Paper received: 13.9.2007 Paper accepted: 19.12.2007 Predicting Order Lead Times Tomaž Berlec* - Edvard Govekar - Janez Grum - Primož Potočnik - Marko Starbek University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Entering on market, companies confront with different problems. But the largest problems of today's time are too long lead times of orders. A client that wants a particular product to be made will select the best bidder considering on delivery time. To make a bid just on the basis of experience of employees is very risky nowadays. Therefore we propose a procedure by which - on the basis of actual lead times of orders processed in the company's workplaces in the past - expected lead times of planned (and indirectly - production) orders can be predicted. The result of the proposed procedure is an empirical distribution ofpossible lead times for the new order, and on the basis of this distribution it is possible to predict the most probable lead time of a new order. Using the proposed procedure, the sales department can make a prediction for the customer about delivery time of the planned order. As an illustration of the procedure for predicting lead times of orders, a case study is presented: lead time of order for the "tool for manufacturing the filter housing" was predicted; the tool is manufactured in the Slovenian company ETI Ltd. © 2008 Journal of Mechanical Engineering. All rights reserved. Keywords: lead times, prediction, operation order, empirical distribution 0 INTRODUCTION Companies on the global market offer similar or the same products at comparable price and quality. The main difference between these companies is in the predicted order development time and in observance of the deadlines for delivery time. Before making a bid, the sales department has to provide data on operations that will have to be carried out for a particular order, data on the time required for performing these operations, and data on requested delivery time. Currently, the data at times of realization of operations are obtained from experienced company employees, while the customer specifies delivery time. However, estimates based on personal experience can be rather misleading. Consequently, the bids may be based on wrong delivery time which can couse that the company does not receive the order. Development of ICT - which are important resources for improving and maintaining the competitive advantages of the company on the market [1] - made radical changes as ICT simplifies many business-related tasks. Every company that wants to be competitive on the global market needs a suitable enterprise resource planning system -ERP system. There are several ERP systems available on the market [2] and it is the task of each company to select the optimum system [3]. The paper will present how the data stored in the ERP system can be used for calculation of lead times of orders (and indirectly: lead times of manufacturing orders) on the basis of theory developed at the IFA Hannover [4] and [5]. Furthermore, the calculation of percentage of manufacturing order lead times will be shown, which allows the calculation of the confidence interval. The purpose of this paper is therefore to propose a procedure for predicting lead times of manufacturing orders on the basis of past gathered data on actual lead times. In our research we have not found an approach for predicting lead times as described in this paper, so we assume that it is a new approach which uses already known and developed theory of IFA Hannover, and adds a new method for predicting order lead times. 1 METHOD FOR PREDICTING MANUFACTURING ORDER LEAD TIMES When talking about "an order", it is necessary to distinguish between operational, manufacturing, assembly and production order [4], as presented in Figure 1. *Corr. Author's Address: University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva 6, SI-1000 308 Ljubljana, Slovenia, tomaz.berlec@fs.uni-lj.si SDi SKi SD2 SD3 Fig. 1. Order lead times [4] When designing a procedure for predicting manufacturing order lead times, it will be assumed that the company uses an ERP system, whose database contains data about past operational and assembly orders in company workplaces. Any ERP system should therefore provide data on: • production-order code, • assembly-order code, • manufacturing-order code, • operational-order code, • type and sequence of operations on manufacturing and assembly orders, • IDs of workplaces where operational orders have been carried out, • actual execution times of operational orders, • date of completing a particular operational or assembly order in the previous workplace, • date of finishing a particular operational or assembly order in the observed workplace. ERP system output data should be available in Microsoft Excel format (xls). Based on previous research on problems of determination of lead times let us to the conclusion, that the proposed procedure for predicting order lead times consists of the following steps: Step 1: Determining actual lead