs becausethey generate the most of the GDP and employment opportunities in developed countries [20]. Therefore, although there are more robust and general-purpose ERP solutions – still a lot of ef­fort needs to be invested into development of dedicated solutions for specific problems. To sumup, dedicated alternatives, such as the proposed solution, may represent a valuable improve­ment of the current pallet management practice and may result with considerable impact in SME industry sectors. Accordingly, we made the proposed solution available on the public repository: https://github.com/ArsoVukicevic/PalletManagement [33]. In this study, the reliability problem of QR readers [34] was solved with the usage of multipleIP cameras. Briefly, if one camera fails to detect a pallet (due to a suboptimal viewing angle,lighting etc.), another IP camera commonly succeeds. On this way, chances that some pallet maybe omitted are drastically decreased. We emphasize that the solution was realized by using four8-megapixel Dahua IP cameras, and we do not recommend to use low-resolution or lower-tierbrands. The aforementioned pixels and the number of cameras have shown to be quite sufficientto cover a space of 10 x 20 meters from the height of about 4.5 meters (which corresponds to theheight of the roof support in the manufacturing hall). Furthermore, we preferred to print QRcodes on a conventional PC printer, in A4 format, which is widely used in offices. Although wehave not experimented with smaller paper sizes, the assumption is that a professional QR print­er could be also used -but, in this way, one would increase the cost of equipment and softwaredevelopment. The major limitation of the proposed solution is that the reading QR code is itssensitivity to folding – which we solved by cardboard carrier. The remaining concern of readingfalse QR codes (e.g. that could appear on products or parts available in factory) or misuse andmisplace of QRs is unlikely to happen in industry environment by company employees. Regard­ing the impact of the developed system on the logistics in the considered company, as the inven­tory list is done in terms of a few seconds – the achieved speed is incomparably higher than thepossibility of a manual search and inspection of the warehouse by employees. In particular, weremind that, based on the employee experience and reports, manual searching for the missingpallets can take up to three hours. For this reason, the advantage of the digitized system is obvi­ous and there was no need for statistical analysis of the performance improvement. Finally, thesolution is easily adaptable to various environments – as the only adjustment needed is mount­ing of conventional IP cameras. The further work on this topic may be regarded to improvementof security, trackability and integrability into existing ICT platform, for which various technolo­gies could be applied including blockchain [35]. 5. Conclusion Beside technological advancements that bring Industry 4.0, the flow of products and raw mate­rials within companies is still underpinned with forklifts and pallets. Since management of pal­lets in inter-warehouse still depends on human factors, many companies are faced with delayscaused by operator’s inability to timely manage large amounts of pallets. As a representativeuse-case, we considered a SME company from the printing industry since there are literally hun­dreds of different variations of paper (formats, weights, colors etc.) in the production process.Although there are available commercial warehouse barcode-based solutions for tracking pal­lets, complexity and cost of such solutions represent major obstacles for their wider usage by SMEs (which budgets are limited). As an alternative, we assessed the low-cost solution for thepallet management with QR code, machine vision and IP cameras (demo is available at https://github.com/ArsoVukicevic/PalletManagement [33]). The compact solution was devel­oped by using free open-source software libraries and conventional surveillance equipment.Although there have been concerns regarding usage of QR code-based solutions for tracking, wereport that it is suitable for the particular purpose of warehouse inventory since pallets are stat­ic. Reliability of the solution was ensured by using multiple IP cameras, which ensures that if onecamera fails to detect QR code another one will compensate for it. The recent evolution of IPcameras (which now have 5+ megapixels) made them affordable and efficient tools for readingQR codes from larger distances. Thus, we conclude that more attention and effort need to beinvested into investigation and adaptation of widely available technologies that could fit theneeds of SMEs. 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Increasing Sigma levels in productivity improvement and industrial sustainability with Six Sigma methods in manufacturing industry: A systematic literature review Purba, H.H.a, Nindiani, A.b,*, Trimarjoko, A.a, Jaqin, C.a, Hasibuan, S.a, Tampubolon, S.a aDepartment of Industrial Engineering, Mercu Buana University, Jakarta, Indonesia bIndustrial Engineering Program, Buana Perjuangan University, Karawang, Indonesia A B S T R A C T Industrial sustainability is an important attribute and becomes a parameter ofthe business success. Quality improvement with an indicator of increasingprocess capability will affect productivity improvements and lead to industri­al competitiveness and maintain industrial sustainability. The purpose of thispaper is to obtain a relationship between the consistency of the DMAIC phase to increase the sigma level in productivity improvement and industrial susta­inability. This paper applied for a systematic literature review from various sources of trusted articles from 2006 to 2019 using the keywords “Six Sigma, Productivity, and Industrial Sustainability.” A matrix was developed to provi­de synthesis and summary of the literature. Six Sigma approach has been successful in reducing product variation, defects, cycle time, production costs,as well as increasing customer satisfaction, cost savings, profits, and competi­tiveness to maintain industrial sustainability. Extraction and synthesis in this study managed to obtain seven objectives value that found a consistent relati­onship between the DMAIC phase of increasing sigma levels, productivity, andindustrial sustainability. The broad scope of Six Sigma literature is very bene­ficial for organizations to understand the critical variables and key successfactors in Six Sigma implementation, which leads to substantial long-term continuous improvement, the value of money, and business. A R T I C L E I N F O Keywords: Manufacturing;Sustainability;Industrial sustainability;Six Sigma;Increase of Sigma level;Productivity improvement;Industrial competitiveness *Corresponding author:aina.nindiani@gmail.com(Nindiani, A.) Article history: Received 30 July 2020 Revised 24 October 2021 Accepted 26 October 2021 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 workmust maintain attribution to the author(s) and the title ofthe work, journal citation and DOI. 1. Introduction Customer satisfaction in maintaining industrial sustainability is the key to business success in anincreasingly competitive industrial era. Organizational / industrial competitiveness is one of theimportant attributes in increasing customer satisfaction to maintain industrial sustainability [1](Ramana and Basavaraj. Maintaining industrial / company competitiveness can be performed byincreasing productivity/sales, expanding marketing reach, and maintaining customer retention/loyalty by maintaining and improving the quality of its products [2, 3, 4]. Improving quality andproductivity and maintaining customer satisfaction are important attributes in increasingcompetitiveness and maintaining industrial sustainability. Quality is an important issue in thehighly competitive modern business world [1] (Ramana and Basavaraj, 2018); even quality is a key factor for consumers to decide on products and services offered by producers. Quality hascustomer satisfaction orientation [5] (Khawale et al., 2017). In order to meet the quality of products expected by customers, an organization / company is always required to understandwhat is desired by customers by conducting various research and development to further design and create a product that has superior characteristics that are oriented to the desires andsatisfaction of customers [6, 5]. Productivity is an indicator of success for an organization /company / country [7] (Maheshwari and Taparia, 2019). Productivity has the concept of how toproduce or increase the production of goods and services optimally by utilizing resourcesefficiently [8] (Thorelli, 1960). Customer satisfaction is a response from the comparison ofproduct performance with several standards before, during, and after consumption [9, 10, 11]. Customer satisfaction can be formed if the organization is able to provide productcharacteristics or attributes that meet customers’ expectations and will have an impact on thereuse of products that have been used and can help improve the company’s image throughinformation about the products to other customers [12, 13, 14]. There are many strategies ormethods or approaches that can be used in an effort to improve quality, productivity, andcustomer satisfaction, one of which is the Six Sigma approach. Six Sigma is a systematic andstructured approach to increase performance / productivity and quality in meeting customersatisfaction to gain increased company profits [15, 16, 17, 18, 19]. Six Sigma has a systematic and structured method namely: Define, Measure, Analyze, Impro­ve and Control (DMAIC) which is a stage of quality improvement with the concept of reducingthe number of defects by up to 3.4 parts per one million opportunities which is very suitable inmodern business that focuses on increasing customer satisfaction, productivity, and financialperformance [15] (John and Areshankar, 2018). The basic concept of Six Sigma is to adhere toprinciples for process improvement through reducing variation, using statistical methods, fo­cusing on customers, paying attention to processes, and management systems that focus on highyields that generate significant and continuous financial gains [20, 21, 22]. The level of readinessof the organization / company such as operating systems, measurement systems, employee in­volvement, environmental conditions, and the concept of continuous improvement greatly affectthe success rate of Six Sigma implementation [23]. Six sigma success indicators in improving quality and productivity can be known by increa­sing the capability of the process (sigma levels) and the financial benefits obtained. Rahman et al. [17] in his research, succeeded in reducing defects such as broken stitches and open seam by35 % and increasing sigma levels from 1.7 to 3.4. Rana and Kaushik [19] in the Six Sigma imple­mentation have proven to reduce defects and increase productivity. In addition to other benefitsthat did not materialize (initiative, competitiveness), the DMAIC results showed that the defecti­ve washer thickness declined from 1550 PPM to near to 100 PPM within four months. In ad­dition, Barbosa et al. [18] in his research using Six Sigma implementation (DMAIC), proved thatit reduces defects and increase the Quality Rate of 41 % from 19 % to 60 % and Cp in Bead Apexprocess of > 1.33. Sardeshpande and Khairnar [24] used the Six Sigma method and succeeded in increasing the sigma level in the four wheels industry from 1.2 to 3.2. Subsequently, Ganguly [25]in his research, succeeded in reducing cycle time from 47 days to 20 days in one productcycle. Syafwiratama et al. [26] in his research, succeeded in increasing process capability (sigmalevels) from 2.2 to 3.1 and making a profit of $ 18,394.2 per month. Furthermore, Malek andDesai [27] state that the Six Sigma approach is a paradigm that leads to business excellence ba­sed on the improvement of processes that have been proven to be widely adopted by variousindustries to respond to changes in customer desires or needs. This research succeeded in in­creasing sigma levels from 3.1 to 3.7 and reduced the reject rate from 15.50 % to 4.47 % orequivalent to 71.2 % and provide a cost-saving of INR 18,27,402. Gandhi, Sachdeva, and Gupta [28] revealed that the Six Sigma approach is a systematic andscientific operations management methodology that aims to increase the ability of the produc­tion process by reducing waste. This research succeeded in reducing cylinder block defects from28,111 to9,708 DPMOandprovidinga profitofINR12,56,640.Kosieradzka andCiechanska [23]in their research with Six sigma implementation succeeded in increasing sigma levels from 3sigma with DPMO = 33333.00 to 6 sigma with DPMO = 0 and Cp value = 1.91, Pp = 0.53, Cpk =1.88, Ppk = 0.52 to Cp = 3.79, Pp = 3.32, Cpk = 3.34, Ppk = 2.29. Based on the statement of theresearch, there was a mistake of the DPMO value of Six Sigma should not be zero but 3.4. Cha-bukswar et al. [29] in his research stated that the basic concept of Six Sigma is to strengthen theprocess by modifying to increase the process capability to be able to produce defect-free pro­ducts so that it can satisfy the customer. This research successfully identified the problem thatwas happening and managed to increase the process capability from 1.5 to 4 and reduce theprocess reworking 50 % and giving a profit of Rs 90 to 95 lakhs per year and increasing overall efficiency by 30 % in improving overall product quality. Morales et al. [30] in his research usingSix Sigma, succeeded in reducing scrap from 18 % to 2 % in improving plant layout in an effortto increase productivity. Chang and Wang [31] in their research using CPFR implementation (Collaborative planning,together with forecasting and replenishment) can increase forecast accuracy by 10-40 %, reduceinventory costs by 10-40 %, save transportation costs by 0.3 % and 1 % and increase customerservice levels by 0.5-4 %. CPFR has been recognized as one of the most efficient methods to im­prove forecast accuracy, minimize inventory, increase service levels and reduce costs, researchresults using Six Sigma were known to reduce the Mean Absolute Percentage Error (MAPE) from 19.37 % to 5.26 %. They could reduce holdout products from 17.7 % to 5.18 % so that CPFR canhelp SCM to be better and can increase the confidence of business partners and increase thecompetitiveness of companies in an increasingly competitive era. Rahman and Talapatra [32] intheir research using the Six Sigma approach in the casting industry, succeeded in reducing defectproducts (DPMO) from 609,302 to 304,651 and increasing the Sigma level from 1.2 to 2.0. Inaddition, Srinivasan et al. [33] used the Six Sigma method in the nozzle furnace industry andsucceeded in increasing the sigma level from 3.31 to 3.67 and providing a cost saving of INR 0.125 million (the US $ 1953). Therefore, increasing the level of sigma proves that DMAIC is ableto improve product quality, which results in cost reduction and increased competitiveness. Ac­cording to the various literature studies above, it can be concluded that Six Sigma provides mea­surable indicators with the help of statistical methods and can be combined with other tools ofanalysis which are proven to be able to reduce product and process variability and be able toimprove process capability through reducing defects, reducing process time so that it can reduceproduction costs, increase customer satisfaction and will certainly increase company profits inan effort to maintain the sustainability of the industry/organization on an ongoing basis. 2. Consistency of D-M-A-I-C phase, increase of Sigma level, productivity improvement and industrial sustainability Six Sigma is a systemic, scientific, measurable, flexible and effective method of defining, mea­suring, analyzing, improving and controlling a problem to get better process capability by redu­cing process and product variations that aim to improve quality, increase productivity, increasesatisfaction customers, increase competitiveness and also increase company profits in mainta­ining industrial sustainability. The structured method is known as the Define, Measure, Analyze,Improve, and Control (DMAIC) cycle, which has a concept of 3.4 defects per one million products[34, 35]. Broadly speaking, the intended DMAIC cycle can be understood in the description, aspresented in Table 1. The table shows a general description of the DMAIC cycle performed in theproblem-solving of each phase, including description and activities carried out in the implementation of the Six Sigma method. Table 1 Description of the DMAIC cycle Phase Description of process activities Define Identify a problem/project base on a business objective Define project scope and goal bases on customer requirements Develop project charter and determined crucial to quality (CTQ) Measure Collect data, facts and carry out measurement systems Mapping process representations base on data collection Measure the process capability and study the differences (gaps) that occur Table 1 Description of the DMAIC cycle (continuation) Phase Description of process activities Analyze Perform data analysis to find the cause of the problemClarify the cause of the problem to find out whether the problem is a vital factorDetermine the priority scale of each cause of the problem Improve Discussion to determine alternative improvements that can be implementedCarry out improvements according to the results of the discussionVerification of key variables in the implementation process Control Control process variations according to customer requirementsDesign monitoring and controlling strategies for improvement resultsVerify project objectives and plan for further improvement 2.1 Consistency of DMAIC phase The Six Sigma approach is a systematic and scientific method of operations management thataims to improve the capability of the production process by reducing all wastes [28]. Six sigmaapproach with systematic phase namely DMAIC with statistical analysis tools has been proven tobe widely adopted in various industries both manufacturing and services that can reducevarious wastes, increase productivity, provide cost savings and increase company profits [36,26, 33]. The consistency of the DMAIC phase in this study was analyzed from various studies toselect research that was consistent in carrying out the entire DMAIC phase with standard tools that have been set on the Six Sigma method. The consistency of the implementation of theDMAIC phase using the Six Sigma method applied in various industries involving various researchvariables has succeeded in identifying, measuring, finding key factors, taking improvementactions and controlling problems so as to get better process capability (sigma levels) which ischaracterized by the reduction of defects, reduced cycle time, reduced accident rates, reducedbreakdown / downtime, also improved planning accuracy with actual production and increasedcompany/organizational profits. Through these indicators, the DMAIC Phase consistency provedto have a positive effect on improving quality and productivity and maintaining industrialsustainability. 2.2 Sigma levels Process capability / sigma level is used to determine the performance capability of a process inproducing goods or services based on established technical specifications [37, 38] so that it isknown whether the process is within the expected limits or strict controls are needed for theongoing process. Gupta et al. [39] in a study of the tire industry in India, revealed that Six Sigmais known to reduce the standard deviation from 2.17 to 1.69, and increase process capability(Cp) from 1.65 to 2.65 and Cpk from 0.95 to 2.66. This study shows that Six Sigma using DMAIC phase successfully lower the deviation standard from 2.17 to 1.69 which means that productvariations can be suppressed so that product quality is better, the stability of the process can beimproved as indicated by an increase in the Process capability index (Cp) from 1.65 to 2.65 andCpk from 0.95 to 2.66. However, the result of the decreasing deviation standard value to 1.69 isquite high. It still gives the possibility to bring up unexpected conditions to happen. Thus, it canbe concluded that an improved process capability index will stabilize the process and producebetter quality so as to indicate better productivity. Primanintyo et al. [40] in his research using Six Sigma and DOE as the Improvement method,succeeded in increasing the sigma levels in the Curing process of the tire industry in Indonesiafrom 3.092 sigma to 4.029 sigma. Gerger and Firuzan [22] in their research, explained that Six Sigma’s main focus is to reduce the potential variability of processes and products by using astructured continuous improvement methodology, namely DMAIC. Six Sigma provides discipline,structure, and a foundation for solid decision making based on simple statistical analysis. Thereal strength of Six Sigma is simple because it combines the strength of people / management(project sponsor, project team leader) with the strength of the process (floor production/projectteam members) to get good process capability to improve organizational competitiveness. Thisresearch succeeded in reducing cycle time by 50 % from the previous conditions and can provide a profitof$167,895 peryear.Zasadzien[41] revealed in the study that a complex and flexible system for achieving, maintaining, and maximizing business achievement is characterized by understanding customer needs and the use of facts, data, and statistical analysis in an organized manner and based on lean management and continually creating newones. The better the solution by referring to the next process, aimed at minimizing the cost ofpoor quality while increasing customer satisfaction, this study succeeded in reducing downtimefrom 18 hours to 9 hours. According to these research examples, interpretation of sigma levelimprovement shows that process capability and level of process and product variation are betterso that the potential for defects produced is more controlled. Customer satisfaction and com­pany profitability can certainly be increased. 2.3Productivity improvement Productivity is an indicator of the success of an organization /company [7]. Productivity has theconcept of how to produce or increase the production of goods and services optimally by utili­zing resources efficiently [8]. An increase in productivity due to the literature can be interpretedas how companies / organizations utilize their resources in the form of tangible and intangibleassets effectively and efficiently to obtain optimum profits. The Six Sigma method (DMAIC) is astructured method for identifying, analyzing cause and effect, as well as opportunities for im­provement of an ongoing problem that aims to maintain the stability of the process to get pro­duct quality improvement and increase company profits [18]. The implementation of Six Sigmahas been proven to reduce disability and increase productivity, in addition to other benefits thatdo not materialize, such as initiative and competitiveness [19]. Six Sigma is a scientific, systema­tic and superior method of responding to changes that occur in the business world and is able toimprove quality and productivity through reducing the variety of processes and products [27,28, 23]. There is a positive relationship between the Six Sigma approach to productivity impro­vement due to some literature, which is characterized by a decrease in variations in processesand defects that result in decreased cost production and increase cost-saving, competitiveness,and company profits. 2.4 Industrial sustainability Industrial sustainability is the key to business success in an increasingly competitive industrialera, even in the last two decades, a total of 92 % of 200 companies published their industrialsustainability reports independently or in an integrated manner [42]. Sustainability reportshave evolved over time and are considered an important component of organizationaloperations that are communicated annually to stakeholders through the sustainability report[43]. In this context, stakeholders increasingly demand transparency and accountability fromcompanies regarding tangible sustainability performance [44]. This proves that the sustaina­bility of an industry is an important attribute in the business world. Improving product /servicequality and satisfaction, as well as maintaining customer loyalty, are strategies that can becarried out by the industrial world in maintaining the sustainability of the industry. [45, 46, 47]state that customer satisfaction affects the creation of customer loyalty, which will affect the company’s revenue or profit and this is a major factor of industrial sustainability. 