times of already processed operational orders in the company's workplaces H. P. Wiendahl [4] says that the lead time of the i-th operational order N. (1 < i < n) which has been executed in the j-th workplace DM. (1 J2 Workplace DM TOu TO21 T0n,i DM TO 1 1,2 T0 T0 DM j TOi, j T0 2,j T0„ DM r T0 1 ^1,1 T0 T0 Assembly Fig. 4. Principle of construction of assembly structure ofproduction order I Legend: I - product SK - mark of asembly SD - mark of component part (x) - number of built ins of component parts and assemblies in assembly of higher degree Figure 5, presents technology and assembly routings for manufacturing parts and components of the production order I. Step 3: Random sampling and summing of vector element values of actual lead times of operational orders of individual manufacturing or assembly order Figure 6 presents the principle of random sampling and summing of vector element values of operational order actual lead times in the past of planned manufacturing and assembly orders. TOSD1 1 - lead time of component part SDp got after first iteration TOSK11 - lead time of assembly SKp got after first iteration TOI1 - lead time of product I, got after first iteration Figure 6 shows a schematic presentation of random sampling and addition of lead times values achieved in the past from workplace vectors, defined by technology and assembly routings for manufacturing parts and assembly of Part / component Prescribed sequence of operations SD 1 Turning DM1 ■ ■ H ■ DM ¡■■ii—i SD 2 Turning DM1 ■ ■ i ■III1 Planina DM2 1 1 üLtji^J|||Lb ijjJ I I SD 3 Planing DM2 1 ■ = ¡ngn g |M IUI 1 SK 1 Assembling DM5 I Assembling DM5: Control DMÉ □ Fig. 5. Technology and assembly routings of parts and components of production order I SD; SK A TOi,i TO2,i r TOi,3 TO2,3 TO1,4 TÛ2.4 TOn,i TOn,3 \ TOn,4 = TOs SKi SD2 TOi,5 TO2,5 TOn- = TOs TOi,7l TO2,iX TOn,i TOi,3 TO2, TOn, TOi,2 TO2,2 TOn,; TOi,4 TO2,4 TOn,4 7-Q sd2i SD3 TOi,4 TO2,4 TOn, TOi,5 TO2,5 X TOi,6 TO2,6 = TO i, TOn,5 JOn,6 DM6 1 = TOs Lead time Fig. 6. Random sampling and summing of vector element values of actual operational order lead times achieved in the past SD; SK Vsd1- TOsd1,1 TOsd1,2 TOsDi.k SKi VSD2- TOsd2,1 TOSD2 , 2 TOsD2,k Vski = TOski,i TOski .2 TOsKI.k SD3 VsD3- TOsd3,1 TOSD3,2 TOsD3,k Vi- TOi.i TO|,2 TOi.k ■ Lead time Fig. 7. Setting up vectors of expected lead times ofplanned manufacturing and assembly orders components. It is necessary to select the number of iterations for random sampling of lead times of manufacturing and assembly orders of planned production order (computer supported). The number of iterations is affected by the order type - by increasing its complexity, the number of iterations should be increased, too. Step 4: Setting up vectors of expected lead times of manufacturing and assembly orders of planned order Results of step 3 allow setup of vectors of the expected lead times of the manufacturing and assembly orders of planned production order, as presented in Figure 7. TOSD1>k - lead time of component part SDp got after k - th iteration VSD1 - lead time vector of assembly SD1 k - number of iteration The number of elements in individual vector depends on the number of performed iterations k. The number of required iterations can be established on the basis of tests, as it is necessary to assure a stable process, which cannot be achieved by a small number of iterations. A criterion for an adequate number of iterations is that multiple use of the procedure must yield comparable results, by which the stability (convergence) of the procedure is achieved. Step 5: Definition of vector of expected lead times of the planned order In order to define the vector of expected lead times of the planned production order Vp it is necessary to transform the Gantt chart of production order (Fig. 7) into an activity network diagram of order and enter into it the vectors of expected lead times of manufacturing and assembly orders of planned order (Fig. 8). Initial data of activity network diagram of planned order are: • date of starting the execution of the virtual order SD„ (4), TZsDo = 0 vector of the virtual manufacturing and assembly order V is: Kn = (5), vectors of expected lead times of manufacturing and assembly orders of the planned order are: SDi Vsd, TZsd, TKsd, sd2 Vsd 2 TZsd 2 TKsd 2 SKi VSK, TZsk, TKsk, SD3 VSD 3 TZsd 3 TKSD 3 I Vi TZi TK| Fig. 8. Activity network diagram of the planned (new) order VSDl,VSD2.....VSKi,Vr TKj = TO (10). For a virtual order SD0, which has no predecessors in activity network diagram, it is assumed that the date of starting the execution of order is (for the first iteration): TZSA,, = 0 (6), and the date of finishing the execution of order is TKm = TZm + TOm = 0 + 0 = 0 (7). For other manufacturing or assembly orders, which have one or more predecessors (Fig. 9) is the date of starting the execution of orders then: TZsn îep" iTZSD»,. + TOSD.i } (8) P* - predecessors of the observed order N. and the date of finishing the execution of orders TKm = TZçn + TOç, (9). Date of completing