3. Materials and methods The systematic literature review (SLR) method is a method of literature review that identifies,evaluates, and extracts / sites research findings that are useful in answering determining rese­arch questions [48]. Bolderston [49] revealed that a good literature review adopts severalimportant rules, such as: (1) is able to extract new ideas from previous research by synthesizingand summarizing previous sources. New theories can be built from the evidence discussed andmay provide new directions for future research. (2) A literature review may also facilitate theuse of the best available evidence in daily practice to provide answers to research questions.This study is a systematic literature review on the implementation of Six Sigma and looks for therelationship between the consistency of the DMAIC phase to improve process capability (sigma levels) and productivity to increase customer satisfaction in maintaining industrial sustain­ability. This study is initiated by collecting a variety of literature in the form of trusted articles fromvarious sources, such as Google Scholar, Research Gate, Proquest, Academia.edu, and othersources using the keywords “Six Sigma, Productivity, and Industrial Sustainability.” Furthermore,the works of literature obtained are then classified by name and country of author, year ofpublication, publisher, research variables, research objectives, tools used, and research resultswith the target of obtaining a literature review matrix that is useful for providing synthesis andsummary of the literature that has been obtained to answer the research question as mentionedearlier. The phases used in this study can be seen in the Conceptual framework of literaturereview, as presented in Fig. 1. Fig. 1 describes the whole phase and a review of each phase in this study that starts fromdefining the research goals, namely: The consistency of the DMAIC phase to increase processcapability (sigma levels) and productivity improvement and industrial sustainability. The concept of sigma level, productivity, industrial sustainability, and Six Sigma approach arepreliminary discussions followed by a collection of literature for the synthesis of the consistencyof the DMAIC phase, sigma level, and productivity improvement, and industrial sustainability.Materials and Methods discuss the concept of Systematic Literature Review (SLR), followed by the conceptual framework of the literature review, which is an overview of the stages of thisstudy. Stages of results and analysis presented include gaps / findings of the literature review,objective of the research, and recommendations for further research. In the last stage, theconclusions and limitations of the study and statements about this study are presented. Define Goal of Research Effect of consistency of DMAIC phase on the increase of process capability (sigma level), productivity and industrial sustainability Fig. 1 Conceptual framework of the literature review 4. Results and discussion 4.1 Gaps/findings of literature review The study is a literature review, which is a review of various journals and proceedings about theSix Sigma implementation in the manufacturing industry from various publishers starting from2006 to 2019. Details of the literature and tools used in this study and the findings obtained canbe seen in Table 2. Table 2 Tools for literature review used and the research findings Author, Year, Tools used No. Country, Industry, Result Variable Define Measure Analyze Improve Control 1 [1]Ramana and VOC, VOB, Brainstorming Pareto diagram Brain-Standardi- Operational Basavaraj, 2018,Business cause and stormingzation standard pro-India, Capacitor, mapping, effect diagrampurpose of cedure, tra-Defects SIPOC dia-(CED) solution ining, and con- gram, CTQ(FMEA) trol plan to analyze reduce defects 2 [17]Rahman et al. Voice of Pareto dia- Defect rate DOE, ANOVA Defect rate Reduce defects 2018, Bangladesh, Customers gram, sigma(DR), CED (DR) by 35 %, incre-Garment, Defects (VOC) level mea-ase sigma level surement 1.7 to 3.4 3 [19]Rana and Ka-VOC, FlowGauge R&R RCA, Brain- Corrective PPM mea- Reduce defects ushik, 2018, India, diagram,study storming Trial Actions with surement, from 1550 PPM Automotive SMEs,SIPOC dia-base on Com-testing standardi-to almost 100 Defects gram parison Worstzation PPM in 4 of Worst months (WOW) vs. Bestof Best (BOB), Histogram 4 [18]Barbosa et al. Data collec-CED, Brain- Cp analysis Taguchi DOE Validate the Increase qua­2017, Italia, Tyre, tion of storming, method experimen-lity rate fromDefects customer Pareto dia-tal results 19 % to 60 % requirements(NC classifica-gram, Xchart and R (cpkand Cp > 1.33 analysis tion parame-and Qualityter) Rate) 5 [24]Sardeshpande SIPOC dia-Control chart, Pareto Chart, RegenerationProcess Increase the and Khairnar, 2014,gram, ProcessCost-benefit Histogram, CED analysis, RCA, capability sigma levelIndia, Automotive, mapping analysis, CTQQFD from 1.2 to 3.2 Defects tree 6 [50]Kumar andData collec-Focused group Pareto dia- Corrective Control Reduce Naidu, 2012, India, tion discussion gram, CED action plan employee Garment, Employee absenteeism Absenteeism from 25-35 % to 11% 7 [25] Ganguly, 2012,Historical Defining all Scatter dia-DOE Control Reduce cycle India, Aluminium, data, VOC,possible cau-gram, linearplan (con-time of RollingCycle Time SIPOC dia-ses (FMEA),regression,trol chart, mill 47 days to gram CTQ matrix, ANOVA MSA) 20 days MSA 8 [26]Syafwiratama et Data collec-Sigma level, Brainstorming DOE X bar chart, Increase sigma al. 2016, Indonesia, tion, Pareto four-block vital factor Sigma level, level from 2.2 Polyester, Defects diagram diagram analysis (t-test) four-block to 3.1 and diagram profit of $18,394.2 /month 9 [27]Malek and De-SIPOC, CTQ Gauge R & R, p CED, Regressi- DOE, monito-Control Increase sigma sai, 2015, India,tree chart, capabili-on analysis, ring impro-plan, Ope-level from 3.1 Casting, Defects ty process why-whyvement pration-al to 3.7 and (sigma level) analysis chart, COPQ standard profit of INRanalysis procedure 18,27,402 Table 2 Tools for literature review used and the research findings (continuation) Author, Year, Tools used No. Country, Industry, Result Variable Define Measure Analyze Improve Control 10 [51] Naidu, 2011,Brain-Data collection Average data Maintenance Regression Decrease India, Steel, Break-storming of repair timebreakdown in schedule & correlati-breakdown down Time and inspection one year, Pare-on analysis from 92.42 time to concept hours To 59.0 hours 11 [28]Gandhi, Sachde-CTQ analysisData collec- P chart, t-test Three possi-Sigma level Reduce rejectva, and Gupta, 2019, with VOC and tion, Pareto (Anderson-ble solutions mea-from 28,111 toIndia, Casting, Reject Pareto dia-diagram, CED Darling), Why-surement, 9,708 DPMO of Product gram why analysis overall and provides a rejectionprofit of INRtrend, t-12,56,640 test, Cost-Benefit Analysis 12 [23]Kosieradzka andSIPOCR Data collection Capability The 8D pro-Cp and Cpk Increase sigma Ciechanska, 2018, and control of analyzed Cpcess and Pp andlevel from 3 to Poland, Various, element, Pare-and Cpk and PpPpk mea-6 and Cp =Defects to concept and Ppk Causesurement, 1.91, Cpk = Effect matrix, SPC (con-1.88, to Cp =PFMEA trol chart) 3.79, Cpk =3.34 13 [29]Chabukswar et VOC, ProcessData collection Verification of DOE Control Increase sigmaal., 2011, India, flow dia-relationshipsplan, SPC level from 1.5 Pharmaceutical, grams, Base-and causality ofto 4.0, andDefects and Rework line of the factors provide a Time manufactu-profit of Rs 90 ring process to 95 lakh/year 14 [30]Morales et al. Process map,Measurements CED, CE matrix Discussions SPC Reduce scrap2016, Mexico, Con-Pareto dia-of the con-relation of from18 % to 2 crete Blocks (Con-gram veyor down-possible%, breakdownstruction), Break-time caused ma-molding fromdown, and Scrap trix 87 to 43 cases 15 [52] Zhan, 2008,Establish a CTQ tree, DOE, Pareto Modeling & SPC Reduce Devia-USA, Motor, Average project scopeNormality test, chart Simulation tion Standard Speed Variation with clear speed motor by 74 %, targetgoals measurement of 60 % 16 [53] Gajbhiye et al. SIPOC, 5-S Audit 5-Why + Safety 5-S Audit, Safety Decrease ha­2016, India, Casting, SMART,(Safety, Sort, Analysis, FMEA, Safety Con-Impro-zards and risk Hazards and Risk PDCA, SWOTStraighten, RCA trol Sheet, vement controls score Controls analysis andShine, Sustain) Safety Im-Plan and machining Cause and provementPost Kaizen section from Effect Plan, andEHS Chec-2.34 to 4.34 analysis Post Kaizen klist EHS Chec­klist. 17 [31]Chang and. Historical Collect data MAPE, autocor- ARIMA model Control Reduce MAPE Wang, 2008, Taiwan, data, Meansales relation func-charts from 19.37 % Various, Forecasting absolute tion (ACF), to 5.26 % and percentagepartial autocor-(holdout) from error (MAPE) relation func-17.7 % to 5.18 tion % (PACF),control chart 18 [54]Chang et al. SIPOC, t-test, Mann– Sigma level, ComparisonCp mea- Reduce avera­2012, Taiwan, Semi-Questionnaire Whitney test, Control chart planning vs. sure,ge delay fromconductor, Produc-and error actual result Question-0.54 to 0.30 tion Planning measures naire Table 2 Tools for literature review used and the research findings (continuation) Author, Year,No. Country, Industry, Variable Define Measure Tools used Analyze Improve Control Result 19 [32] Rahman andData collec-Talapatra, 2015,tion, Pareto Bangladesh, Casting, diagram Defects Baseline per­formance (sigma level), Pareto dia­gram CED DOE, ANOVA Control comparisonplan of data be­fore vs. after improvement Reduce defects (DPMO) from609,302 to304,651, in­crease Sigma level from 1.2 to 2.0 20 [33] Srinivasan et al. Pareto dia­2016, India, Furnace,gram, VOC,Defects SIPOC dia­gram Descriptive statistic, Gau­ge R and R Brainstorming, DOE, sigmaCED level mea­surement ComparisonIncrease sigmabefore after level from 3.31 of data to 3.6 and provide cost-saving of INR 0.125 million (US$1,953) 21 [5] Khawale et al. 2017, India, Piston, Defects SIPOC VOC to CTQ CED DOE Control plan New standard operation procedure 22 [55] Purnama, Gu-Data collec­nanto, and Sugengri­tion adi, 2019, Indonesia, Manufacturing (ot­her), Environment Management Pareto dia­gram Stratify of dataCorrective analysis, RCA action (tra­ining) SOP Increase posi­tive trend from 220 % to 700 %. 23 [56] El Hassani, 5W 1H, Pro-Benlaajili and Nokra, cess map, a2017, Maroco, Sugar,Black box of Defects the process Study of R & R,DOE, ParetoANOVA, Con-chart trol Charts, Process Capa­bility Desirabilitystudy, Theboxplot,Process Ca­pability Control Charts, standardi­zation Increase Ave­rage cp Aper­ture/ OpeningMedium (OM) from 0.43 to 1.47 Coeffici­ ent of Variati­ on (CV) from 0to 1.5 24 [57] Sokovic,PavleticHistorical and Krulcic, 2006,data Slovenia, Automotivepart, Cycle Time Pareto chart, discussion FMEA, ANOVA,Brain-Control Correlation storming, plan matrix Experiment, Cp analysis, and gage R & R Reduce pro­duction time, control time ($72,000) 25 [20] Hassan, 2013,Egypt, Wire, Waste Reduction SIPOC Dia­gram Process Map­ping, DataCollection CED, AHP Action plan Control plan Increase the sigma levelfrom 3.2 to 3.6 (Pareto chart),Sigma levelcalculations, Down Time Measurements 26 [58]Rathilall andQuestionnaire validity andGap analysis Pearson’s Gap Found six-item Singh, 2018, SouthreliabilityChi-squared analysis Critical factors Africa, Automotivemeasure with test of LSS imple-Part, Key Factor LSS Cronbach’s mentation alpha test 27 [41] Zasadzien,2017, Data collec-Process map FMEA Creation Control Reduce down-Poland, Plastic, tion matrix plan, stan-time from 18 Downtime dardization hours to 9 hours 28 [15]John andBrain-Normality test, Individual DOE, ANOVA Individual Increase Cp ofAreshankar, 2018,storming, Cp analysis chart, CED chart, Cpdiameter and India, Machining, Pareto dia-analysis, thickness from Defects gram Pareto 0.27 and 0.35 diagram to 1.03 and 1.69 Table 2 Tools for literature review used and the research findings (continuation) Author, Year,No. Country, Industry, Variable Define Measure Tools used Analyze Improve Control Result 29 [16] Anand et al. FGD, data2007, India, Automo-history tive Part, Reject ofProduct Critical to DOE, Control Quality (CTQ),Chart QFD Fuzzy-rule, Anova CPk analysis, control chart Increase punch loadCpk from0.447 to 1.33 30 [59] Kaushik and Khanduja, 2007,India, Thermal Power, Defects SIPOC dia­gram Gauge R&R Run chart, SWAS (SteamDocumenta-Increase sigma process capabi-water tion level 2.0 to 3.0 lity analysis, analysisand reduce CED, Bar chart system),COPQ Rs fromTraining, 304,77 lakh toaction plan Rs 331,2 lakh per year 31 [60] Desai and Pra­japati, 2017, India, Plastic, Defects SIPOC dia­gram, Paretodiagram, process map Data collection Brainstorming, CED, Multi-voting, Causevalidation, Why-whyanalysis Preventive SOP with maintenance, visual aids SOP, kaizen Defects redu­ced and gave savings of INR10.80 lacs 32 [22] Gerger andData collec-Firuzan, 2016, Tur­tion key, Aerospace, Cycle Time Production flow chart, CED Effect of weightComprisingon human bone of ex and new appara­tus weight Control plan Reduce cycle time by 50 %and provide a profit of $167,895 / year. 33 [21] Slawik et al.2010, Poland, Auto­motive Part, The Variation Rate Modeling ComparisonCED differences between time scales in which DOE analysis,Gage R&R Simulation Reduce varia­tion of absor­ber lake from 92 % to 2.4 % aeration pro­cesses occur with a variati­on of tolerance base Gage R &R 710 by 68 % 34 [36] Hussain,Data collec-Jamshaid and Sohail, tion, flow2014, Pakistan, process dia-Textile, Defects gram Cp mea­surement CED, Paretochart Risk matrix SPC, FMEA table, correc­tive actions Increase sigma level from 2.2 to 3.0 with a profit of $26,000 permonth 35 [61] Gijo et al., 2011,SIPOC dia- Gage R & R, CED, cause DOE, TaguchiCause solu- Defects reduc- India, Automotive, gram, process Kappa statistic validation plan, S/N Ratio, tion matrix, tion from 16.6 Defects map Pareto, cause ANOVA standardiza-to 1.19 %,validation plan, tion sigma levelprocess capabi-improvement lity analysis from 2.47 to 3.76, annuali­zed savingsabout US$2.4 million 36 [62]Anderson andSIPOC dia-Histogram, CED, FMEA Prioritization Control The weld Kovach, 2014, USA,gram, Process Pareto charts matrices, plan, run repair rateConstruction, Repairmap training, chart, visual decreased byrate inspection, more than 25 checklist %, whichtranslated into a savings of $90,000 37 [63]Sharma et al, SIPOC dia-P-chart, Pareto CED, CurrentTraining, P-chart, Improving the2018, India, Amplifi-gram diagram Reality Tree process Pareto dia-sigma level ofer, Defects (CRT) map instruction gram the anodising guide process from3.62 to 3.91 Table 2 Tools for literature review used and the research findings (continuation) Author, Year, Tools used No. Country, Industry, Result Measure Analyze Improve Control Variable Define [64]KumaradivelSIPOC dia-CTQ tree, Cp analysis, Experimental Histogram, The rejection and Natarajan, 2013,gram Cause-and-FMEA, Keydesign ma-SPC, PDCA percentage India, Flywheel effect matrix, Process Inputtrix, ANOVA declined to Casting, Defects Pareto chart and Output 4.69 from 6.94 Variables (KPIV, KPOV), Pareto diagram 39 [65] Lo et al., 20019,Abberation Process capa-Taiwan, Optic Ele-measurement bility ments, Defects for good-precision molded len- CED, Taguchi,ANOVA Optimal combination of process capabilities Standardiza-CPU for optical tion, built-in lenses is en-monitoringhanced from system 0.57 to 1.75 40 [66] Chen et al., 2009, USA, PlasmaCutting, Defects ses, process analysis Brain­storming Cause and Multi-Vari Effects Matrix,Analysis, T-System capabi-tests lity mea­surements Taguchi Control Plan, The optimal Continuous setting combi­impro-nation gave no vement defects from the 30 plasma-cut holes in the confirma­tion run. It maintains feed rate for pro­ductivity andimproves quality. Fig. 2b Grouped sources of literature: Countries of Author Fig. 2d Grouped sources of literature: Industries Type Reduce Reject Increase Sigma SOP Increase Cp Fig. 3 The research result and variables 4.2 Objective value of the study Systematic DMAIC phase According to the literature used in this study, the Six Sigma phase can be synthesized with thetools used and the expected goals in implementing the DMAIC phase, as presented in Table 3. Table 3 Systematic DMAIC phase Table 3 Systematic DMAIC phase (continuation) Phase Define Measure Analyze Description activity • Define the problem • Determine CTQ • Determine improvement targets • Create a charter project • Collect data and facts • Mapping to represent data • Measurement of the condition base on data and facts obtained • Perform analysis base on dataand fact • Vital factor testing • Planning improvements Tools VOC/VOB, SIPOC diagram/process map, Historical data, Pareto diagram, Questionnaire, Brainstorming. Gage R &R, Pareto diagram,Control chart, Cp (sigma level)measurement, four-blockdiagram, descriptive dan non-descriptive statistic analysis. Brainstorming, CED, CE Metrik, RCA analysis, Comparison WOWvs. BOB, Scatter diagram, linearregression, Anova, why-whyanalysis, three possible analysis, FMEA, gaps analysis. Main of Goals • Obtain the CTQ • Build a team of improvement • Obtain improvement targets • Obtain a process capability(sigma level) that representsthe condition before improvement. • Know the potential causes ofthe problem • Know the main causes (vital factors) of the problem • Develop an effective improvement plan. 320 Advances in Production Engineering & Management 16(3) 2021 Phase Description activity Tools Main of Goals Improve • Discussion to determine alternative improvements that can be implemented • Carry out improvementsaccording to the results of thediscussion • Verification of key variables in the implementation process Control • Control process variationsaccording to customers' requirements • Design monitoring andcontrolling strategies forimprovement results • Verification of objective andstandardized projects, sharing new standards and determining the further project DOE, FMEA, Gage R &R, Pareto diagram, Control chart, Cp(sigma level) measurement,four-block diagram, Descriptiveand non-Descriptive statistic analysis, Three possible solutions, Corrective action. SPC/Control chart, Control plan, SOP, Historical data,Questionnaire, Brainstorming. • Carry out improvement • Strive for the effectiveness of improvements by looking at the comparison of the resultsof improvements withconditions before improvement • Obtain a controlled process. • Obtain new standards /documentation from the improvement process • Ensuring new standards are known and implementedthroughout the entireorganization. • Make further improvement plans. Increase of Sigma Levels, Productivity Improvement and Industrial Sustainability Using the Six Sigma Method The consistency of the DMAIC phase in Six Sigma implementation has been proven and has suc­ceeded in increasing quality, reducing unnecessary production costs, and increasing producti­vity. Khawale et al. [5] in his study, stated that the DMAIC (Six Sigma Methodology) approach could be used to reduce defects and increase productivity. Six Sigma is a method that results inbusiness excellence with a focus on the needs and expectations of customers. It is the key to thesuccess of this method, based on facts and analysis with measurable statistical methods so thatthe results can be accounted for in managing businesses currently both manufacturing and ser­vices. The Six Sigma implementation is directly related to the company’s finances, resulting incustomer satisfaction being the target of this method and with innovative ways to exceed theexpectations / desires and satisfaction of the customers. Jacob and Jenson [67] in their study ofthe tire industry in India using the VSM and Six Sigma methods, succeeded in increasing speedcalendering machines and reducing cycle time from 17 hours 37 minutes to 16 hours 15 minu­tes. This study explains that by running the entire DMAIC phase combined with the Value StreamMapping (VSM) method, it can reduce the cycle time of the calendering process, which meansthat the productivity of the calendering process can be improved. Sokovic, Pavletic, and Krulcic [57] in their research on the Automotive industry explainedthat Six Sigma with the help of tools of analysis is proven to be able to reduce product andprocess variability and be able to improve process capability through reducing defects andreducing cycle times so as to reduce production costs and certainly will increase company profits. In general, increases obtained through reduced production time and control time canprovide an annual profit of $ 72,000. The expected annual profit from implementing this system is $ 100. Based on several research findings using the Six Sigma method as explained earlier, it is pro­ved that the consistency of the implementation of the structured phases in Six Sigma, namelyDMAIC phase, may provide positive results in solving problems. It may improve process capability / sigma levels and productivity as indicated by decreasing variations, defects, cycletime, customer complaints, non-value-added, and production cost, as well as increasing productquality, customer satisfaction, cost-saving / profit, competitiveness and maintaining industrialsustainability. Fig. 4 illustrates the relationship between the consistency of the DMAIC phasewith increasing sigma levels, productivity, and industrial sustainability. Fig. 4 Relationship/effects of Six Sigma method on increasing Sigma levels, productivity and industrial sustainability According to the literature review on the consistency of DMAIC in the implementation of SixSigma based on the literature that has been obtained and after going through analysis andsynthesis based on the rules of systematic literature review (SLR), it can be concluded that theobjective values obtained from this study are as follows: 1. Process capability (sigma levels) is an indicator of process stability or capability to produce aquality product. The higher the value of process capability (sigma levels), the process will beable to produce products with better quality, vice versa. 2. Productivity is an indicator of the success of an organization/company that has the conceptof how to produce or increase the production of goods and services optimally by utilizing re­sources in the form of tangible and intangible assets effectively and efficiently. 3. Implementation of Six Sigma in a business organization system is a systemic approach (hasdefinite stages), Scientific (based on data and facts), Measurable (has definite measurement standards with statistical methods), Flexible (can be combined with methods and other tools of quality) and Effective (is able to increase productivity at a low cost by reducing defects) torevolutionize the scope and use of quality systems in the business currently. 4. Six Sigma is a complex and flexible method/system for achieving, maintaining, and maximi­zing business achievement that is characterized by understanding customer needs by usingfacts, data, and statistical analysis and is based on organized management to performcontinuous improvement. 5. Six Sigma implementation has varying results depending on the level of readiness of theorganization/company, operating system, measurement system, information integrationsystem, employee involvement, the concept of continuous improvement, environmentalsupport, and top management commitment. 6. There are two main benefits of implementing Six Sigma to the effectiveness of the company. (1) Direct benefits: these benefits are in the form of financial side obtained from the Six Sig­ma implementation which is characterized by increasing quality and productivity which willdefinitely provide cost savings and increase the profit of the company / organization; (2) In­direct benefits: these benefits are in the form of the non-financial side including increasedteamwork, increased sense of belonging among employees, increased employee competence,increased employee initiative, increased quality, increased trust in business relationships,which will further increase competitiveness in maintaining the continuity of the company /organization. 7. Quality, process capability (sigma levels), and productivity are attributes of customer sa­tisfaction to maintain competitiveness and industrial sustainability and have a positive rela­tionship and are directly proportional between these attributes. Recommendation Referring to the literature that has been reviewed, various previous studies show that theimplementation of Six Sigma is more likely to provide tangible / direct benefits such as; reducedefects, reduce downtime, reduce cycle time, forecast accuracy and others that will all providefinancial benefits, yet very rarely research that discusses the hidden/indirect benefits of SixSigma that will provide non-financial benefits. It is recommended that more subsequent studiesdiscuss research methodology that will provide results in terms of hidden / indirect benefits so that research on Six Sigma is more varied. 5. Conclusion This paper is a systematic literature review on the consistency of DMAIC using the Six Sigmamethod from various previous studies in the manufacturing industry of 2006 to 2019 from 14countries with 27 types of industries and involving 14 research variables and 30 publishers.According to the literature reviews, it shows different results from each research that indicatedifferences in the level of analysis ability of researchers and the level of readiness of thecompany/organization in implementing Six Sigma, however, overall the Six Sigma approach hasbeen successful in reducing product variation, reducing defects, reducing cycle time, reducingproduction costs and increasing customer satisfaction, providing cost savings, increasing profitsand increasing competitiveness in order to maintain the sustainability of the company/industry.The study also succeeded in obtaining seven objective values , which are the main results of thisstudy and managed to find a consistent relationship between the DMAIC phase of increasingsigma levels, increasing productivity, and industrial sustainability as the research questions inthis study. 