the last manufacturing or assembly order I is equivalent to the expected lead time of the planned order TO in the activity network diagram: Figure 8 shows the calculation for one vector element of expected lead time of the planned order. Such a calculation must be done for a selected number of iterations of randomly sampled values from vectors of individual component partsand assemblies of planned order. The calculation is carried out as follows: • For sequential operations, individual randomly sampled lead times from vectors of sequentially listed workplaces are summed up. The result of each iteration is stored into a new vector, which represents the sum for one component or part. • For parallel operations it is necessary to collect randomly sampled lead times from vectors of parallel workplaces, and then find a maximum lead time for each parallel path. Thus obtained results in each iteration should be stored in the common vector of maximum times of parallel paths, as the critical path in the activity network diagram is always the path with the longest required lead time for realization the manufacturing order. SDa SDb C ) ' VsDa TZsDa,1 TKsDa,1 VSDb TZsDb,1 TKsDb,i Fig. 9. Basic element of activity network diagram b,1 Calculation has to be repeated for the selected number of iterations. Thus obtained expected lead times of the planned order will represent empirical distribution of lead times of the planned order. Step 6: Predicting delivery time of the planned order Step 5 in predicting order lead time has lead to the vector of expected lead times of order, i.e. to a certain distribution of lead times. In real life, however, an exact value of lead time for delivery of order is required. The most probable delivery lead time for the planned order can be estimated by using median, which means that there is a 50% probability that the actual delivery time will be shorter, and 50% probability that it will be longer than stated. As the 50% risk is usually unacceptable for the client, so the estimated value should be stated for a wider confidence interval. For instance, 90% confidence interval is defined as 90% probability that the order will be delivered before the stated time. Therefore, maximum delivery time that can be guaranteed to the customer with 90% reliability, corresponds to the 90th percentage of empirical distribution of prediction of the planned order. Percentage [6] and [7] provides the value of Y, which is larger than P % of the values in the X set. In other words, e.g. 90th percentage gives the value, which is larger than 90% of all values (sorted from smallest to largest) in the X set (Fig. 10). In order to obtain the P-th percentage of X sorted values, it is necessary to calculate the R rank [8]: Lead time of planned ' production order [Wd; Cd] R = P(X+1)/100 which is rounded to the first integer and then the value from the X set is selected, which corresponds to this rank. R - percentage rank P - percentage X - number of sorted set elements Based on the above explanation and our tests, we propose that the 90th percentage be used as a standard. In this way it is possible to state with 90% confidence that the order will be completed within the expected time. If the company wants to achieve even higher reliability, it can use an even higher percentile (for example 99th) - and thus minimize the risk. Naturally, the choice of the percentage may depend on importance of the order and the customer - the more important the customer, or the more important the order, the higher is the interest of the company to get a particular order. In the proposed procedure for predicting manufacturing order lead times, in addition to MS Excel, the MATLAB software will be used [6], which allows execution of mathematical operations and graphical presentation of results. 2 TESTING THE PROCEDURE FOR PREDICTING ORDER LEAD TIMES The procedure for predicting order lead times was tested in the tool shop of ETI Ltd. company from Izlake, Slovenia. It produces tools for transforming and cutting, tools for injection moulding of thermoplastic and duroplastic materials, jet and press machines for duroplastic 90% X values r 10% Fig. 10. An example of the 90th percentile materials, press machines for ceramic materials, and automated assembly appliances. This tool shop speciality is design and manufacturing of high-quality tools for injection moulding of thermoplastic and duroplastic materials. Thanks to its many years of experience in making tools for ETI company, the tool shop started producing tools and appliances for external customers in the following fields: automotive industry, household appliances, medical technology, electrical engineering, electronics and illumination. Tool shop uses Largo ERP system, developed by Perftech Ltd. company from Bled [9], Slovenia. Because of their way of production (tools are made for known customers and each tool is unique) it is very difficult to precisely predict duration of production - but this is essential data for making bids and winning orders. Company