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Taguchi-based six sigma approach to optimize plasma cutting process: An indu­strial case study, The International Journal of Advanced Manufacturing Technology, Vol. 41, 760-769, doi: 10.1007/s00170-008-1526-1. [67] Jacob, J.J., Jenson J.E. (2014). Reducing the throughput time by value stream mapping in a tyre manufacturingindustry, International Journal of Engineering Research & Technology, Vol. 3, No. 11, 385-388. Modeling and optimization of finish diamond turning of spherical surfaces based on response surface methodology and cuckoo search algorithm Kramar, D.a,*, Cica, Dj.b aUniversity in Ljubljana, Faculty of Mechanical Engineering Ljubljana, Slovenia bUniversity in Banja Luka, Faculty of Mechanical Engineering Banja Luka, Bosnia and Herzegovina A B S T R A C T Surface roughness is one of the most significant factors to indicate the prod­uct quality. Diamond turning is an efficient and highly accurate material re­moval process to improve the surface quality of the workpiece. In the presentstudy, the arithmetic mean absolute roughness (Ra) and total height of profile (Rt) of spherical surface during finish turning of a commercial brass alloyCuZn40Pb2 were modeled using Response Surface Methodology (RSM). The experimental investigations were carried out using the Central CompositeDesign (CCD) under dry conditions. The effect of cutting parameters such asspindle speed, feed rate and depth of cut) on spherical surface quality wasanalyzed using analysis of variance (ANOVA). A cuckoo search (CS) algorithm was used to determine the optimum machining parameters to minimize the surface roughness. Finally, confirmation experiments were carried out to verify the adequacy of the considered optimization algorithm. A R T I C L E I N F O Keywords: Brass alloy;Diamond turning;Surface roughness;Spherical surface;Modeling;Optimization; Response surface methodology(RSM);Cuckoo search (CS) *Corresponding author:davorin.kramar@fs.uni-lj.si (Kramar, D.) Article history: Received 31 May 2021 Revised 3 September 2021Accepted 15 September 2021 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 workmust maintain attribution to the author(s) and the title ofthe work, journal citation and DOI. 1. Introduction Brass (copper-zinc) alloys are used in a wide range of industrial applications such as mechanical,electrical and hydraulic systems due to their excellent formability, high thermal and electricalconductivity, corrosion resistance and excellent antibacterial properties. To improve machina­bility, various alloying elements are commonly added to brass. The most important of these ele­ments is lead, which improves machinability in terms of tool wear, cutting forces, chip breakingand surface quality [1-3]. Extensive research has been carried out in recent decades to improvethe machinability of brass alloys. In [4], a comparison of the machinability of three lead-free brass alloys and one leaded brass alloy in terms of energy consumption and chip morphology was carried out. The influence ofdifferent coating types and the use of diamond tools on cutting forces, chip formation and sur­face quality was investigated by Klocke et al. [5]. Nobel et al. [6] analyzed the chip formation process in different low lead brass alloys. Schultheiss et al. [7] analyzed cutting forces, surfacequality and tool wear during longitudinal turning to evaluate the machinability of leaded andlead-free brass alloys. The effects of minimum quantity lubrication (MQL) and cutting parame­ters on surface quality during turning of commercial brass were studied by Davim et al. [8]. A comparison with conventional flooding conditions was also made. The machinability of the high­ly leaded brass alloy CuZn39Pb3 [9] and commercial lead-free brass alloys [10] was also ana­lyzed. Vilarinho et al. [11] studied the influence of the chemical composition of brass alloys onsurface quality and machining forces during turning. Schultheiss et al. [12] compared the ma-chinability and manufacturing costs in turning of conventional leaded brass alloys and a low-lead alternative. Toulfatzis et al. [13] studied the chip morphology and tool wear during longitu­dinal turning of two leaded brass alloys. The Taguchi method with the utility concept was intro­duced for simultaneous optimization of surface quality and specific cutting force in turning ofbrass CuZn39Pb3 under MQL cutting [14]. Toulfatzis et al. [15] used the signal-to-noise ratio forsingle optimization of surface roughness and cutting force in longitudinal turning of lead-free and leaded brass alloys. Some researchers also used artificial intelligence based methods. Gaitonde et al. [16] applieda genetic algorithm to determine the optimum machining parameters for minimizing surfaceroughness when turning leaded brass alloys under MQL conditions. Raja and Baskar [17] pre­sented a multi-objective optimization method based on particle swarm optimization with twoobjectives, namely machining time and surface quality. Optimum cutting conditions during turn­ing for different materials namely brass, aluminum, mild steel and copper were selected. Nata-rajan et al. [18] estimated the surface roughness in longitudinal turning of brass using artificialneural networks. After a review of the literature, it is apparent that a considerable amount of research has beenconducted on turning of brass alloys. However, none of the literature reviewed dealt with finish diamond turning of spherical surfaces. As market competitiveness increases, surface roughnessis probably one of the most widely used indicators of surface quality of machined parts today[19-27]. Surface roughness affects several functional properties of products, especially friction,fatigue strength, wear, heat transfer, light reflection, lubricant distribution, etc. Ensuring surfacequality is one of the most critical issues in the fully automated mass production of parts withspherical surfaces. However, surface roughness is strongly influenced by the variation of processparameters and analytical modeling is difficult due to its nonlinearity. Therefore, it is imperativeto develop a mathematical model of surface roughness, exploit the influence of machining pa­rameters, and finally optimize the surface quality in brass ball turning. 2.Experimental procedure The machining tests were performed on the special machine tool Picchi Diamantatrice to pro­duce spherical parts with a spindle power of 5.5 kW and a maximum spindle speed of 7000 rpm.This lathe was equipped with two tools: a carbide turning tool for roughing and a diamond toolfor finishing and machines spheres with a diameter of 2" (Fig. 1). Commercially available brassCuZn40Pb2 (CW617N) workpieces were used for machining. The chemical composition of thematerial is summarized in Table 1. The working material has a hardness of 90-100 HRB and a tensile strength of 390-440 N/mm2. This alloy provides good corrosion resistance together with good formability. Table 1 Chemical composition of the studied brass alloys Others: Mn, Si, Sb, As, Bi, Alloy Cu (%) Zn (%) Pb (%) Al (%) Fe (%) Ni (%) Sn (%) (%) CuZn40Pb2 57-59 rest 0.3 max 0.3 max 1.6-2.5 0.05max 0.3max 0.2max The diamond cutting tool was used for precision machining of a ball valve. The tool nose doesnot have a radius like conventional cutting tools, but a flat nose that allows very fine machining.The dimensions of the tool were 95 × 12 × 12 mm, with the sides at a 45° angle and a 1.3 mmwide cutting edge. The main angles of the tool cutting wedge were 2° for clearance anglea, -10.5°forrake angle .andconsequently98.5°forwedge angleß. The cutting depthof the dia­ mond segment is 0.4 mm and represents the maximum theoretical cutting depth, but due to thepossibility of pulling the diamond segment out of the tool holder, the depth of cut is usually notused deeper than 0.2 mm. Fig. 1 Experimental setup for diamond fine turning of CuZn40Pb2 The arithmetic mean of the absolute roughness (Ra) and a total height of profile (Rt) of the ma­chined workpiece were measured with the surface roughness measuring device Tesa Rugosurf20 (Fig. 2). The examined length was 3.2 mm with a basic span of 0.8 mm. Fig. 2 Surface roughness measurements In the present study, three cutting parameters, i.e., spindle speed (n), feed rate (f) and depth of cut (a) were selected, and the ranges of machining conditions were defined through initialexperiments. The cutting parameters and their levels are given in Table 2. The experiments were designed and carried out according to the Central Composite Design(CCD). All experiments were conducted under dry conditions. The measured values of Ra and Rt are shown in Table 3. Table 2 Machining parameters and their levels Levels Parameter Unit Level 1 Level 2 Level 3 Spindle speed, n min-1 4800 5500 6200 Feed, f mm/rev 0.48 0.64 0.80 Depth of cut, a mm 0.075 0.125 0.175 Table 3 Experimental layout for central composite design No. n (min-1) Process parameters f (mm/rev) a (mm) Response measurements Ra (µm) Rt (µm) 1 5500 0.64 0.125 0.140 0.97 2 4800 0.48 0.075 0.208 1.38 3 6200 0.80 0.075 0.164 1.11 4 5500 0.48 0.125 0.173 1.18 5 4800 0.48 0.175 0.212 1.76 6 4800 0.80 0.075 0.249 2.10 7 5500 0.64 0.125 0.154 1.00 8 6200 0.64 0.125 0.155 1.07 9 5500 0.80 0.125 0.152 1.11 10 4800 0.64 0.125 0.179 1.29 11 5500 0.64 0.125 0.156 1.06 12 5500 0.64 0.075 0.149 1.05 13 4800 0.80 0.175 0.224 1.56 14 6200 0.80 0.175 0.150 1.14 15 6200 0.48 0.175 0.215 1.56 16 6200 0.48 0.075 0.145 1.35 17 5500 0.64 0.175 0.218 1.51 3. Results and discussion The reduced quadratic polynomial model, given as a function of the machining parameters for anarithmetic mean of the absolute roughness (Ra) and a total height of the profile (Rt) using theResponse Surface Methodology (RSM) is represented by equations (1) and (2), respectively ........ = 0.4063 -3.4714 ·10-5....+ 0.212....-2.1591....-1.7656........+ 13.9886....2 (1) ........ = 8.5175 -3.2011 ·10-3....+ 9.2605....-14.7502....-1.317 ·10-3........-17.1875........ (2) + 3.4347 ·10-7....2 + 107.3208....2 The adequacy of the developed models was examined using analysis of variance (ANOVA).The results are given in Table 4 and Table 5 for Ra and Rt, respectively. The F-values for Ra and Rt are 5.80 and 7.85, respectively. For the desired confidence level (95 %), the F-values of the es­tablished model exceed the F-value of the standard tabulated F-values for Ra and Rt of 3.204 and 3.293, respectively. Thus, the two reduced quadratic models can be considered appropriatewithin the confidence limit. P-values smaller than 0.05 imply that n and the product a2 are statis­tically significant terms for the arithmetic mean of absolute roughness Ra, while n and the prod­ucts n × f, f × a and a2 are also observed to be significant terms for the total height of the profile Rt. Other parameters have no statistical significance for the surface quality responses consid­ered. The squared correlation coefficient (R2) values of 0.7250 and 0.8593 for Ra and Rt, respec­tively, show good agreement among the experimental and predicted values for both models. The 3D response surfaces were also created to study the effects of the machining parametersand their interactions. Figs. 3-5 show the contour plots for the surface roughness parameters (Ra and Rt) as a function of spindle speed (n), feed rate (f) and depth of cut (a). Table 4 The ANOVA table for Ra Source Sum of squares DF Mean square F-value P-value Model 0.014 5 2.728·10-3 5.80 0.0073 n 5.905·10-3 1 5.905·10-3 12.56 0.0046 f 1.96·10-5 1 1.96·10-5 0.042 0.8419 a 1.082·10-3 1 1.082·10-3 2.30 0.1575 f ×a 1.596·10-3 1 1.596·10-3 3.39 0.0925 a2 5.036·10-3 1 5.036·10-3 10.71 0.0074 Error 5.172·10-3 11 4.072·10-4 Total 0.019 16 Kramar, Cica Table 5 The ANOVA table for Rt Source Sum of squares DF Mean square F-value P-value Model 1.31 7 0.19 7.85 0.0031 n 0.35 1 0.35 14.53 0.0041 f 4.41·10-3 1 4.41·10-3 0.19 0.677 a 0.029 1 0.029 1.22 0.2971 n×f 0.17 1 0.17 7.31 0.0242 f×a 0.15 1 0.15 6.35 0.0327 n2 0.086 1 0.086 3.60 0.0902 a2 0.22 1 0.22 9.16 0.0143 Error 0.21 9 0.024 Total 1.52 16 The effects of spindle speed and feed rate on roughness parameters are shown in Fig. 3, where the depth of cut is kept at an intermediate level. The minimum value of Ra was obtained at high spindle speed and low feed rate, as shown in Fig. 3a. It should also be noted that the Ra val­ue is almost directly proportional to these two parameters, with feed rate having less signifi­cance. Fig. 3b shows that Rt is significantly affected by spindle speed, while feed rate has less influence on it. The minimum value of Rt was also found at the maximum values of spindle speed and feed rate. Therefore, to obtain better roughness parameters, higher spindle speeds and feed rate should be preferred for diamond finish turning of spherical surfaces. Fig. 3 Surface plot of Ra (a) and Rt (b) with spindle speed and feed rate Fig. 4 shows the estimated response surface with respect to the spindle speed and the depth of cut, while the feed rate is kept at an intermediate level. The minimum values of both parame­ters were obtained at high spindle speed and medium depth of cut. It can also be observed that both cutting parameters strongly influence the surface quality. Fig. 4 Surface plot of Ra (a) and Rt (b) with spindle speed and depth of cut Fig. 5 shows the influences of feed rate and depth of cut on the surface roughness parameters (Ra and Rt), while the spindle speed is kept at an intermediate level. The plots show that the min­imum values for both parameters were found at a high feed rate, while the depth of cut was about 0.1 mm. This figure shows that both roughness parameters are almost directly propor­tional to the feed rate. It is also worth noting that the depth of cut is more significant compared to the feed rate. Fig. 5 Surface plot of Ra (a) and Rt (b) with feed rate and depth of cut 4. Optimization 4.1 Cuckoo search The cuckoo search (CS) algorithm, originally introduced by Yang and Deb [28], is one of the re­cent swarm intelligence-based optimization algorithms. The CS algorithm was inspired by the brood parasitism behavior of certain cuckoo bird species and the characteristics of Lévy flights discovered in the flight behavior of numerous insects and animals. Female cuckoos lay their eggs in the nests of other, typically different species of host birds. These eggs also resemble the host birds' eggs in color and pattern. When the host bird realizes that the eggs are not its own, it ei­ther discards them or simply leaves the nest and builds a new one elsewhere. Cuckoos must therefore mimic their host birds' eggs very closely to minimize the likelihood that their eggs will be abandoned. Optimization is about replacing a less good nesting solution with a new and po­tentially better one (cuckoo). The CS algorithm is essentially based on three idealized rules [29]: (i) each cuckoo lays one egg at a time in a randomly selected nest; (ii) an elite selection procedure is used in which only the best nests with superior quality eggs are passed on to the next generation; (iii) the number of available host nests is fixed and a host bird can detect a foreign egg with probability in the range of [0, 1]. While producing new solutions x(t+1) for the i-th cuckoo, Lévy flight is performed (....+1) ........= ........(....)+ .....Lévy(....) (3) where x(t)i denotes the i-th candidate solution at iteration t and a > 0 denotes the step size factor. In most cases, a = 1 can be used. The product . denotes inputwise walking for multiplications. Basically, the Lévy flight results in a random walk, where the random step length is deter­mined by a Lévy distribution with infinite mean and infinite variance Lévy ~....= ....-....,(1 < ....=3) (4) 4.2 Optimization model The optimization process in this paper aims to find the best combination of process parameter levels that results in the lowest value of Ra and Rt. To formulate the optimization problem, the regression models for Ra (Eq. 1) and Rt (Eq. 2) were used as the objective function. In this study, Advances in Production Engineering & Management 16(3) 2021 three variables, namely spindle speed, feed rate and depth of cut were considered as optimiza­tion variables. Normalization of each subobjective was also introduced to compensate the differ­ences in numerical values between them. Thus, the resulting objective function (ROF) to be min­imized is a weighted combination of the two objectives as follows: ........ ........ ROF (...., ...., ....)= ....1 + ....2 (5) ........min ........min where w1 and w2 are the weight factors of Ra and Rt, respectively. In this paper, equal weights for Ra and Rt were selected, i.e. w1= w2 = 1/2. The minimization of the ROF (Eq. 5) is subject to the limits of the cutting parameters. Theboundary conditions were the upper and lower limit of the experimental machining parameters (Table 2)andwere givenasfollows:4800 = n = 6200 min-1,0.48 = f = 0.8 mm/rev,0.075 = a = 0.175 mm. After formulating the optimization problem and its constraints, the CS optimization algorithmwas employed to solve the problem. The proposed CS algorithm requires some setting parame­ters for implementation. The minimum value of the resulting objective function (ROF = 0.916)was obtained for a population size of 20, termination probability of 0.25, and termination crite­rion of 100 generations. The results of the CS optimization algorithm showed that the best com­bination of turning parameters for simultaneous optimization of the arithmetic mean of absoluteroughness (Ra) and total height of profile (Rt) was: 6200 min-1 for spindle speed, 0.8 mm/rev for feed rate, and 0.13 for depth of cut. 4.3 Confirmation experiments The confirmation tests were carried out at the optimum values of the process parameters toverify the quality characteristics of the spherical fine turning process recommended in the study.In accordance with the obtained optimum results, four new experiments were carried out (Table6). The mean values of Ra and Rt were 0.139 µm and 1.04 µm, respectively, which were in goodagreement with the predicted values. Consequently, the proposed CS optimization algorithm was efficient to find out the optimal set of machining parameters for spherical finish turningassociated with minimum surface roughness. Table 6 Results of confirmation tests Confirmation test 1 2 3 4 Mean Ra (µm) 0.143 0.149 0.134 0.141 0.139 Rt (µm) 1.19 0.89 1.10 0.97 1.04 5. Conclusions In the present research work, the influence of machining parameters such as spindle speed, feedrate and depth of cut on the arithmetic mean of absolute roughness (Ra) and total height of pro­file (Rt) in diamond finish turning of brass CuZn40Pb2 was investigated. The following conclu­sions can be drawn from the analysis of the results, subsequent model development and optimi­zation: • The response surface methodology in combination with the central composite design hasbeen successfully applied to study the effects of different machining parameters on two quality characteristics, namely the arithmetic mean of the absolute surface roughnessand the total profile height, during diamond finish turning of spherical surfaces. The de­veloped mathematical models of both responses in terms of the actual design factors,their interactions and quadratic terms are suitable for the analysis of the sphere turning process. • The spindle speed and the quadratic term of the depth of cut were the significant param­eters affecting the arithmetic mean of the absolute roughness, according to the results ofANOVA. The ANOVA also showed that the spindle speed, the quadratic term of the depth of cut, the interaction terms between the spindle speed and the feed rate, and the feed rate and the depth of cut were significant terms affecting the performance of the totalheight of the profile. Spindle speed showed the greatest influence on both surface pa­rameters compared to depth of cut and feed rate. • The best combination of cutting parameters to simultaneously minimize the arithmeticmean of the absolute roughness and the total height of the profile, obtained by the opti­mization model based on the cuckoo search algorithm, was as follows: 6200 min-1 forspindle speed, 0.8 mm/rev for feed rate and 0.13 mm for depth of cut. This study and the determined combination of parameters allow a more detailed technology planning forthe production of high-quality spherical components, both from the point of view of pre-machining and productivity itself. The results obtained do not confirm the theory of turning. In fact, in our case, we obtain the best results at the highest feed rate, which iscontrary to expectations. 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Cuckoo search: Recent advances and applications, Neural Computing and Applications, Vol. 24, No. 1, 169-174, doi: 10.1007/s00521-013-1367-1. Tactical manufacturing capacity planning based on discrete event simulation and throughput accounting: A case study of medium sized production enterprise Jurczyk-Bunkowska, M.a,* aFaculty of Economics and Management, Opole University of Technology, Poland A B S T R A C T The article presents the application of the original methodology to support tactical capacity planning in a medium-sized manufacturing company. Its essence is to support medium-term decisions regarding the development ofthe production system through economic assessment of potential changescenarios. It has been assumed that the developed methodology should be adapted to small and medium-sized enterprises (SMEs). Due to their flexibil­ity, they usually have limited time for decision-making, and due to limited financial resources, they rely on internal competencies. The proposed ap­proach that does not require mastery of mathematical modelling but allows streamlining capacity planning decisions. It uses the reasoning of throughput accounting (TA) supported by data obtained based on discrete event simula­tion (DES). Using these related tools in the design and analysis of changescenarios, make it possible for SME managers to make a rational decisionregarding the development of the production system. Case studies conducted in a roof window manufacturing company showed the methodology. The application example presented in the article includes seven change scenariosanalyzed based on computer simulations by the software Tecnomatix Plant Simulation. The implementation of the approach under real conditions has shown that a rational decision-making process is possible over time scale and with the resources available to SMEs for this type of decision. A R T I C L E I N F O Keywords: Decision process; Capacity planning;Discrete event simulation (DES); Throughput accounting (TA);Plant simulation;Small and medium-sized enterprises (SME); Production scenarios;Tecnomatix Plant Simulation *Corresponding author:m.jurczyk-bunkowska@po.edu.pl (Jurczyk-Bunkowska, M.) Article history: Received 7 June 2021 Revised 12 October 2021 Accepted 13 October 2021 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 workmust maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction Balancing supply-to-demand production capacity is a key consideration to ensure the viability ofthe company's operating activities. The need for changes in the manufacturing system is dictatedby adapting to increasingly precisely projected demand [1], the increasing possibility of auto­mating and robotizing monotonous work requiring physical exertion [2], implementing technol­ogies in the field of Industry 4.0 that significantly improve production processes [3]. Rationalimplementation of changes requires an understanding of their consequences. The right decisionsallow maintaining the right balance between system capacity and production costs. Productioncapacity is the most strategic internal capability that manufacturing firms must create, sustainand plan for. Capacity management aims to ensure that a manufacturer has the ‘right’ capacity to act within a complex structure and how best to ‘utilise’ their internal capabilities [4]. They referto the amount of output that a system is capable of achieving over a specific period of time [5]. Both capacity expansion and contraction are called capacity planning [6]. The level of production capacity directly influences on the one hand the possibility of carrying out orders and on theother hand the level of fixed costs of the company. Therefore, the cost of production is deter­mined by the level of capacity utilisation and thus its match with demand [7]. With regard to themedium -term capacity planning, appropriate capacity planning methods are key, which assessthe consequences of these decisions on the production system [8]. Observations made in small and medium-sized manufacturing companies indicate managersare under pressure to ensure that the decision-making process for tactical capacity planningdoes not exceed a few weeks. It includes an analysis of the production situation leading to thedevelopment of change scenarios and their assessment, which results in a recommendation forinvestments. These are issues so complex that leaving their intuition even an experienced man­ager is irrational. The literature on the problem of capacity planning offers solutions based onmathematical modelling and/or artificial intelligence. There are lack of approaches that would ensure a rational solution to the problem, even with a reduction in its optimization. As part ofthe presented research, it sought a method that would enable the decision-making process to becarried out within a few weeks using the knowledge available to a typical process engineer. Itsessence is to recommend solutions to the problem of tactical capacity planning, considering pro­duction and economic issues. The article attempts to respond to this challenge by proposing atactical capacity planning method verified by a case study of a medium-sized roof window com­pany. The essence of the suggested approach is to combine discrete event simulation (DES) withthroughput accounting (TA). DES allows analysing the current production situation and aids todesign change scenarios. TA is used to diagnose financial effects based on data from simulation experiments and estimated costs of implementing changes. The proposed approach to the capacity planning issue is assigned primarily to small and me-dium-sized enterprises (SMEs). Limited time and competencies inhibit them to use methodsbased on mathematical programming or artificial intelligence, which are discussed in the nextchapter of the article. It is also discussed in it the new opportunities for SMEs give by DES soft­ware development. Chapter three provides a detailed description of the problem, researchmethods, and the starting state of the analyzed manufacturing system. Chapter four shows thestep-by-step process of planning of tactical capacity according to the proposed method. Chapterfive discusses the significance of the results got in a broader context relating to operationalmanagement. Chapter six outlines the advantages of the proposed method and points to limita­tions in its application. 2. Theoretical background 2.1 Overview of tactical capacity planning methods Capacity can be defined as the total productive capability of all the utilized productive resourcesincluding workforce and machinery [9]. Capacity management aims to ensure that a manufactur­er has the ‘right’ capacity to act within a complex structure and how best to ‘utilise’ their internal capabilities [4]. The capacity decisions can be made in all decision-making hierarchies: strategic,tactical and operational [9]. The scope of tactical capacity planning decisions includes [10]: • considering the mid-term demand, to decide whether the capacity of the existing factoriesshould be expanded by buying new auxiliary tools (purchase or replace bottleneck ma­chines; purchase or replace auxiliary tools), • considering the mid-term demand, to decide the best portfolio of products (decide the bestportfolio of products). The analysis in this article is limited to the first scope of decisions oriented towards increas­ing production capacity through changes in the production process. Many of the solutions to the capacity planning problem presented in the literature are basedon the Integer Linear Programming (LP) or Mixed Integer Programming (MIP) models, [11, 12]. They work very well in large, automated companies, as well as with production allocation prob­lems in various production facilities [13], or the combination of strategic and tactical decisionsin the design of the distribution network including storage capacity, [14]. The problem is theadequacy of linear models, which is often not satisfactory. Complex systems may not reflect thedecision-making situation well enough when uncertainties need to be taken into account. In suchcases, models based on stochastic programming [15] are used. The literature reports good re­sults in the use of such an approach [16], but the high complexity and difficulty of using themleads to the search for metaheuristic algorithms combining deterministic and stochastic ap­proaches [17]. A large group of tactical capacity planning solutions is based on combining simulation andoptimization techniques. Examples include the use of artificial neural networks in connectionwith genetic neural networks [18], or the link between genetic algorithms and Monte Carlo sim­ulation [19]. However, the use of such solutions requires advanced knowledge and time, which iswhy the publications presenting them refer to industries dominated by large companies. Itshould also be noted that hasty imposition in the model of certain assumptions may lead to a situation where the real problem of the company is not solved. The latest capacity planning solutions take advantage of the opportunities offered by Indus­try 4.0 application. The capacity planning model for prefabricated housebuilding elements usesreal-time data entry to improve assembly line performance planning [20]. This approach devel­ops short-term capacity equalization in make-to-order production systems [21]. Small and me-dium-sized enterprises, however, generally do not have sufficient resources to collect largeamounts of data or do not have the skills to process it [22]. The solution proposed for them is a computer simulation, increasingly recommended in publications based on practical problemspresented on the basis of a case study of enterprises [23]. 2.2 Discrete event simulation in manufacturing capacity development Simulations represent imitation of some process in the real world. Process simulation often re­quires generating a model that will represent the key characteristics of the selected system orprocess and will present its behaviour [24]. Discrete event simulation (DES) is an instrument for analysing dynamic processes taking into account stochastic parameters and uncertain events [25]. Simulation modelling aims to qualita­tively or quantitatively support decisions by building a model of a real system and experiment­ing with that model [26]. The increasing importance of simulation methods in solving complexproduction problems is demonstrated by the growing number of studies in this field [27]. Among them, methods based on discrete event simulation [28] occupy an important place. Theysupport the resolution of many different capacity planning problems, such as: • configuration of flexible modular mounting systems [29]; • matching capacity to uncertain demand for hospitals and other healthcare providers [30]; • analysis of employee productivity in a production process with high variability due to lowlevel of automation [31]; • decision-making tool in the complex production configuration of the automotive assemblyline [32]. DES modelling uses the software of various types. Commercial systems such as TecnomatixPlant Simulation, ARENA, Enterprise Dynamics and FlexSim are the most popular among indus­trial engineers. The first was used in the presented studies because it provides advanced optionsfor each component of the model to accurately match it to the actual production system. Also notwithout significance is the extensive help in the form of online guides and training offered by themanufacturer and the community using this software. Open source systems such as Salabim,JaamSim, whose usability is compared to commercial systems [33] are also becoming increasing­ly popular. The greatest benefit of using DES in capacity planning is the ability to represent even complexprocesses without losing the accuracy of the results or significantly increasing the calculationtime. Conducting experiments using DES provides an understanding of the system's behaviourbefore it is built, the detection of unexpected incompatibilities, the ability to investigate variousapplications of case scenarios [34]. However, it should be remembered that simulation modelsonly allow you to predict the outcome of different scenarios. Thus, the "best" solution is chosen from the scenarios analysed, not from all possible, in contradistinction to optimization models,where the "best of all" is expected. The use of computer simulation, therefore, does not guaran­tee an optimal solution to the problem of capacity planning. 3. Problem statement and used methodology 3.1Problem statement A research gap is identified regarding the use of decision support tools to solve tactical planningproblems in real-world production conditions [35]. The article considers the problem of capacityplanning in the company manufacturing roof windows. It is one of the manufacturing plants for awell-known brand in Europe. Of the 150 people employed, 122 serve production and ware­houses, and the rest are technical and administrative staff. The company's current productioncapacity is 800 pcs/business day when working on two shifts. The plant received from the head­quarters (from the window distributor) a question about the possibility of increasing productionfor half a year to 1100 pcs/day, a decision must be made within 1 month, and possible changesmade within 3 months. At the moment, the company makes such decisions based on the opin­ions of internal specialists. The analyses are limited to a specific brainstorming session in which2-3 variants of change are considered. This approach, in the opinion of managers, is insufficient.They would like the decision-making process for capacity planning to be based on a structureddecision-making process supported by reports containing reasonable estimates of the effects ofchange. The analysis time offered by consulting companies is not adequate to the requirementsof tactical planning. In addition, the company has experienced and committed employees in­volved in the development of its competencies. 3.2 Research objectives The practical purpose of the research was to find an answer to the question of how the tacticalcapacity planning decision-making process should proceed so that it could be used by the win­dow manufacturer. In a broader context, the research aims to propose a capacity planning meth­odology that is useful for the resources available to small and medium-sized enterprises. This includes providing theoretical guidance on how to approach the design of organisational chang­es and to assess their production and financial performance in the real world. Combining theminto an orderly methodology is intended to promote rationalisation of the decision-making pro­cess, taking into account the constraints typical of small and medium-sized enterprises. Qualita­tive studies that answer the 'how' question require an understanding of the conditions for im­plementing the methodology and should therefore be supported by case study methods [36]. 3.3 Methodology Most of these scientific publications in the field of capacity management seek to obtain practicalresults by confronting existing theories with problems occurring in industrial reality. In the fieldof operations management, case research is seen as one of the most powerful methods [37]. Thecase study method is very often used in the study of production systems because it allows for acomprehensive and broad view of complex issues in highly diverse environments [38]. The re­search presented in the article leads to the development of solutions that are valuable from apractical point of view while generating theoretical knowledge. Efforts were made to present indetail the data collected during the analysis of the current situation of the production system.They were collected by: • observation of the production system by the investigator, which made it possible to identi­fy the elements of the system and understand the connections between them, • testing of production documents, including, in particular, reports from the SAP ERP sys­tem, • measurements made in the production system for the preparation of its computer model, • semi-structured interviews on production system constraints and unstructured interviewsrelating to the company's capacity planning capabilities and needs, • simulation experiments leading to verification of the developed model. The data collected in this way was used to: • development of a computer model illustrating the current state of the production system, • formulate assumptions for change scenarios, • develop a concept for evaluating change scenarios. In the second phase of the study, the following research techniques were used to develop andanalyse change scenarios: • participant observation when designing change scenarios, • experiments based on computer simulation to determine the production effects of a givenchange scenario, • structured interview on estimating the financial parameters of the change scenario. The aim of the second phase was to characterise the scenarios of change in order to recommendone of them or to reject the proposal to increase production capacity. 3.4 Model of current state of roof window plant The case study involved a roof window manufacturer that is part of a global network of sales,production and services. The article only analyses the assembly line bypassing the process ofpainting components and material handling, because their flexibility is much higher than theassembly process and allows a much larger volume of production. There are 20 workstations onthe line. The daily production plan is generated by the SAP ERP system, which determines theorder in which orders are run. The plant works two shifts five days a week. The current demandvolume is 800 units/day. In the system, you can distinguish 5 sections presented in Fig.1. Thedescription of which is given in Table 1. The upper part of Fig. 1 shows the layout of the entire assembly line, which distinguishes sec­tions such as interior wing assembly line (In_sash), external wing assembly line (out_sash), in­stallation station of both window wings (Sash_assembly), window assembly section (pane_assembly), packaging section (Packaging). The lower part of Fig. 1 presents the positionsin the different sections of the production line. The model was made using Tecnomatix PlantSimulations by Siemens software. In the section where the outer wing is joined (sash_assembly) and in the section where theglass is inserted, there is a large share of manual work. The triangular distribution was used forits modelling. It is defined by three parameters (c, a, b), where the most probable value is c, theminimum value is a and the maximum value is b. In Tecnomatix Plant Simulation triangular dis­tribution is called triangle distribution. Table 1 describes the object parameters in each sectionof the model and describes them. This data allows you to recreate the model in any DES envi­ronment. Based on production reports from SAP – ERP, it is assumed that the frequency of overarchingbest aggregates the batch size of 25 units. In practice, the size of the production batches variesand is a multiple of 5 pcs. Table 1 Description of the individual positions of the modelled production process Section description Model marking Section characteristics Installation of internal wing elements Installation of external wing elements Installation of the outer and inner wings Installation of the glass Packing In_sash One worker on each station Out_sash One worker on each station Sash_assembly Two cooperatedworkers Pane_assembly One worker on each station Packing One worker on each station cartoning heap wrap A string of 7 mounting tables bound by roller relays.Processing time for each position 30 s. A string of 7 mounting tables bound by roller relays.Processing time for each position 30 s.In position SO4 1 % waste. Processing time: triangle (0:40, 0:20, 1:00) Set-up time: triangle (5:30, 4:15, 6:00) Set-up after 25 parts before next part 4 independent stations equipped with slatted glass mountingtables and aluminium profile mounting machines.Processing time: triangle (2:10, 1:30, 4:00)Set-up time: triangle (8:00, 6:00, 15:00) Set-up after 25 parts before next part. Equipment assembly: cartoning machine, robot for stacking win­dows into packages of 5 pieces (heap), foiling machine and prepa­ration of packages for transport (wrap).Processing time: 35 sSet-up time: 1 minSet-up after 25 parts before next partLoading time 5 sUnloading time 10 sProcessing time: 30 sSet-up time: triangle 20 s Set-up after 5 parts before next part. 4. Results and discussion: A case study for designing and analysing changes in the production system 4.1Proposed approach to designing change scenarios in manufacturing system The proposed methodology for capacity planning is largely based on the Theory of Constraintslogic. If demand exceeds the company's capacity in terms of production volume and is of a physi­cal nature, it identifies a resource constraint [39]. The process of improving the production sys­tem should begin with such a limitation called a bottleneck [40]. The next step in improving theproduction system is to determine how to exploit the bottleneck. Typically, there are more than a dozen potential improvement scenarios focusing on bottlenecks [38]. Their development takestime and is determined by the experience and creativity of the management team.Because of the limited time, it is proposed to design change scenarios taking into account thedecreasing likelihood of their success. It is assumed that it is due to difficulties relating to theorganisational effort of the staff and the risks associated with the novelty of the changes, whichaffect the uncertainty about the expected results and the error of financial estimates. The follow­ing order in which change scenarios are formulated is proposed: • Balance the production flow to a consistent rate imposed by the bottleneck. • Elimination of losses on bottleneck according to Lean Production methods. • Introduction of cooperation and outsourcing in the production process. • Introducing incremental and radical innovations in the production process. 4.2 Assessment of production parameters of changes scenarios Bottleneck-focused improvements are typically strongly linked to other components of the pro­duction system, so the capacity increase of the entire production system should be estimated asa basis for their implementation. The use of DES in the proposed methodology is not limited toanalysing the current state of the manufacturing system but is extended to include an analysis offuture conditions on the basis of “what if” experiments. Table 2 presents a summary of the ana­lysed scenarios of change with scenario details, where ti means processing time and tsu means set-up time. In addition, the scenario resulting from the frequent belief that in the event of ashortage of capacity, it is sufficient to install a new manufacturing unit, a scenario marked withthe letter B, which involves the duplication of the mounting position of the inner wing and theouter roof window. Table 2 Summary of analysed scenarios of changes in the production system A: Put the three buffers into the manufacturing system for blockade limitation on the stations: sash_assembly and pane_assembly. Buffers are on the tables with roller conveyers. Scenario details: Buffer capacity = 2, Buffer1 capacity = 4, Buffer2 capacity = 4 Total throughput of the manufacturing system after changes: 970 roof window B: Duplication the sash_assembly station. Scenario details: Interposing stadion: Sash_ass2; ti -> (0:40, 0:20, 1:00)F; tsu -> (5:30, 4:15, 6:00) Total throughput of the manufacturing system after changes: 1021 roof window Table 2 Summary of analysed scenarios of changes in the production system (continuation) A+C: Case A combined with introducing the standardization on the station sash_assembly for shortening processing and setup time. Scenario details: Buffer capacity = 2, Buffer1 capacity = 4, Buffer2 capacity = 4, Sash_assembly: ti -> (0:30, 0:20, 0:40), tsu -> (4:00, 3:00, 4:30) Total throughput of the manufacturing system after changes: 1107 roof window A+E: Case A combined with supporting operations on sash_assembly station by cobot. Scenario details: Buffer capacity = 2, Buffer1 capacity = 4, Buffer2 capacity = 4, Sash_assembly: ti -> (0:30, 0:20, 0:40) tsu -> (2:30, 1:15, 3:00) Total throughput of the manufacturing system after changes: 1124 roof window Table 2 Summary of analysed scenarios of changes in the production system (continuation) A+F: Case A combined with vision system(worker free) for sash quality (scratch, dimension, angles, colour) control. Scenario details: Buffer capacity 2, Buffer1 capacity 4, Buffer2 capacity 4, Sash_assembly: ti -> (0:30, 0:20, 0:50) tsu -> (3:30, 2:15, 4:00), Station qual_in: ti -> 0:30 Station qual_out: ti -> 0:30 Total throughput of the manufacturing system after changes: 1112 roof window 4.3Estimating the financial impact of production system change scenarios It is not sufficient to limit the decision-making process solely to assessing the production effectsof change options. Recommending the selection of one of them requires at least taking into ac­count the financial parameters of the scenario. In the methodology being developed, it is pro­posed to use throughput accounting (TA) to estimate the financial impact of the options forchange being analysed. TA is a simplified management accounting method that provides manag­ers with support in making decisions aimed at increasing the profitability of the company. Theundoubted advantage of TA is simplicity in assessing the investment made through practical andsimple measures that take into account the impact of the changes on the whole functioning ofthe company. Those that have been used in the proposed methodology are presented in Table 3. Table 3 TA meters used to estimate the cost-effectiveness of change scenarios Throughput = Sales Revenue -Totally Variable Cost Throughput (T) is net sales (SR) less totally variable cost (TVC), T = SR -TVC generally the cost of the raw materials, transportation charges, outsourced processing, commissions deducted for sales.*Labour and energy in manufacturing organizations are usuallynot tied to units produced. Net profit = Throughput - Operating Expense Operating Expenses: Operating expenses (OE) refer to other NP = T -OE cash outflows needed for creating the throughputs like pay­ments made for salaries and benefits of employees, mainte­nance, rental expenses, lease expenses, taxes and license fees,cost of utilities, etc. Return on Investment = Net Profit / InvestmentInvestments (I) represent funds tied up in physical assets suchROI = NP / I as machinery and equipment, land and buildings, product in­ventory, etc. In the TOC these all referred to as inventory Based on: [40] TA is designed as a direct cost approach and as such supports in particular short-and medi-um-term production decisions [41]. Although it does not provide such precise answers as tradi­tional accounting, it is sufficiently accurate for tactical investment decisions. Table 4 compilesestimates of financial parameters for each production system change scenario. It is assumed thatthe throughput/unit is 5 €, and during the year the company work for 250 days. It should benoted that the investment costs have been estimated and are all the more precise the less inno­vative the solution proposed in the scenario. The very high ROI results show that the company should decide to make investments to in­crease production capacity to 1100 units per day. The most cost-effective option was the intro­duction of three buffers to mitigate the effects of variable technological operations times andstandardisation at the installation site of the inner wing and the outer window (scenario C). Thissolution provides for the introduction of additional bonuses for employees in this position of €150/day, but the assumed effects in the form of a capacity increase of € 1480/day justify thisexpenditure. Such an increase in earnings (about 40 %) should ensure that workers with keyskills are maintained over a longer period of time. The danger was that the quality would be re­duced, so when implementing this solution, the company decided to make a 4h shift for eachemployee in this position and move it to a neighbouring position (pane assembly). Table 4 Financial parameters of the analysed changes in the production systemA B A+C A+D A+E A+F .units/day 166 217 296 296 296 296 .T/day (€) 830 1085 1480 1480 1480 1480 .OE (€/day) 12.5 492 160.5 153.5 40.9 43.5 .depreciation €/day 10.5 8 10.5 18.5 32.9 22.5 .salary €/day 0 480 150 120 0 0 .maintenance €/day 2 2 0 10 4 15 .energy €/day 0 2 0 5 4 6 .NP (€/day) 817.5 593 1319.5 1326.5 1439.1 1436.5 .NP (€/year) 204375 148250 329875 331625 359775 359125 .I (€) 2625 2000 3125 4625 8225 5625 ROI = .NP/.I 77.86 74,13 105.56 71.70 43.74 63.84 4.4 Discussion The study presented was based on a case study of a medium-sized production company. Itshowed the use of the proposed capacity planning methodology to answer the question of whichof the available scenarios for changes that adapts capacity to demand should be implemented bythe company. Analyses leading to the selection of the change plan option were carried out withina month. It should be noted that the development of the computer model of the system itself(together with the collection of data) took 2 weeks. If such a model were already available at the time of the question of the possibility of changing capacity, the response time could be reduced,or more change scenarios could be designed. A key advantage of computer simulation approaches is the ability to deal with complex sto­chastic problems without the need for advanced mathematical skills [42]. The article shows howDES can easily support mid-level managers in managing the company's operations. Although it isnot a precise tool, it is accurate enough to allow for rational decision-making in the case of me-dium-term investments. DES systems are constantly being improved. In addition, the growingoffer of textbooks, tutorials, and discussion forums makes it possible to acquire competenciessufficient to model a production system in a specific enterprise relatively quickly (about amonth). This task is also facilitated by access to production documentation from ERP class sys­tems. Thus, the limitations of the availability of computer simulation tools for SMEs due toknowledge, cost, data availability and development time (limited by knowledge, cost, data avail­ability and development time) [43] are systematically losing their importance. The methodology proposes to design change scenarios in a predetermined sequence. Thus,plans are created with increasing complexity, which allows, among other things, for combiningscenar-ios of change. This was the case, where further capacity expansion was based on the im­plementation of scenario A and expanding it with new elements. The initial simulations alreadyconcluded that buffers are the solution to the volatility resulting from short-term stochastic ir­regularities [44]. Their introduction involves the dilemma of increasing work-in-process (WIP)to fully utilize resources. In the proposed methodology, the investment profitability analysis is evaluated based on theROI determined according to the TA principles. The assumptions of the cost analysis TA methodused proved simple to understand for the engineers implementing the project. However, thisapproach does not account for the uncertainty with which the costs of innovative solutions areestimated. In the case study, this applies to the scenarios labelled A+E and A+F.The specificity of the object of the investigation lies in the fact that the company does not fore­cast demand itself, but rather adjusts its production capacity to the limits imposed by the centraldistributor. This is quite a typical situation in the case of Polish companies, which often carry outproduction for European brands. The proposed methodology is adequate for enterprises implementing complex discrete pro­duction. The effectiveness of the method developed has been demonstrated by applying it in areal-life production process. The results show that using the associated DES and TA tools allow managers to successfully design scenarios of changes in the production system, analyze themand assess their financial impact. The rationalization of tactical capacity planning enables aquick response to emerging opportunities to increase revenues related to changes in demand orreduce costs by implementing new technological solutions.It is a challenging skill that constitutes a competitive advantage in various SME enterprises withcomplex production systems. The use of DES software enables the design and analysis of changescenarios taking into account technical constraints. It allows the extrapolation of production capacity, providing the basis for economic assessments. The proposed approach is the founda­tion for planning the development of a production system that have regard both technical con­straints and profit-making aspects. 5.Conclusions and future research Digital models and simulation experiments make it possible to bring a lot of relevant infor­mation into the capacity planning process that is not otherwise possible in practice. The im­portance of DES in tactical capacity planning stems from the fact that different decision optionsfor organising the process can be tested before they are implemented. The concept of combiningDES and TA-based financial analysis is related to the need for decision support that: • must be carried out in a relatively short and limited period of time, • has little recourse to external consultancy, (e.g. for financial analysis), • is not routine and may not follow a set pattern, such as the entry of overtime, • requires a good understanding of the production situation. Among other things, tactical capacity planning decisions are made under such conditions. Theproposed methodology enables a small team of engineers to find answers to the questions: whatwill happen if certain changes are made [1], where their weaknesses are [2], how individualchange scenarios will affect the capacity of the overall system [3]. However, it must be empha­sized that the proposed methodology does not lead to an optimal decision. Nor does it guaranteeto find solutions that are workable. It requires employees involved in the decision-making pro­cess to be creative in designing change scenarios and skilled in operating the computer system.The need to support decision-making processes in terms of tactical changes in production sys­tems is not only due to the need to match capacity to demand. It is also related to the analysis ofthe effects of implementing solutions that fit into the Industry 4.0 concept. Many SMEs are al­ready facing a dilemma regarding this type of investment. The proposed methodology makes it possible to estimate the impact of changes on system capacity and seems adequate to supportthis type of decision as well. However, this requires verification of not only the manufacturingsystem but the entire production system. 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An exploratory study of protective inventory in a re-entrant line with pro­tective capacity, International Journal of Production Research, Vol. 48, No. 14, 4153-4178, doi: 10.1080/002075 40902991666. Simulation-based optimization of coupled material–energy flow at ironmaking-steelmaking interface using One-Ladle Technique Hu, Z.C.a,b, Zheng, Z.a,*, He, L.M.c, Fan, J.P.b, Li, F.b aCollege of Materials Science and Engineering, Chongqing University, Chongqing, P.R. China bCISDI Engineering Co., Ltd., Chongqing, P.R. China cChongqing College of Electronic Engineering, Chongqing, P.R. China A B S T R A C T The ironmaking-steelmaking interface of the steel manufacturing processinvolves the hot metal ladle circulation and the energy dissipation which arecoupled processes with an interrelated but independent relation. Therefore, the synergistic operation of the material flow and the energy flow at the inter­face is momentous to the effective production of the ironmaking-steelmaking section. However, there is a lack of solutions to realize the synergy. Here, wepresented a coupling simulation model for the material flow and energy flowof the ironmaking-steelmaking interface, based on the mathematical descrip­tion of their operation behaviors, the operation and technical model of the production equipment and the temperature-decreasing model of the ladle.Further, the coupling simulation model was applied to a concrete ironmaking­steelmaking interface using the One-Ladle Technique. The coupling simula­tion model proved its performance in providing comprehensive decision-making supports and optimized production management strategies by achiev­ing a solution that results in a decline of 10 .in the average temperature dropof the hot metal and a reduction in the cost per tonne of steel by CNY 1.02. A R T I C L E I N F O Keywords: Metallurgy;Ironmaking process;Steelmaking process;Ironmaking-steelmaking interface;Coupled material-energy flow;Discrete event simulation;Optimization;One-ladle technique *Corresponding author:zhengzh@cqu.edu.cn(Zheng, Z.) Article history: Received 8 August 2021Revised 17 September 2021Accepted 19 September 2021 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 workmust maintain attribution to the author(s) and the title ofthe work, journal citation and DOI. 1.Introduction 1.1Problem background and description The important ironmaking-steelmaking interface serves as the interconnection between theironmaking plant and the steelmaking plant in the long-route steel manufacturing process. Thissection involves three processes, i.e. blast furnace (BF) for ironmaking, Kambara Reactor (KR)for hot metal pretreatment and basic oxygen furnace (BOF) for steelmaking. The transportation of the hot metal is the main logistics process in this section. The “One-Ladle Technique” of theironmaking-steelmaking interface is a new technology for metallurgical process and transporta­tion optimization emerged in the past decade [1]. The specific process is shown in Fig. 1: Theempty ladles are pushed, usually, by a locomotive to the BF to charge the hot metal, after whichthe empty ladles become full ones. The full ladles are then transported to the buffer zone before the KR process. A crane lifts a ladle and transports it to the KR station for processing. Next, theladle is again lifted by a crane to the BOF, into which the hot metal is poured. The full ladle be­comes empty and then is directly put into the buffer zone by the same crane. Finally, the ladle isagain transported by a locomotive to the BF and another circulation begins. The ladle circulating rate affects the temperature drop of the hot metal and the ladle itself. In the circulation process, the material flow and the energy flow show an interweaved and interac­tive relationship. The multi-flow coupling phenomenon is the inherent characteristics that can­not be neglected when analyzing and optimizing the ironmaking-steelmaking interface [2]. The"One-Ladle Technique" puts forward higher requirements for ladle circulation, energy conver­sion, and time coordination in the production process. If too many ladles are running in the cir­culation, the charging waiting time increases, thereby increasing the temperature drop of the hotmetal. However, the tapping temperature after the BOF process is constant, therefore the lowertemperature of the hot metal poured into the BOF, the more heating agent is necessary to in­crease the temperature and longer processing time are required, which leads to a longer waitingtime for the subsequent full ladle to be handled and a larger temperature drop. In summary, too many ladles will increase the waiting time, temperature drop, process processing time and auxil­iary material cost. In turn, the lack of ladles will cause logistics interruption which affects theproduction. Therefore, the number of online ladles requires scientific decision-making. The optimization analysis on the flow-coupling should focus on the optimization of logisticsparameter configuration with the goal of reasonable cycle time, low production temperaturedrop, and low production cost. Therefore, aiming at the optimization of the ironmaking­steelmaking interface using the One-Ladle Technique, this paper develops a simulation model toconduct the analyses based on a real steelworks. Fig. 1 Schematic of process flows at ironmaking-steelmaking interface 1.2Previous work Remarkable progress has been made in recent years in studying the ironmaking-steelmakinginterface in terms of layout planning [3-8], connection mode of the interface [9-10], transporta­tion scheduling [11-16], ladle circulating control [1, 2, 17-20], and hot metal temperature drop[21-23]. As regards layout planning, Fan et al. [3] analyzed and summarized the characteristics ofthree modes of transportation: railway, crane + transfer car and special roads at the ironmaking­steelmaking interface, and the relations with One-Ladle Technique and the general layout plan­ning. Wiyaratn et al. [6] employed the SLP method in researching and evaluating the connectionrelationship between processes and compared the optimal schemes of the system under differ­ent layout plans. Concerning respect to the connections at the interface, Qiu et al. [7] analyzedthe technological characteristics of the ironmaking-steelmaking interface in six typical processroutes from the aspects of time, temperature, flow rate, production management, hot metal pre­treatment effect, energy consumption, environmental pollution, etc. by using systematic scien­tific reduction theory and holism. As far as transportation scheduling is concerned, Tang et al. [11, 12] studied the issues concerning the scheduling of arriving and departing torpedo ladlelocomotives, and established a mixed integer programming model for scheduling of the hot met­al transportation locomotives. And for ladle circulating control, Zhao et al. [1] adopted the multi-agent system to simulate the production logistics system of steel producers, and pointed out thatthe logistics efficiency should be improved by shortening refining cycle, increasing transporta­tion speed, upgrading desulfurization equipment, etc. Xiao et al. [17] made analyses on possibleoptimization of production management schemes involving ladle preparation mode, number ofonline ladles at the ironmaking-steelmaking interface with One-Ladle Technique by materialflow simulation. As for hot metal temperature drop, Du et al. [21] analyzed the heat dissipationmechanism of hot metal during hot metal receiving, transportation and pretreatment, etc. at theironmaking-steelmaking interface from a heat transfer viewpoint, and established a mathemati­cal model of hot metal temperature drop at the interface between hot metal ladle and chargingladle. Chen et al. [24] studied the fuel gas operation management practices for reheating furnace. Chen et al. [25] studied the effect of the production fluctuation on the process energy intensity in iron and steel industry, which revealed the relation of process energy intensity to the productionoperating rate and qualification rate. In summary, the current research on the optimization of operation at the ironmaking­steelmaking interface focuses on optimization of the ladle circulation in the material flow or thetemperature drop control in the energy flow but ignores the intrinsic rule of coupling controland synergy of material flows and energy flow during the operations at the interface. Operationsat the ironmaking-steelmaking interface bear information on five dimensions: plan, time, equip­ment, operation, and temperature and composition of hot metal. As a single math or modelmethod usually cannot take all the information of different dimensions into comprehensive con­sideration, it’s necessary to perform dimensionality reduction to simplify the information [26],making it difficult to analyze the influence of various factors on production when the materialflow is coupled with energy flow, thus offering limited guidance for optimization of the produc­tion. Based on the Tecnomatix Plant Simulation development platform, this paper builds a coupledsimulation model. The model considered the operation behaviors of the material flow and ener­gy flow, the operation and technical model of the production equipment and the temperature-decreasing model of the ladle that reflects the energy flow. Different organizing strategies wereemployed, the performances were evaluated by the production indicators, i.e. ladle cycle time,the temperature of hot metal charged into BOF, operating cost. 2. Simulation model description 2.1Model description Driven by the time flow, the material flow and the energy flow in the manufacturing process con­verge in a certain production process where the processing is handled under the interaction ofthe two flows. The synergetic coupling of the two flows are reflected through the product outputand the energy consumption. Therefore, the simulation model ............, which consists of Plan ...., Time t, Equipment .... and ...., Operation .... and Material Temperature Component .... as shown in Eq. 1, realize the simulated expression to the real manufacturing processes by abstracting theirphysical characteristics and running rules, as shown in Eq. 2. ............ = ....(...., ...., ...., ........) (1) ........(................, ........, ........) . . ........(............, ............) ........ = (2) .........................., ...................., ..................... . . ............(............, ............, ........) In Eq. 2, ........ refers to the system status at time t. ........(................, ........, ........) is the modeling rule where­by the ME (main equipment), TE (transportation equipment) and the directed ................ constitute a model operation network. ........(............, ............) describes the operation rules on how the positions andproperties change of the material entities ............ (hot metal) and the containers ............ (ladle). ........................., ...................., ..................... expresses the energy flow rules. According to the roles of the energyplayed in the production, the rules contain the energy changing rule ................ characterized in tem­peratures during transportation between processes, auxiliary energy adding rules .................... charac­terized by the addition of auxiliary materials during the processing, and energy consuming rules.................... characterized by the consumption of materials when equipment is running. ............(............, ............, ........) is the production (operation) rules at time .... of the equipment or transporta­tion devices (crane ............and span car ........) under a production schedule. Through its four simulation modules on logistics, equipment, control and information, asshown in Fig. 2, the simulation model above can simulate the interaction and conversion processof the material and energy during the ladle circulation in a way much closer to the reality: 1)When modelling, the equipment module is first selected to build the simulated productionenvironment. The equipment parameters set include the operating procedures, durations,types and amounts of energy consumed; 2)When running, the logistics rules in the operation control module and the control modelsin the material-energy control module can be called to push the simulation running asplanned and calculate the changes in transportation temperature, material and energy medium consumption occurred during the ladle circulation. Various process data is rec­orded by the information module, which realizes the quantitative analysis of the simula­tion system. Fig. 2 Modules in simulation model 2.2Functions of two key modules The control modules in the simulation model contain the operation control module and thematerial-energy control module, as shown in Table 1, which serve as the running brain of themodel, directing the orderly changing of the materials and energy in the logistical network. Theoperation control module controls the orderly transportation and processing of the materialunits between or in the process(es); while the material-energy control module is responsible forcalculating the energy media needed to achieve the target temperature. Table 1 Technical parameter design for two key modules Type Model Description Function Decide the production plans, target composition Production plan model ....................h and temperatures for each process according tothe casting plan Order the cranes to complete the transportation Crane operation and scheduling model ............h.... tasks Span car operation and schedulingOrder the span car com transporting task across ............h.... model bays Executing production task according to Process equipment operation model ............h.... equipment operating procedures Production Set the consumption per ton of steel in a certain .................... specification model process Linear consumption Material consumption has a linear relationship .................... Material model with the components to be processed consumption Material consumption has a linear non- Non-linear relational model .................... relationship with the components to be model processed Temperature Adopt physical heating method to reach target .................... compensation model temperature Electric energyElectric energy consumption for equipment ........................ Energyconsumption model operation medium Water consumption Consumption of water of various types for ........................ consumption model equipment operation model Gas consumption ................ Consumption of gases for equipment operation model Temperature dropmodel for hot metal Temperature drop caused by change of the hot ........h............ charged into different metal containers ladles Temperature Temperature drop change Temperature changes of hot metal under model for hot metal ........................ model different working conditions transportation Temperature change Temperature changes of empty ladle under model for the lining of........................ different working conditions an empty ladle Operation control Material-energy control module module 2.3Logic flow of simulation operation The actual production can be deemed as the combination of a series of chronological events,including the transport events and processing events of the unit material. Therefore, the cou­pling simulation model employs the trigger-based discrete simulation mechanism in which thetemperature and material composition information carried by the hot metal is set as the condi­tions to activate various sub-models of the control modules under different events. The activat­ing conditions are shown below: Start Simulation Call ....................h for production plan Do Scan task queueSelect task characteristics Case transportation task If Crane transportation then Call ............h.... and ........h............ and ........................ and ........................ End If Span car transportation then Call ............h.... and ........h............ and ........................ and ........................ End Case process processing task Call ............h.... Call .................... and .................... and .................... and .................... If using power, then Call ........................ End If using water, thenCall ........................ End if using gaseous media, thenCall ................ End End inspectLoop until Simulation End In the simulation operation, the temperature of hot metal is used as the condition to decidethe priority of related transportation tasks. When reaching the process equipment, the tempera­ture and composition of hot metal is firstly corrected according to the transportation situationand then treated as the inputting condition for the processing tasks. The corresponding material-energy model is enabled to calculate the materials and energy added to bring the temperatureand property of the hot metal to reach the target. After that, the new information on hot metaltemperature and composition is achieved and a loop starts until the end of the final process.More details are shown in Fig. 3. Fig. 3 Model operation flow 3.Results and discussion: Case studies 3.1Simulation cases The advantages the One-Ladle Technique offers vary greatly with the enterprises where it wasemployed. Aiming at offering optimal recommendations to improve the ironmaking-steelmakinginterface logistics of Steelworks, A using One-Ladle Technique, a simulation model is built toobtain the operation solutions under different production strategies. Fig. 4 shows the modelbuilt on the operating relationships between specific equipment, material flow and energy flowof Steelworks A. The interface is composed of 2 BF, 4 KR, 3 BOF and other auxiliary devices. Theladle is transported by the span car between BF and buffer zone, and by crane between buffer zone, KR and BOF. The moving path of the full ladle is marked by the directed red lines while thepath of the empty ladle by the directed green lines. Fig. 4 Model simulation operation In Fig. 4, each circle represents an empty ladle, and each red filled circle, and yellow filled cir­cle stands for a ladle fully charged and a ladle half charged. When a filled circle is in the center ofthe equipment, it means a ladle is under processing at that station. By setting different processparameters in the model, the simulation operation provides indicative parameters describingthe operating characteristics of the system quantitatively, allowing for analyses on how to en­sure optimization of the production with the One-Ladle Technique. According to the historical performance record of the two BFs in Steelworks A, 4 to 5 ladleson average are prepared to charge hot metal from the two under normal conditions, and 6 ladlesare used at the peak period. Each BF has two tapping outputs through which the hot metal istapped, the ladles prepared and tapping lines of each BF are set as shown below in Table 2. In real operation, the tapping durations of the two BFs is different. Therefore, two tappingconditions are considered for #1 BF and #2 BF: One is that both BFs tap at the same time, andthe other is that one taps 1 hour earlier than the other. These two tapping conditions, whencombined with the ladle preparation patterns as mentioned above in Table 2, lead to 6 differentworking conditions, as shown below in Table 3. In order to analyze the impact of different logistics parameters on production, the simulationis modeled according to the 1:1 layout of the ironmaking-steelmaking interface of Steelworks A.The simulation span is 24 h, during which 92 heats of hot metal are transported into the BOF.The hot metal output rate of the BFs is set to be 400 t each time, the hot metal tapping rate is 5t/min, the initial temperature of the hot metal is 1500 .. The BOF processing time is 38 min/while the KR processing time 36 min. The speed of the span car carrying a full ladle is 20 m/min,and 30 m/min when carrying an empty ladle. The running speed of the crane is 60 m/min and thehoisting/dropping time 2.5min. The temperature drop in the transportation process is 1 ./min. Table 2 Number of ladles prepared for each tapping line Ladle prep. pattern1 Ladle prep.pattern 2 Ladle prep.pattern 3 Number of tappings per day 12 12 13 Total number of ladles made available per BF 6 5 4 Number of tapping lines 2 2 2 Taphole A Number of pallets per line Number of ladles for #1 tapping line 3 3 3 3 3 2 Number of ladles for #2 tapping line 3 2 2 Number of tapping lines 2 2 2 Taphole B Number of pallets per line Number of ladles for #3 tapping line 3 0 3 0 3 0 Number of ladles for #4 tapping line 0 0 0 Table 3 Establishment of simulation cases Case No. Ladle preparation pattern Tapping condition Case I Pattern 1 Two BFs tapping at the same time Case II Pattern 1 One BF tapping 1 hour earlier than the other Case III Pattern 2 Two BFs tapping at the same time Case IV Pattern 2 One BF tapping 1 hour earlier than the other Case V Pattern 3 Two BFs tapping at the same time Case VI Pattern 3 One BF tapping 1 hour earlier than the other 3.2 Analyses of the simulation model results Analyses of the simulation model results are included in the comprehensive evaluations of thematerial flow and the energy flow. Therefore, the ladle cycle period .ladle is used to evaluate the material circulation efficiency (see Eq. 3). It shows that when the proportion of heats is higherwhile the cycle time for those heats is shorter, the material flow operation efficiency is higher.And, the average temperature of the hot metal charged into BOF tcharge is adopted to analyze theenergy losses of the system (see Eq. 4). It suggests that the higher the average temperature ofhot metal charged into BOF, the lower the temperature drop of the system. The operating costs C comprehensively reflects the situation of various material energy consumed by the system un­der the action of the material flow coupled with the energy flow, which is useful to evaluate theproduction outcomes (see Eq. 5). ............(................=........................<................) = ........................ .... × 100 % (3) .... ........h................ = ......... /.... (4) ....=1 .... ....= .(........ × ........)/....................h.... (5) ....=1 In these equations, ............(................ =........................ < ................) represents the number of heats within the ladle cycle time, between ................ and ................; ....means the total number of heats; ........ is the tempera­ture of the hot metal in a heat when it can be charged into the BOF; ........ refers to the unit price of the Material j consumed; ........ stands for the weight of the Material j consumed; m is the total types of materials consumed, and ....................h.... is the amount of the molten steel produced. 3.3Analyses of simulation results The simulation test was carried out according to the aforementioned input conditions. From theperspective of material flow operation efficiency, production condition is a significant impactfactor. As shown in Fig. 5, there is a significant difference in the distribution of the .ladle of each case. Both Cases I and . have a production situation where the ladle cycle period is greater than6 hours. This means that some ladles are in a condition waiting for the hot metal tapping; thelogistics operation efficiency of Case VI is the highest, and the ratio of the number of furnaces in the range of 0 to 2 hours for the turnover time of the iron ladle is 48.11 %, which is the lowest(case 1) 18.78 % higher. It can be seen that the tank allocation system 3 and the interval tappingof the two BFs are beneficial to improve the operating efficiency of the material flow. Temperatures of the hot metal charged into the BOF are used as an indicator to measure theenergy flow conversion. Under the same initial temperature conditions, the higher the tempera­ture of the hot metal transported into BOF, the smaller the temperature drop of the system. Fig. 6presents the effect of different material flow operation efficiencies on the energy flow. The aver­age temperature of the hot metal charged into the BOF in Case VI with the highest material flowoperation efficiency is 10.3 °C higher than that in Case I. This indicates that the higher the mate­rial flow operating efficiency, the smaller the temperature drop of the system. Different transportation time of the hot metal causes temperature fluctuation when it arrivesat the BOF, thus influencing the consumption of production materials. In the simulation, the ma­terial consumption model is used to calculate the consumption of material and energy for eachprocess realization of equal changes in the nature of hot metal material flows at different tem­peratures, and the production effects are comprehensively reflected in the operating costs. Fig. 7shows the comparison of operating costs between different cases by using Case I as the bench­mark. The costs per tonne of steel in Case VI are CNY 1.02 yuan lower than in Case I, which is anannual CNY 10.2 million yuan saving considering a steel plant with a 10 million tonnes capacityof the steel production. The built simulation model is, as shown above, able to reproduce the processes in which thematerial flow and the energy flow interact at the ironmaking-steelmaking interface. It also can quantitatively reflect the impact of different production strategies on operation in terms of indi­cators such as ladle cycle time, temperature of hot metal charged into BOF, and operating costs,thus eliminating the restrictions of evaluating production only from the perspective of materialflow efficiency or temperature control in energy flow. The analyses of the simulation results alsoindicate that application of the optimization strategies, e.g., increasing the tapping frequency,reduces the total number of ladles prepared for each BF. Moreover, an 1 hour tapping interval oftwo BFs enables Steelworks A to increase the average temperature of the hot metal charged intoBOF by 10.28 °C, and reduce the cost per tonne of steel by CNY 1.02. Fig. 5 Distribution of the .ladle of each case Fig. 6 Comparison of temperatures of hot metal charged into BOF Fig. 7 Comparison of operating costs (in CNY per tonnes of steel)Note: The operating cost in Case I is used as the benchmark reference 4. Conclusion The coupling simulation model built in the study considered the operation behaviors of the ma­terial flow and energy flow of the ironmaking-steelmaking interface, the operation and technicalmodel of the production equipment and the temperature drop model of the ladle. The energy-flow-driven moving process of the material simulated by the model reflects the interrelated butindependent relation between material flow and energy flow. The simulation results suggest that the simulation model can provide comprehensive deci-sion-making supports for actual operation control and optimization of production managementstrategies. The optimized production management strategies result in an increase of 10 °C in the average temperature of the hot metal charged into BOF and a reduction in the cost per tonne ofsteel by CNY 1.02. The methodology for building the coupling simulation model can be extended to the entiresteel manufacturing process and become an optimizer to steel producers by providing decision-making supports in achieving efficiency improvements and cost reductions. Acknowledgment This work was financially supported by the National Natural Science Foundation of China (Grant No. 51734004) andpartly by the National Key Research and Development Program of China (Grant No. 2020YFB1712803 and No. 2017YFB0304005). References [1] Zhao, J.Y., Wang, Y.J., Xi, X., Wu, G.D. (2017). 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(2021) A multidimensional information fusion-based matching decisionmethod for manufacturing service resource, IEEE Access, Vol. 9, 39839-39851, doi: 10.1109/ACCESS.2021.3063 277. Recharging and transportation scheduling for electric vehicle battery under the swapping mode Huang, A.Q.a,*, Zhang, Y.Q.b, He, Z.F.a,*, Hua, G.W.b, Shi, X.L.b aSchool of Economics and Management, Beijing Jiaotong University, Beijing, P.R. China bBeijing Wuzi University, Beijing, P.R. China A B S T R A C T Electric vehicle battery recharging on the swapping mode has grown up as animportant option other than the plug-in recharging mode in China, given thatseveral auto giants have been dedicated in constructing their battery swap­ping systems. However, the lack of effective operational methods on batteryrecharging and transportation scheduling has aroused a big challenge on thepractical application of the swapping mode, which enables the necessity ofour work. This study proposes a joint optimization model of recharging andscheduling of electric vehicle batteries with a dynamic electricity price systemwhich is able to identify the optimal charging arrangement (the recharging time and the quantity of recharging batteries) as well as the optimal transpor­tation arrangement (the transportation time and the quantity of transportingbatteries). For the validation purpose, a numerical study is implementedbased on dynamic electricity prices in Beijing. A sensitivity analysis of param­eters is carried out to increase the robustness and provide more managerialinsights of the model. A R T I C L E I N F O Keywords: Electric vehicle;Battery recharging;Battery swapping;Battery logistics; Transportation scheduling *Corresponding author:aqhuang@bjtu.edu.cn(Huang, A.Q.)hezefang@bwu.edu.cn(He, Z.Q.) Article history: Received 17 August 2021Revised 24 October 2021 Accepted 28 October 2021 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 workmust maintain attribution to the author(s) and the title ofthe work, journal citation and DOI. 1.Introduction Carbon emission reduction is becoming a privilege for an increasing number of countries acrossthe world to counter global warming effects. At the Climate Ambition Summit in December 2020,the leaders of the 27 EU member states stated that by 2030 their net greenhouse gas emissionswould be reduced to no more than 45 % of 1990. China has also made a commitment to peakcarbon dioxide emissions before 2030 and achieve carbon neutrality before 2060. Given thatautomobile exhaust is one of the major sources of carbon emissions while electric vehicles (EVs)are clean, the use of EVs has considerable potential in reducing vehicle emissions [1-5]. There­fore, the extensive application of EVs is an important available measure to help the countriesfulfill their commitments. Furthermore, for a country, some pillar industries like manufacturingcould enjoy extra emission credits saved by the transportation sector using EVs, and thus havemore development vigor. However, the range anxiety of consumers has severely limited the popularity of EVs. It usual­ly takes hours for EVs to recharge an EV, which is a matter of great concern for consumers, in addition to the imperfect recharging infrastructure [6, 7]. According to the Development Strate­gy Report of the Ministry of Industry and Information Technology, the number of EVs in Chinawill reach 60 million by 2030. If a large scale of EVs is charged in a disordered way (randomlyconnected to the power grid for charging), it will bring damages to the power grid [8]. Differentfrom in the plug-in recharging mode, the depleted battery of an EV in the swapping mode is re­placed with a full one, then the EV could continue to run and the depleted battery is left to berecharged. The swapping mode separates the recharging process from the battery swapping,which enables three advantages: (1) the whole operation takes less than 10 minutes, which ismuch faster than plug-in recharging; (2) the charging time and the quantity of charging batteriescan be scheduled reasonably so as to reduce the impacts on the safety and quality of power grid[9-10]; (3) the depleted batteries can be charged during off-peak hours of a discounted electrici­ty price and consequently reduce the charging cost. Actually, the swapping mode has beenbooming in China, e.g., NIO, a Chinese giant EV-maker, has set up 139 swapping stations, BAICGroup made a plan to construct 100 swapping stations capable to serve no less than 10,000 EVs,Changan Auto set up a battery swapping alliance to promote the swapping business, etc. Although the key challenges for operating battery swapping mode is to optimize both thecharging time of depleted batteries and the battery transportation scheduling between batteryswapping station (BSS) and battery charging station (BCS) [11], current studies on the batteryswapping mode rarely address the joint optimization of the above two problems, not to mentionthe joint problem with the dynamics of electricity price. To bridge this gap, we study a joint op­timization problem of charging time and transportation scheduling based on a battery swappingand charging system (BSCS). Although the BSCS hereby has a simple structure to comprise oneBSS and one BCS, it is able to unveil the nature of the swapping and charging systems and couldbe easily extended to complex ones. This study aims to answer the following two questions: (1)how to determine the optimal charging time and quantity of the charging batteries; (2) how tooptimize the transportation scheduling of batteries between BCS and BSS. All abbreviations aredetailed in Table 7 in Appendix. The uniqueness of this work is multifold. First, the proposed model takes into account thedynamic electricity prices, which not only maintains the security of the grid but also reducescharging costs. Secondly, this work is the first to address the joint optimization problem of thecentralized charging and the transportation scheduling of batteries with consideration of thedynamic electricity price, which could identify the optimal charging time of the depleted batter­ies, as well as the optimal time and quantity of the battery transportation between BSS and BCS.Finally, we highlight the managerial implication by carrying out a sensitivity analysis. The remainder of this paper is organized as follows. Section 2 reviews the latest studies onthe battery swapping mode. Section 3 elaborates the problem and the mathematical model. Sec­tion 4 shows the details of a numerical study and a sensitivity analysis, based on which, Section 5provides managerial insights. Section 6 concludes this study and discusses some potential futuredirections. 2. Literature review Substantial studies have been made on the charging strategies of EVs [12-15], however, thereare also many insurmountable challenges on the charging strategies, such as long charging time,charging inconvenience, etc. In recent years, with the invention of battery swapping station, thebattery-swapping mode has been obtaining increasingly more attention from industries and theacademia [16]. Most of the studies on the battery swapping strategy focus on the optimal charging time ofbatteries. Kang et al. [17] proposed a novel centralized charging strategy of EVs under the bat­tery swapping scenario based on spot electric price and design a population-based heuristicapproach to minimize total charging cost while reducing power loss and voltage deviation ofpower networks. Zheng et al. [18] focused on EV battery swapping station coordinated chargingdispatch method based on CS algorithm to achieve the optimization of daily charging plan ofbattery swapping station (BSS). Yang et al. [19] propose a dynamic operation model of BSS in electricity market based on the short-term battery management, and acquires additional reve­nuebyrespondingactively totheprice.uctuationin electricitymarket. Song et al. [20] designeda typical connection mode of electric vehicle charging and battery exchange infrastructure,which can provide guidance for the planning of electric vehicle charging and battery exchangeinfrastructure interconnected with the grid. Zhang et al. [21] proposed an optimized charging mode (OCM) to determine the impact of drivers' switching behavior on power grid and power generation cost. Wang et al. [22] proposed a comprehensive optimal allocation method for EVswitching stations based on orderly charging strategy. Infante et al. [23] considered the demandof EV users and the load of power grid, and proposed a strategy model of EV switching station tooptimize the benefits. Sarker et al. [24] proposed the optimization framework of the batteryswitching station operation model. Wang et al. [25] proposed an integrated optimization modelwith EV charging station, battery-swap station and energy storage system, which aims to find abalance status between the power grid and the EV users during the power flow exchange in thebackground of internet energy. To the best of our knowledge, most of the existing studies focus on the charging process ofthe battery exchange system, while ignoring the transportation scheduling between BCSs andBSSs. Given that the operation of BSCS needs to coordinate the two perspectives, it is necessaryto propose a joint optimization model to identify the optimal charging time and the optimalquantity of the charging battery, as well as the optimal battery transportation schedule (trans­portation time and transportation quantity) between BCS and BSS. 3. Model definition 3.1Problem formulation We study the battery charging process of the battery charging station (BCS) and the swappingprocess of the battery swapping station (BSS) in the battery swapping and charging system(BSCS). There are three subsystems in BSCSs: the battery swapping station (BSSs), the batterycharging station (BCSs) and the logistics system between them. In this system, users send thedepleted batteries (DBs) back to BSSs and remove the fully charged batteries (FBs). After awhile, BSSs will ship the accumulated depleted batteries back to BCSs. The depleted batteries(DBs) will be charged centrally by BCSs within a reasonable time and then shipped back to BSSsfor further use by future customers. Based on the above process, we propose a mathematicalmodel of battery centralized charging and transportation scheduling. Furthermore, we assumethat the service time of logistics system will not be discussed in our model. We introduce a mathematical formulation of this problem. First, the model discretizes thecontinuous time according to a certain time granularity. According to the time-of-use electricityprice mechanism and the uncertainty of demand, managers need to make decisions at the end­points of each time grain. For BSS, the managers need to make decisions about when totransport how many batteries from BCS to meet the customer's demand for electricity conver­sion. For BCS, the decision is when to charge the depleted batteries, so as to meet the demand ofBSS while minimizing the charging cost. Certain transportation costs will be incurred in the pro­cess of transportation. For the whole system, in order to minimize the total cost, on the basis ofmeeting the demand, when to transport and how many batteries to transport are also the con­tents to be decided. The model makes the following assumptions: 1. On the BSCS side, we assume that there is only one BCS, which is responsible for chargingthe battery. There is only one BSS, which is responsible for battery replacement for users.The logistics process between BCS and BSS does not consider the transport time and routetemporarily, we only study the number and quantity of transport. 2. In terms of electricity price, this section assumes that electricity price only change at thetime granularity endpoint. According to the State Grid, electricity price is divided intothree levels, peak, normal and trough, and only change at the hourly point of each day. The electricity price fluctuates periodically in a stepped manner. Therefore, this setting is alsorealistic. 3. In terms of battery charging process, we assume that each battery will charge for the sametime. In fact, the residual power of the battery is random and the time required for fullcharge should also be random. But EV users who generally go to BSS for energy renewalhave a relatively low battery surplus. We generally set the initial SOC of depleted batteriesas 0.2, and the SOC at full charge is between 0.9-1. Consider that the batteries currentlyused by car manufacturers are mostly made by BYD (mainly for BYD's own use) and Ning­de Times. So even if the car brand is different, the battery specifications are similar, whichmakes the time required for different batteries to be fully charged is basically the same, sothis assumption will not lead to a greater deviation from reality. 3.2 Model specification Without loss of generality, we characterize the scenario of our model as follows: 1. The battery belongs to BSS in BSCS; 2. There is only one BCS; 3. BSS cannot charge DBs; 4. The battery type is the same. DBs all have the same SOC, so does WBs, so they are chargedat the starting point of time granularity, and all batteries have the same charging time; 5. The battery delivery time between BCS and BSS is not considered; 6. The total operating period is divided into discrete time periods. Let g represent the timegranularity; 7. Electricity prices change over time and only at the end points of time granularity. 8. To extend battery life, the battery does not stop charging until it is fully charged. It is notable that although the BSCS hereby comprise one BSS and one BCS, it is sufficient toreflect the nature of the swapping and charging systems and could be easily extended to com­plex ones. The natation of variables and parameters are shown in Table 1. Table 1 Variables and parameters of the model Variable Meaning .... t time granularity; TP Single vehicle single transport cost ........ Electricity price at the ....time granularity W.... The number of full batteries in the BSS at the beginning of the ....period D.... Power exchange demand at the beginning of .... * ........ BCS full battery number at the beginning of .... ........ Number of batteries charged at the beginning of .... + ........Number of batteries charged in ....period ............ ............Number of batteries shipped from BSS to BCS at the beginning of .... ........ ............Number of batteries shipped from BCS to BSS at the beginning of .... ............ ........Number of vehicles transporting batteries from BSS to BCS at the beginning of .... ........ ........Number of vehicles transporting batteries from BCS to BSS at the beginning of .... ........ The maximum transport capacity of a single vehicle ........................ The ratio of full batteries to the capacity of the swapping station at initial time ........ The proportion of charging piles that are not occupied in the initial BCS M Number of time particles required for a single battery to be fully charged ................ The maximum number of cells a BCS can hold ................ The maximum number of cells a BCS can hold PoC Charging power T The total time window length of this study The model: ........+....-1 ............ + ..................... Min S =.....=1.....·............·........·.....=.... ......... + .............=1.........(1) Advances in Production Engineering & Management 16(3) 2021 Subject to ....1 = ................ × ........................ (2) ........ ........ = ........-1 -........-1 + ............-1 (3) ........ =........ (4) * ........ ....1 = (1 -........) × ................ -........1 (5) * * + ........ ........ = ........-1 + ........-1 -............ (6) ........ =........ * ............ (7) +.........-....+1, ....=.... ........0, ....=.... (8) .... .... ............ ......... =............. (9) ....=1 ....=1 .... .... ............ .............=......... (10) ....=1 ....=1 .... .... ........ ............ .............-.............=.................1 -......................... (11) ....=1 ....=1 .... .... ............ ........ .............-.............=........·................ (12) ....=1 ....=1 ............ ............ ........................ =............ =........+1 (13) ........ ........ ........ ........ .................... =............ =........+1 (14) ........ ........ * +........................................ =0 t,........, ........, ........ , ........, ........, ............, ............, ........, ........(15) Objective function Eq. 1 is the minimum sum of battery charging cost and transportation cost.Specifically, the total cost of BSCS consists of two parts: (1) The electricity cost for battery charg­ing under the time-of-use tariff mechanism; (2) The transportation cost of batteries dispatchedbetween BCS and BSSs. The constraints can be divided into 4 categories, including: Constraints on the number of fully charged batteries in BSS Constraint Eq. 2 indicates that the number of full batteries in the initial BSS is equal to the num­ber of available batteries placed in the initial BSS. Constraint Eq. 3 indicates that the number of full batteries in BSS in period ....is equal to the sum of the number of full batteries in BSS in period ....-1 and the number of batteries shipped into BSS, minus the number of batteries required in period ....-1. Constraint Eq. 4 indicates that the electrical changing demands that can be met in each phaseshould not exceed the total amount of fully charged batteries available in the current phase ofthe electrical changing station. Constraint Eq. 11 is the inventory capacity constraint in BSS, indicating that the difference be­tween the number of batteries shipped in and out of BSS in period ....should not exceed the inven­tory capacity in BSS in period ....-1. Constraints on the number of fully charged batteries in BCS Constraint Eq. 5 The number of fully charged cells in the initial BCS is equal to the number ofavailable cells placed in the initial BCS minus the number of fully charged cells shipped out of thefirst BCS. Constraint Eq. 6 indicates that the number of fully charged cells in BCS at period ....is equal to the sum of the number of fully charged cells in BCS at the beginning of period ....-1 and the number of fully charged cells at the beginning of period ....-1 minus the number of cells shipped out of BCS at the beginning of period ..... Constraint Eq. 7 indicates that the number of batteries shipped out of BCS in each periodshould not exceed the total amount of fully charged batteries available in the charging station inthe current period. Constraint Eq. 12 is the constraint of BCS internal free charging capacity, indicating that the difference between the number of batteries transported in and out of BCS in period ....should not exceed the spare charging capacity in BCS in period ....-1. Battery charge time constraint Constraint Eq. 8 indicates that when the charging time of the battery is greater than or equal tothe time particle size of M, the battery is fully charged. Battery transport constraints in logistics system Constraint Eq. 9 indicates that the number of batteries charged from the initial period to thecurrent period should not exceed the total number of empty batteries in each BCS period. Constraint Eq. 10 indicates that the number of batteries shipped out of BSS from the initialperiod to the current period should not exceed the demand for changing electricity. Constraints Eq. 13 and Eq. 14 are vehicle constraints for transport. Constraint Eq. 15 indicates that all variables are integers not less than 0. This is a typical nonlinear mixed integer programming problem that can be solved by mathemat­ical softwares such as MATLAB, CPLEX, and LINGO. 4. Numerical study and sensitivity analysis To illustrate the effectiveness of the model, this section is based on the time-of-use electricityprice mechanism of the power grid, and parameters are set according to the actual situation. Wesolve the problem by using LINGO mixed integer programming solver. In order to show thequantitative relationship among demand distribution, initial battery storage ratio and optimalcharging time, we study the influence of demand distribution and initial battery storage ratio onthe centralized charging strategy. 4.1 Parameter settings • g = 0.5: The time particle size is 0.5, indicating that a decision should be made every 0.5hour in the charging station, including whether to start charging a new batch of empty bat­teries and whether to transport the fully charged batteries to the changing station; • M = 10: Suppose it takes 5 hours to fully charge a battery. That is 10 time granularities; • ................ = ................ = 400: BSS and BCS can hold up to 400 batteries; • ........................ = 0.8: Initially, 20% of the inventory capacity of BSS is idle, which means 80% of theexisting inventory is occupied by full batteries; • ........ = 1: There is no battery in the initial state of BCS; • ........ = 50: The maximum transport capacity of a single vehicle is 50 batteries; • TP = 200: A transportation cost is 200 yuan; • PoC = 3: The charging power is 3 kWh; • D~Passion(15): Referring to the average visit times of gas stations in real life, the demandis set to follow the Poisson distribution with an average of 15; • P: According to the peak hours and corresponding electricity prices published by ChinaPower Grid. The specific setting of electricity price is shown in Table 2: • T: The research time is set as the time for all the initial fully charged batteries in BSS to beswapped out plus an integer multiple of M, combined with the above parameters, ................................h.................... = 21+3· ...., considering the continuity of the model for the study cy­cle and repeatability, will postpone back 10 research cycle time granularity, namely the to­tal time of this study window set to 21 + 3 · ....+ 10, the start time of study based on real life set to 7:00 in the morning. Table 2 Electricity price distribution in different periods Electricity Intensity Period of time Electricity price (yuan/kWh) Peak 7:00-11:00 1.234 Normal 11:00-19:00 0.856 Peak 19:00-23:00 1.234 Trough 23:00-7:00( Next day) 0.376 4.2 Model solving This part assumes that the electrical changing demand D follows the Poisson distribution withan average value of 15, and a group of samples with a capacity of 61 are randomly sampled. Ac­cording to the electrical changing demand represented by this group of samples, the optimalcharging time and quantity distribution as well as the battery transportation time and quantitydistribution between the electrical changing station and the charging station are solved. Fig. 1 shows the quantity distribution of electrical changing demands represented by thisgroup of samples. According to the determination principle of total time window length, the study cycle is 61time granularity. The optimal solution under this sample electrical changing demand is shown inFig. 2. Fig. 1 Electrical changing requirements for each timeFig. 2 Optimal charging time and quantity distributiongranularity during the study period of BCS Fig. 3 Optimal time and quantity distribution of batteriesFig. 4 Optimal time and quantity distribution of thefrom BSS to BCS battery from BCS to BSS In the scenario of EV energy update set in this article, the following conclusions can be drawn: • The optimal charging time and quantity distribution are shown in Table 3. Obviously, mostbatteries avoid the peak electricity consumption period and choose to start charging whenthe electricity price is normal or low. • Table 4 shows the distribution of transportation time and quantity of batteries betweenBCS and BSS. We can found that the battery transportation time is relatively concentrated.As shown in Tables 4, the battery transportation presents asymmetry. The amount oftransportation from BSS to BCS is greater than that in the opposite direction. The reason isthat batteries are transported between BCS and BSS, and some batteries are still placed inBSS when the research time is cut off. Therefore, although there are inconsistencies in bat­tery transportation in this experiment, it does not violate business logic and actual opera­tion. The continuous operation of charging and changing station can be regarded as theperiodic repetition of the time period studied in this paper. Therefore, we can use thesame method to make optimization decisions regularly, so as to ensure the minimum charging and transportation costs under the premise of meeting the electrical changingneeds in each cycle. • As shown in Figs. 3 and 4, in the optimal time and quantity distribution of battery trans­portation between BSS and BCS, the number of batteries to be transported in the decisionof the individual time granularity is very small. The research results show that the numberof transport batteries is less than 10 in some cases, especially when the batteries aretransported from BCS to BSS, the minimum number of transport is even one or two. Infact, the transportation cost is generally determined by the number of trips the vehicletakes, regardless of whether the vehicle is fully loaded. Therefore, it is necessary to in­crease the vehicle carrying rate to reduce transportation times and reduce the transporta­tion cost when time permits. The reason why this situation still occurs is to meet urgentneeds. Although the charging cost is high during the peak period, the prerequisite for re­ducing the cost requires priority to meet the demand for power exchange. Therefore, sucha low single shipment would not be desirable from a cost standpoint, but such an ar­rangement is necessary from a demand standpoint. Table 3 Optimal charging time and quantity distribution Number of batteries to start Period of time Electricity intensity Electricity price charging 7:00-11:00 1.234 0 11:00-19:00 Normal 0.856 267 19:00-23:00 Peak 1.234 74 23:00-7:00 (Next day) Trough 0.376 247 Peak Table 4 Optimal transportation time and quantity distribution of batteries Period of time Electricity intensity Number of batteries shipped (BSS to BCS) Number of batteries shipped (BCS to BSS) 7:00-11:00 Peak 0 0 11:00-19:00 Normal 366 260 19:00-23:00 Peak 40 1 23:00-7:00 (Next day) 7:00-11:00 (Next day) 11:00-13:30 (Next day) Trough Peak Normal 0 0 0 314 6 0 4.3 Sensitivity analysis The influence of demand distribution D on charging strategy We did 100 rounds of sampling, and the sample size of each round was 61 to form 100 groups ofsamples. Fig. 5 and Fig. 6 show the distribution characteristics of 100 sets of samples. We substituted 100 groups of random demand samples into the model to solve the optimalcharging time and quantity distribution of batteries, as well as the transportation time and quan-tity distribution of batteries between BSS and BCS. The results show that the optimal chargingtime is basically concentrated in the 9th, 28th to 32nd and 33rd time particle size, and the num­ber of batteries starting charging at the 9th and 33rd time particle size is the largest, with thenumber not less than 200. The number of batteries that started charging at time 28 to 32 wasapproximately 65. It can be seen that the uncertainty of demand has little influence on the finaloptimization result. Fig. 5 100 sets of sample boxplot of electrical Fig. 6 100 sample mean and standard deviationchanging requirements distribution of electrical demand The influence of initial battery storage ratio on charging strategy The parameter represents the ratio of the available battery storage capacity in the BSS at theinitial time. When the capacity of the BSS is determined, the value of represents the number offull batteries available in the initial BSS. It takes M (M = 10) time granularity for a depleted bat­tery to be fully charged, which means that the system's electrical changing demands need to bemet by artificially placed full batteries in the BSS during the initial 10 time granularity. There­fore, the value of has a very important impact on the operation of the system. Fig. 7 and 8 show the value of ....(....) at each time granularity when ........................ takes values 0.5, 0.6, 0.7, 0.8, 0.9 and 1, respectively. When ........................ changes between 0.5 and 1, the model can concen­trate most of the batteries on normal and low electricity prices. As the number of full batteriesplaced in the initial BSS increases, the number of batteries charged in the peak period decreases.This is because the system will give priority to meet the demand for electricity exchange. Whenthe initial full battery quantity is low, the number of rechargeable batteries will increase at thepeak. Fig. 7 The sensitivity change of ........................ to the optimal charging time Fig. 9 is obtained by summing up ....(....) when ........................ takes different values according to the power consumption intensity. Obviously, as the value of ........................ continues to increase, the total number of batteries chargedduring the research period decreases, and the number of batteries charged during peak periodsalso decreases. As the value of the parameter ........................ continues to increase, the minimum cost value continues to decrease. This is because if the demand remains unchanged, the more fully charged batteriesare artificially put into the system at the beginning, the fewer batteries need to be charged andtransported in the later period of the system, thus reducing the cost. But in practice, the morebatteries you put in, the more upfront costs you have. Table 6 shows that when ........................ takes 0.8, 0.9and 1, the number of batteries charged in the peak period is not much different. Taking intoaccount the trade-offs between the front and later costs, we recommend that the value of ........................ is 0.8. Fig. 8 The sensitivity change of ........................ to the optimal charging time Fig. 9 Sensitivity analysis of ........................ to optimal charging time Table 6 Distribution of optimal charging time and cost when takes different values Peak Normal Trough ........................ = 0.5 284 243 ........................ = 0.6 137 284 247 ........................ = 0.7 86 295 247 ........................ = 0.8 74 267 247 ........................ = 0.9 74 227 241 ........................ = 1.0 74 187 242 177 5. Managerial implication Based on the battery swapping mode, this study aims to introduce the joint optimization of bat­ tery charging and transportation and enrich the application of EVs in practice. Some constraintson the centralized battery charging and scheduling model are given special consideration. Alt­hough algorithm parameters and computational instances affect the calculation results, somespecific conclusions are generalized as follows: First, the model results are robust and easy to support the actual decision. In the example, theoptimal solutions of 100 groups of random samples generated according to Poisson(15) areroughly the same, indicating that the random fluctuation of demand does not have a great im­pact on the final optimization results. This means that in the actual decision, even if there issome deviation in the estimation of future requirements, the optimization results still have highavailability. What needs to be pointed out is that the above results are obtained on the premisethat the electricity changing demands are subject to the Poisson(15) distribution. If the electrici­ty changing demands are subject to the Poisson distribution with greater fluctuations or otherrandom distributions, further tests are needed. Second, the enterprises should focus on the time of centralized charging batteries to savecharging costs and reduce power grid losses. From Table 3, nearly 90 % of the batteries can becharged in the off-peak period to avoid the peak period, so as to enjoy a discounted chargingprice. Furthermore, considering that the higher the power grid load is, the shorter the servicelife will be, our optimized charging scheme is helpful to reduce the peak load of the power gridand reduce the power grid loss, thus extending the power grid life. An interesting phenomenonis that about 10 % of the batteries are charged in the peak period, mainly because BSS mustmeet the demand of electrical changing in each period, but charging takes a certain time, so insome cases it must be charged in time regardless of the cost. In order to save the charging cost in BSCS and improve the life of the power grid, when enter­prises need to charge the depleted batteries, the optimization model should be adopted to cen­tralized charge the rechargeable batteries in the period of low power consumption. Differententerprises have different requirements on service quality and response speed, so managersshould choose a reasonable balance of charging time points according to their business status and demand network characteristics. Third, the enterprises need to evaluate the tradeoffs between reducing charging costs andpurchase cost of batteries at the initial time of BSS. From Table 9, if enterprises did not putenough full batteries in BSS at initial time, then in the later stage of BSCS operation, some batter­ies will be charged in the peak period in order to give priority to customer needs, which will increase the cost of battery charging. However, if enterprises placed more full batteries in theinitial BSS, although in the later operation process there will be less batteries need to be chargedand the charging cost will also be reduced, they need to pay more for the initial battery purchasecost. Considering that different enterprises have different service scope and volume, the config­uration of parameter especially the purchase cost of EV batteries at initial time and batterycharging costs should be well-balanced according to their business condition and demand net­work characteristics. This paper makes full use of the dynamics of electricity prices to reduce the operating costs ofenterprises and improve the security of the power grid. The battery swapping mode of electricvehicles has been tested and operated in many countries. This paper can provide relevant man­agers with a basis for decision-making. It contributes to the realization of the standardization ofthe electric vehicle battery industry and the optimal allocation of resources, and can also im­prove the satisfaction rate of demand, reduce charging costs, and accelerate the popularizationand promotion of battery swapping mode. 6. Conclusion and the future work In this study, the electrical changing behavior of EVs is decoupled into two processes of battery charging and battery exchange, and the problem is modeled as a mathematical model of trans-portation and charging cost minimization in the BSCS closed-loop supply chain to achieve rea­sonable battery scheduling. The validity of the model is proved by solving an example with LIN­GO. Finally, the results of the example are explained and analyzed, and the managerial implica­tions of the centralized charging strategy and the optimal scheduling method of EV under themode of electrical changing is emphasized. The future work should further consider the benefit distribution among the three entities inBSCS under the cost optimization scheme. Transportation times between BSSs and BCS shouldalso be further studied in the future. In addition, this study does not discuss the initial SOC of thebattery in the battery swapping mode. In fact, the battery capacity for the battery exchange has acertain randomness. Future research can divide the battery initial SOC into segments to furtherrefine the battery charging time. Acknowledgement This work is supported by Beijing Social Science Fund (Grant no. B19SK00630), Beijing Intelligent Logistics SystemCollaborative Innovation Center (Grant no. BILSCIC-2019KF-24), and Beijing Logistics Informatics Research Base. References [1] Jie, W., Yang, J., Zhang, M., Huang, Y. (2019). 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An integrated optimization model of charging station/battery-swap station/energy storage system considering uncertainty, In: Proceedings of 2017 IEEE International Confer­ence on Energy Internet (ICEI), Beijing, China, 77-82, doi: 10.1109/ICEI.2017.21. Appendix Table 7 Abbreviations of variables Abbreviations Meaning EV Electric vehicle BCS Battery charging station BSS Battery swapping station BSCS Battery swapping and charging system SOC SOC is the state of charge, which is used to reflect the remaining capacity of the battery DB The depleted battery FB The fully charged battery A multi-objective selective maintenance optimization method for series-parallel systems using NSGA-III and NSGA-II evolutionary algorithms Xu, E.B.*,a, Yang, M.S.a, Li, Y.a, Gao, X.Q.a, Wang, Z.Y.a, Ren, L.J.a aSchool of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an, P.R. China A B S T R A C T Aiming at the problem that the downtime is simply assumed to be constant and the limited resources are not considered in the current selective mainte­nance of the series-parallel system, a three-objective selective maintenance model for the series-parallel system is established to minimize the mainte­nance cost, maximize the probability of completing the next task and mini­mize the downtime. The maintenance decision-making model and personnel allocation model are combined to make decisions on the optimal length of each equipment’s rest period, the equipment to be maintained during the rest period and the maintenance level. For the multi-objective model established, the NSGA-III algorithm is designed to solve the model. Comparing with the NSGA-II algorithm that only considers the first two objectives, it is verified that the designed multi-objective model can effectively reduce the downtime of the system. A R T I C L E I N F O Keywords: Maintenance;Series-parallel system;Maintenance decision model;Multi-objective optimization;Selective maintenance;Evolutionary algorithms;Non-dominated sorting genetic algorithm;NSGA-II;NSGA-III *Corresponding author:1180211005@stu.xaut.edu.cn(Xu, E.B.) Article history: Received 1 July 2021Revised 22 October 2021 Accepted 25 October 2021 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 workmust maintain attribution to the author(s) and the title ofthe work, journal citation and DOI. 1. Introduction The safe and reliable operation of equipment is the primary condition for enterprises to ensureproduction efficiency. Reasonable maintenance methods can effectively guarantee the reliableoperation of equipment and reduce the maintenance cost of enterprises. Effective, reliable andeconomical equipment maintenance plays an increasingly important role in enterprise produc­tion and operation [1]. In the manufacturing environment, manufacturing systems often containmultiple devices, forming a multi-device system, and there are often complex dependencies be­tween them. How to make reasonable maintenance and maintenance decisions is the research focus of predictive maintenance. Common maintenance decision-making methods include math­ematical model analysis method, Markov decision model method, simulation model method, etc.[2]. Mathematical analytic method is generally based on the knowledge in the field of operationsresearch to study the application and planning of various maintenance resources, establish thecorresponding model and solve it. Rashidnejad et al. proposed a dual-objective model and solu­tion to the geographically dispersed asset maintenance plan based on NSGA-II (Non-DominatedSorting Genetic Algorithm II) algorithm, and evaluated the effectiveness and performance of theproposed model through the actual case of bank ATM (Automatic Teller Machine) maintenance[3]; Pandey et al. made decisions about the selection of equipment to be maintained and the lev­el of maintenance to be performed by the maintenance equipment during the fixed downtime ofthe continuous generation system [4]; Dao et al. established a maintenance optimization modelof multi-state serial-parallel system based on resource availability and component maintenancetime and cost dependence, and used genetic algorithm to solve the optimization problem [5]. Khatab and Khatab assumed that the duration of the next task and the duration of rest were random variables with known distribution, and modeled the final selective maintenance optimi­zation problem as a mixed integer nonlinear stochastic programming [6-7]; Chaabane proposeda selective maintenance planning (SMP) model to optimize maintenance and allocation decisionsin systems running multiple tasks[8]; Cheng et al. conducted joint modeling and Optimization onoutput, product quality and predictive maintenance of series parallel multi-stage production system, and reasonably allocated maintenance resources according to the importance of equip­ment [9]; Lu et al. optimized the preventive maintenance problem of multi equipment seriesproduction system with buffer zone by using genetic algorithm [10]; For the Series production system without buffer, Leng et al. made decisions and optimized the production lot size and theimperfect preventive maintenance of the equipment under the conditions of both shortage andinventory [11]. According to the resource demand priority of each process in the productionsystem, Li et al. established the opportunity maintenance strategy of multi-resource constrainedserial-parallel system. Apart from the above example, a different structure of manuscript may beaccepted if it is the most suitable and effective style for the contents of the manuscript [12]. Markov decision model is a mathematical model to simulate the Random Strategy and Return of agents in the environment, and the state of environment has Markov property, which is wide­ly used in dynamic programming, random sampling, decision optimization and other fields.Bousdekis et al. proposed a main event-driven model for joint maintenance and logistics optimi­zation in the Industrial Internet environment, which combines the Markov decision process (MDP) and embeds the model into the event driven information system to make maintenanceand logistics optimization decisions [13]; Gerum et al. proposed a new method to predict raildefects, and determined the best maintenance strategy through Semi-Markov decision processmodel [14]. Xu et al. Proposed a Dynamic state maintenance decision model based on Markov,which was used to make maintenance decisions for the Major components of equipment [15]. Pei et al. constructed an imperfect maintenance stochastic degradation model based on theWiener process, and established a maintenance decision model to decide variables by the in­spection intervals and maintenance threshold, and solved the model through numerical simula­tion [16]; Nguyen et al. proposed a predictive maintenance strategy with multi-level decision,which considers respectively system level and component level maintenance decision-makingprocess, and uses Monte Carlo simulation technique to evaluate the maintenance cost rate [17];Dao and Zuo studied the selective maintenance problem of a multi-state series system workingunder variable load conditions in the next task, and simulated the degradation of multi-statecomponents through Monte Carlo simulation methods and evaluated the system reliability todetermine the best choice maintenance strategy to maximize the expected reliability of the sys­tem for the next task within the range of available resources [18]. Studies have shown that the shutdown time is usually assumed to be constant, most scholarsonly consider the two optimization objectives of minimizing maintenance cost and maximizingthe probability of completing the next task. However, in the enterprise continuous productionline, the maintenance decision-making model and personnel allocation model are not consideredtogether, when making maintenance decisions for the common series-parallel system of multipledevices. In each decision-making cycle, it is not only to solve the problems of which equipmentneeds to be maintained, the maintenance level of each equipment and the task assignment, but also to obtain the optimal downtime of the system. Therefore, we take the minimizing downtimeas the third objective of the decision scheduling model. Then, we design a NSGA-III algorithm tosolve the three-objective model. Compared with the NSGA-II algorithm of two objectives, thethree objective decision model can achieve optimal downtime of system maintenance and de­tailed dispatch of maintenance tasks, and effectively reduce the downtime of the system. 2. Description of selective maintenance problem for series-parallel system In the continuous production process, the production line is generally composed of multipledevices in series and parallel. In the multi equipment system, there are complex relationshipsamong the equipment, such as economic dependence, structural dependence, random fault de­pendence and resource dependence. Economic dependence refers to the maintenance or inspec­tion of multiple equipment at the same time under the condition of limited budget. This moment,there is an economic dependence among the equipment. Random dependence means that thedeterioration process or failure time of various equipment has random correlation to some ex­tent. Structural dependence refers to that the failure of one equipment may lead to the deterio­ration or failure of other equipment, and the maintenance of one component in the unit alsomeans the maintenance of other components. Resource dependence refers to that the mainte­nance personnel are responsible for the maintenance activities of various units or systems, thelimited spare parts inventory is used to replace multiple equipment, or selectively maintain themulti-equipment system in a limited time window. Therefore, it is necessary to consider various dependence relationships between equipmentin maintenance decision-making. The structure of series-parallel system is shown in Fig. 1. Se-ries-parallel system usually performs continuous production tasks. Selective maintenance ofequipment in the time interval between two continuous tasks can improve the reliability of thesystem when new tasks start. Due to the limited resources to complete maintenance activities, itis particularly important to determine the maintenance strategy based on the system require­ments. In the maintenance of series-parallel system, not only the loss cost of each equipment, but al­so the probability of the overall failure system should be considered. Therefore, it is necessary todetermine the system shutdown time and the length of shutdown time during the maintenanceof series parallel system, because the shorter the shutdown time, the smaller the impact on pro­duction. In order to solve the problem that traditional maintenance decision-making model ofseries-parallel system does not consider task dispatch and the system downtime is usually as­sumed to be constant, a multi-objective maintenance decision-making model of integratedmaintenance assignment system is established by taking the shortest system downtime as one ofthe optimization objectives, and genetic algorithm is designed to solve the model. Suppose that a production system is composed of n independent subsystems in series, each subsystem i is composed of mi independent identical subsystems in parallel. Each device in the system can be expressed as Eij, where i is the sub-system index and j is the sub-device index. Each device in the system has two possible states, denoted by 0 (Complete failure state) and 1(normal operation state). Since the whole system is composed of several subsystems in series,the whole system can work when all subsystems are running normally, and the device parallelstructure in the subsystem, at least one device can work when they are all in normal operation. Fig. 1 Series parallel system structure Within a given time period, the system needs to perform a series of consecutive identicaltasks, and maintenance activities are performed only during the rest time between adjacenttasks. In order to facilitate future discussion, it is assumed that the amount of maintenance re­sources (budget, time, etc.) required for a maintenance activity is determined, and the reliabilityof components, subsystems or systems is given in advance, which is the possibility of successfulcompletion of a given task. Question hypothesis: 1. The system is composed of multiple independent repairable binary state devices, that is,the device is in a normal working state or a failure shutdown state. The life of each devicein the initial state is different, and the life distribution parameters are known. 2. Maintenance activities (imperfect maintenance, preventive replacement, corrective maintenance) are performed at most once for each equipment during each rest cycle, inwhich corrective maintenance and preventive replacement are both perfect maintenances. 3. System components will not be aging during rest, that is, the life of components dependson the operation. 4. The cost of corrective maintenance is higher than that of preventive maintenance, and themean time for corrective maintenance on each device is longer than the average time forpreventive maintenance. 5. During the mission, the system does not perform any maintenance activities. When thefaulty components are repaired to a minimum degree, the failure rate remains unchanged. 6. When necessary, all essential maintenance resources (maintenance personnel, tools andrest hours) are available. If the maintenance resource constraints are exceeded, the corre­sponding parameters should be punished, and the model is still holding. 3. Modeling of series-parallel maintenance system In order to establish the selective maintenance model of series-parallel system, the followingsymbols are defined: • Aij is the effective service age of each equipment at the beginning of maintenance period; • Bij is the effective service age of each equipment at the ending of maintenance period; • Yij is the state of each equipment at the ending of maintenance period; • Xij is the state of each equipment at the beginning of maintenance period (if the equipmentworks normally at the beginning of maintenance Xij = 1, otherwise it is 0. if the equipment works normally when the maintenance ends Yij = 1, otherwise it is 0); • lij is the level of maintenance performed by the equipment in the current rest cycle (0 indi­cates that no maintenance is performed, 1 indicates preventive imperfect maintenance, 2indicates preventive substitution, and 3 indicates corrective maintenance); • K is the number of maintenance personnel; • k is the index of maintenance personnel; • Pij,t is the cumulative failure probability of equipment at time, which is given by the predic­tion model; • DTij is the expected downtime for unexpected equipment failure; • ............ is the unit downtime cost for equipment; • TIJkL is the time it takes for maintenance personnel k to perform maintenance level l on equipment Eij; • CIJkL is the cost it takes for maintenance personnel k to perform maintenance level l on equipment Eij; • when equipment Eij is maintained at level l by maintenance personnel k, wijlk is 1, other­wise it is 0; • Tstop is the length of downtime for maintenance; • f(t) is the downtime cost of the system over time; Assuming that the life of each device Eij in system obeys Weibull distribution, and the distri­bution of its shape parameters and scale parameters are ............ and ............, then the reliability Rij(t) of equipment Eij is: ............ ............(....) = exp .-...... . (1) ............ The total reliability of the whole system at time t is: .... .... .... R(....)= .........(....)= ..1 -.(1 -............(....)) . (2) ....=1 ....=1 ....=1 The probability that device Eij can still run normally after performing the next task with length u is as follows: .... = ......................... + ..... ............(3) .......................... The reliability of the whole system to successfully complete the next task with length u is as follows: .... .... R.... ..... = ..1 -..1 -............. (4) ....=1 ....=1 The cost of maintenance: .... .... .... ............ ............ = ........................ ·........................ (5) ....=1 ....=1....=1....=0 The maintenance personnel cost: ....h............ = ....·........·.................... (6) The maintenance time: .... .... ............ .................... = ..............· .· ..................... ·......................... ......... (7) ....=1 ....=1 ....=1 Objective function 1: Minimize maintenance costs Min ........................ = ............ + ....h............ (8) Objective function 2: Maximize the probability of the system successfully executing the nexttask .... .... ..... Max R.... = ..1 -..1 -............. (9) ....=1 ....=1 Objective function 3: Minimize maintenance time Min .................... (10) Constraint condition: • Maintenance activities are performed at most once for each equipment during shutdown: .... ............ ...................... =1, ....., .... (11) .... ....=0 • Maintenance duration cannot be greater than system downtime: .... ........ ............ ....................... · .................... =...................., ..... (12) ....=1 ....=1 ....=0 • If the equipment is faulty at the start of the rest, correction must be performed: .... ............ ......................= 3, ............ = 0, ....., .... (13) .... ....=0 • The constraint of Maintenance decision and failure probability: .................... .{0,1}, 0 =............(....) =1, ....., ...., ...., ...., .... (14) 4. Designing of multi-objective genetic algorithm The traditional genetic algorithm is only suitable for the single-objective optimization problem,and cannot solve the optimization model similar to the selective maintenance of series-parallel system. Srinivas and Deb proposed a Non-Dominated Sorting Genetic Algorithm (NSGA), using thecharacteristics of genetic algorithm parallel batch to obtain as many Pareto solutions as possible,but in the later use process there are high computational complexity, lack of elite and need toshare parameters [19]. Therefore, Deb et al. proposed a Non-Dominated Sorting Genetic Algo­rithm II, which solved the above problems of NSGA, and could find the non-dominated solution set with good convergence and dispersion in the two-objective optimization problem [20]. Zhao et al. [21] proposed a time-dependent and bi-objective vehicle routing problem withtime windows (TD-BO-VRPTW). The non-dominated sorting genetic algorithm II (NSGA-II) isadopted to obtain the Pareto optimal solution set. Through comparing these results with solu­tions in the Pareto front, the results in Pareto front are competitive because there is a trade-off between two objectives. Liu and Zhang [22] established a multi-objective planning model. Thismodel can solve the dual uncertainty demand problems of number and delivery time when or­ders are emergent or are modified for equipment manufacturing enterprises. The NSGA-II genet­ic algorithm is used to solve the model. Targeting at the problems existing in the multi-objectivescheduling of traditional flexible job shop and the complexity of multi-resource allocation, Zhong et al. [23] established an improved calculation model considering the optimization of such fourtargets as completion time, labour distribution, equipment compliance and production cost. Themulti-objective integrated constraint optimization algorithm was designed and the Pareto solu­tion set following different rules based on the NSGA-Pi algorithm was finally obtained. However, when the optimization objectives increase, the multi-objective optimization algo­rithm encounters new challenges: 1) the proportion of non-dominated solutions in the targetvector set increases exponentially; 2) the calculation quantity of diversity protection operator ishuge;3) surface visualization is difficult to achieve. In order to solve the above problems, Deb et al. proposed a multi-objective algorithm based on the framework of NSGA-II, which is calledNSGA-III [20]. This algorithm has obtained good results in solving the multi-objective optimiza­tion problem with 3-15 objectives. Therefore, we select the three objectives in the NSGA-III algo­rithm to solve the multi-objective selective maintenance problem. The NSGA-III algorithm flow is shown in Fig. 2. In essence, NSGA-III adopts a similar frame­work of NSGA-II, the difference is mainly the change of selection mechanism. NSGA-II mainlyuses crowding to sort, its effect in high-dimensional target space is not obvious, and NSGA-III maintain population diversity by introducing widely distributed reference points. Fig. 2 NSGA-III algorithm flow Aiming at the multi-objective optimization model for series-parallel system, the coding,crossover and mutation operators of NSGA-III algorithm are designed as follows. 4.1Encoding For the multi-objective optimization problem of selective maintenance in series-parallel system,each chromosome needs to determine three problems: 1) the equipment that needs to perform maintenance operation during rest period; 2) The level of maintenance operations performed bythe equipment to be maintained; 3) Maintenance task assignment issues, so three issues need tobe covered when encoding. Assuming there are N devices in the system, the chromosome is rep­resented by a matrix of 2N rows. Among them, the first N columns of the chromosome corre-spond to the equipment in the system, and the coding of the corresponding position representsthe maintenance operation level that needs to be performed during the current rest period (0indicates that no maintenance is performed, 1 indicates preventive imperfect maintenance, 2indicates preventive substitution, and 3 indicates corrective maintenance). The latter N is the distribution of the corresponding equipment maintenance tasks. If the equipment i decides not to perform any maintenance operation, the corresponding position is 0. If the maintenance per­sonnel 2 decides to perform preventive replacement, the corresponding position is 2, indicatingthat the maintenance operation is performed by the maintenance personnel 2. Therefore, Fig. 3shows an example of chromosome encoding. Team1 Team2 E1 E2 E3 E4 E5 E6 E7 E8 E9E10 0 0 1 0 2 0 1 0 0 3 0 0 1 0 1 0 2 0 0 2 Fig. 3 Encoding 4.2Crossover operator The crossover operation adopts the double-cut point crossover method. First, two positions aregenerated in the chromosome part that determines the maintenance level of the equipment.Then, the fragments of the two chromosome crossover intervals are exchanged, and the corre­sponding task assignment gene fragments are exchanged in the same time. This crossover meth­od ensures the feasibility of generatingnewoffspring. The crossover operation is shown inFig.4. intersection intersection point1 point2 Parent1 Parent2 offspring1 offspring2 Fig. 4 Crossover operator 4.3Mutation operator In this paper, two types of mutation operators are used, and one is randomly selected from thetwo mutation operators for mutation operation each time. The first mutation operator performsmutation operation on the chromosome part which determines the equipment maintenancelevel, and the second mutation operator performs mutation operation on the chromosome partof equipment maintenance allocation. The first mutation operator generates two arbitrary points in the first half of the chromo­some, cross the encoding of the corresponding position, and exchange the encoding of the corre­sponding dispatching chromosome region, as shown in Fig. 5. The second mutation operator randomly generates two non-zero gene positions in the sec­ond half of the chromosome, and then cross codes the corresponding positions, as shown in Fig. 6. 0 0 3 0 2 0 1 0 0 1 0 0 2 0 1 0 2 0 0 1 Fig. 5 Mutation operator 1 mutation point1 mutation point2 0 0 3 0 2 0 1 0 0 1 0 0 2 0 1 0 2 0 0 1 Fig. 6 Mutation operator 2 The above two mutation methods ensure the feasibility of chromosome after mutation, so it isnot necessary to verify the rationality of coding. 5. A case study and a comparative analysis of NSGA-II and NSGA-III The equipment composition of a production line is shown in Fig. 7, which is consisted of fivesubsystems composed of 14 components. The Weibull distribution life of each equipment andthe shape and scale parameters represented have been given. PM represents the implementa­tion of preventive replacement, IPM represents the implementation of imperfect maintenance,and CM represents the implementation of corrective maintenance. In addition, other parametersare given in Table1, in which the units of various maintenance costs are all yuan, and the unit ofmaintenance duration is day. Suppose the downtime cost of the system is RMB500 per day andthe hiring cost of a single maintenance worker is RMB50 per day. In order to verify the validity of the model in this paper, NSGA-II algorithm and NAGA-III al­gorithm are used to solve the model respectively. The goal of NSGA-II is to minimize mainte­nance costs and maximize the success rate of the next task, the goal of NAGA-III algorithm in­creases the minimum downtime maintenance time on the basis of NSGA-II. In both algorithms,the population is 500, the crossover probability is 0.8, the mutation probability is 0.1, and thenumber of iterations is 500. Fig. 7 System structure Table 1 Example parameter table Serial number a ß PM cost PM time CM cost CM time Operatingtime IPM cost IPM time E11 1.5 250 476 1 952 1.5 110 158 0.5 E12 2.4 380 653 3 1306 4.5 150 217 1 E13 1.6 280 962 2 1924 3 170 320 1 E21 2.5 400 323 2 646 3 120 107 1 E22 1.5 280 185 3 370 4.5 180 61 1 E31 2.4 340 639 2 1278 3 100 213 1 E32 2.5 260 812 2 1624 3 130 270 1 E33 2 280 391 3 782 4.5 170 130 1 E41 1.2 260 672 1 1344 1.5 150 224 0.5 E42 1.4 350 188 1 376 1.5 120 62 0.5 E51 2.8 400 294 3 588 4.5 180 98 1 E52 1.5 350 297 1 594 1.5 130 99 0.5 E53 2.4 300 394 2 788 3 100 131 1 E54 2.2 450 712 1 1424 1.5 150 237 0.5 380 Advances in Production Engineering & Management 16(3) 2021 The running time of NSGA-II algorithm is 460 s, and the number of Pareto solutions is 500.The calculation results are shown in Fig. 8. The surface formed by the optimal set in space iscalled Pareto fronts. All solutions in Pareto front are not dominated by other solutions outside orwithin the Pareto front curve. Therefore, these non-dominated solutions have the least goal con­flict than other solutions, which can provide a better choice space for decision makers. So, aftercalculation, the number of Pareto front solutions is 26. The running time of NSGA-III algorithm is 474 s, and the number of Pareto solutions obtainedis 496. The results of NSGA-III algorithm are shown in Fig. 9. After calculation, the number of Pareto front solutions is 19. The Pareto optimal solution set obtained by the algorithm only provides the non-inferior so­lution of the problem to three objectives, and there is no single objective optimal. Therefore, it isnecessary to select according to the expected degree of each objective of the decision maker.Assuming that the decision maker is most concerned about the probability of the system suc­cessfully completing the next phase of the task and the maintenance cost, the chromosome withthe smallest maintenance cost can be selected from the solution set with the reliability of com­pleting the next task greater than 0.85. The maintenance scheduling decision scheme solved by NSGA-II algorithm is shown in Fig. 10.The equipment that performs maintenance is selected as E11, E12, E22, E31, E33 and E42.The maintenance level is preventive replacement, and the final maintenance cost is 3182. Theprobability of the system successfully completing the next task is 0.853. The shutdown mainte­nance time of the system is 5 days, and the number of maintenance personnel enabled is 1. Fig. 8 NSGA-II algorithm results Fig. 9 NSGA-III algorithm results The maintenance scheduling decision scheme solved by NSGA-III algorithm is shown in Fig. 11. The equipment that performs maintenance is selected as E11, E12, E22, E31, E33, E42, andE52. The machine E33 performs imperfect maintenance, and the other equipment performs pre­ventive replacement maintenance. The final maintenance cost is 3168. The probability of thesystem successfully completing the next task is 0.850. The system shutdown maintenance timeis 2 days, and the number of maintenance personnel enabled is 3. The comparison of the two algorithms is shown in Fig. 12. It can be seen that when themaintenance cost is close to the probability of completing the next task, the downtime of themaintenance scheduling result solved by NSGA-III algorithm is less than that of NSGA-II algo­rithm. 6. Conclusion Aiming at the problems of selective maintenance for series-parallel systems, including simplyassuming downtime and not considering resource maintenance dispatch, firstly, we establish amulti-objective selective maintenance model with the purpose of minimizing downtime, mini­mizing maintenance cost and maximizing the probability of completing the next task. Then, thegenetic algorithm is selected to solve the model, and the coding method, crossover operator andmutation operator are designed in detail. Finally, in order to verify the effectiveness of the de­signed strategy, we design NSGA-II and NSGA-III algorithms with specific examples. These twoalgorithms are respectively used to solve the two objective maintenance decision-making modelwhich only considers minimizing maintenance and maximizing the probability of the systemcompleting the next task, and the three objective maintenance decision-making model which additionally considers minimizing the downtime of the system. By comparing the results of thetwo schemes, the decision-making scheme of NSGA-III is better than that of NSGA-II, which veri­fies that the three-objective decision-making model considering minimizing downtime can effec­tively reduce the downtime of the system. Acknowledgement This research is supported by Doctoral innovation fund of Xi'an University of Technology (No. 310-252072013),National Natural Science Foundation of China (Grant No. 52005404) and China Postdoctoral Science Foundation (No. 2020M673612XB). References [1] Zhang, Y.P., Yang, K.X., Shi, L. (2018). Economic optimization model for imperfect preventive maintenance underreliability constraints, Computer Integrated Manufacturing Systems, Vol. 24, No. 12, 3019-3026, doi: 10.13196/ j.cims.2018.12.010. [2] Laggoune, R., Chateauneuf, A., Aissani, D. (2010). 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APEM journal Chair of Production Engineering (CPE) University of Maribor APEM homepage: apem-journal.org Advances in Production Engineering & Management Volume 16 | Number 3 | September 2021 | pp 265-388 Contents Scope and topics 268 A new solution to distributed permutation flow shop scheduling problem based on NASH Q-Learning 269 Ren, J.F.;Ye, C.M.;Li, Y. Using the gradient boosting decision tree (GBDT) algorithm for a train delay prediction model considering the delay 285 propagation feature Zhang, Y.D.; Liao, L.; Yu, Q.; Ma, W.G.; Li, K.H. A smart Warehouse 4.0 approach for the pallet management using machine vision and Internet of Things (IoT): 297 A real industrial case study Vukicevic, A.; Mladineo, M.; Banduka, N.; Macužic, I. Increasing Sigma levels in productivity improvement and industrial sustainability with Six Sigma methods in 307 manufacturing industry: A systematic literature review Purba, H.H.; Nindiani, A.; Trimarjoko, A.; Jaqin, C.; Hasibuan, S.; Tampubolon, S. Modeling and optimization of finish diamond turning of spherical surfaces based on response surface methodology 326 and cuckoo search algorithm Kramar, D.; Cica, Dj. Tactical manufacturing capacity planning based on discrete event simulation and throughput accounting: 335 A case study of medium sized production enterprise Jurczyk-Bunkowska, M. Simulation-based optimization of coupled material–energy flow at ironmaking-steelmaking interface using 348 One-Ladle Technique Hu, Z.C.; Zheng, Z.; He, L.M.; Fan, J.P.; Li, F. Recharging and transportation scheduling for electric vehicle battery under the swapping mode 359 Huang, A.Q.; Zhang, Y.Q.; He, Z.F.; Hua, G.W.; Shi, X.L. A multi-objective selective maintenance optimization method for series-parallel systems using NSGA-III and 372 NSGA-II evolutionary algorithms Xu, E.B.; Yang, M.S.; Li, Y.; Gao, X.Q.; Wang, Z.Y.; Ren, L.J. Calendar of events 385 Notes for contributors 387 ISSN 1854-6250 771854 625008 Published by CPE, University of Maribor apem-journal.org