management decided to test the suitability of the proposed procedure for predicting lead times of orders in a case study of determining lead time of order for the "tool for manufacturing filter housing # 705429" (Fig. 11). Steps of the procedure for predicting manufacturing order lead time for the "tool for manufacturing filter housing # 705429": Step 1: Determining actual lead times of operational orders finished in the past in the company's workplaces For the experiment, the Largo ERP system data were used in the period from December 12, 2002 till August 22, 2005. First it was necessary to export data from Largo ERP system to MS Excel format. The following data were exported from the database: order number, arrival date, departure date, manufacturing time, and sequence of operational orders. Largo ERP system uses calendar dates and does not take into account the company's labour-days calendar. Therefore the data which are not adapted to the company's labour days are useful mainly for predicting the duration of production from the sales department's point of view and not that much for manufacturing planning - for this purpose it would be necessary to take into account the company's labour-days. In agreement with the tool shop management it was decided that for determining actual lead times of operational orders finished in the past, the data from the ERP system would be used from December 12, 2002 till August 22, 2005. During that time, 22,850 manufacturing orders were processed in the production, with 57,951 operational orders in 35 workplaces (Table 2). It can be seen that during the observed time a rather varying number of operational orders passed across workplaces (minimum of 2 orders over workplace 44321 and maximum of 7307 orders over workplace 44253). Actual lead times of individual operational orders were calculated on the basis of the data obtained from the ERP system. The calculation was made in MS Excel on the basis of Equation (1). Figure 12 presents a part of the calculation of actual lead times of operational orders in Excel table. The results have shown that majority of actual lead times shorter then 1 Cd or 1 Cd, exceptions to the rule are some extreme cases, e.g. 464 Cd. Table 2. Number of operational orders finished on workplaces in the tool shop Number of finished orders in Code: Workplace name: three years: 44000 Cooperation - service 21 44141 Design of devices 151 44142 Machine electronics 130 44143 Design of tools 2288 44211 Slitting 1420 44221 Turning 3706 44222 CNC turning 1052 44231 CNC programming 371 44232 CNC Milling Micron 2660 44241 CNC programming 668 44242 CNC Milling Picomax 60 4153 44243 CNC programming 9 44244 CNC Milling Deckel Maho 1400 44251 CNC Milling Picomax 54 2018 44252 Milling 235 44253 Rough milling 7307 44261 Plane grinding 1972 44262 Plane/profile grinding 4225 44263 Round grinding 2894 44264 Tools sharpening 159 44265 CNC coordinate grinding 7 44271 CNC programming of wire erosion 1126 44272 Wire erosion 1927 44273 Wire erosion -Makino 3161 44281 Dip erosion - AGIE 439 44282 Dip erosion - Charmilles 1565 44283 Dip erosion - Sinitron 513 44286 Omega punching 745 44291 Heat treatment 5172 44311 Manual machining 4288 44312 Assembly of tools 812 44313 Assembly of machines and devices 197 44321 Sampling 2 44331 Measurement 885 44332 DEA Omicron measurement 273 Three years production: 57951 Step 2: Using or forming assembly structure of the planned order and technology routings of parts and components of order - for tool # 705429 In this step known assembly structure is formed (Fig. 13), as well as known type and sequence of operations (Fig. 14) for the tool under discussion - tool # 705429. It can be seen from Figure 13 that the tool consists of two parts: ejecting and feeding part. The tool consists of bought parts and ofparts/components made in the tool shop. There is just one assembly operation at the end, which is followed by testing. For tool parts and components that are manufactured in the tool shop it was necessary to gather data on type and sequence of required operations, which □ Microsoft Excel - odatki igjsi vv^ i^fP SflS^S Sätä MSS HI » iûjjBjuaiîuiiii /il- -*-it in a 4)ii9% -®8 :«rn * • - i i a e s ■ m i m • »älßrli- • ii- A-h m i B C D E F G H J 1 Order Nr. Nr.workinq order Workplace Sequence Workplace name Production time [Ehl Arrival date Departure date Lead time [Cdl 2 6229 700609 44232 30 CNC Mllllnq Micron 4 22.5.2003 22.5.2003 0 3 6229 700609 44311 20 Manual machlnlnq i.5 15.5.2003 2.6.2003 18 4 6231 700609 44253 10 Rouqh milling 3,5 13.5.2003 15.5.2003 2 5 6231 700609 44262 30 Plane/profile grinding 2 17.5.2003 30.5.2003 13 6 6231 700609 44242 20 CNC Milling Plcomax 60 3 15.5.2003 17.5.2003 2 7 6231 700609 44272 40 Wire erosion 6 30.5.2003 3.6.2003 4 s 6232 700609 44253 10 Rouqh millinq 3 14.5.2003 14.5.2003 0 9 6232 700609 44253 20 Rouqh millinq 3,5 14.5.2003 16.5.2003 2 10 6232 700609 44262 50 Plane/profile grlndinq 7 19.5.2003 28.5.2003 9 11 6232 700609 44242 30 CNC Millinq Plcomax 60 9 16.5.2003 17.5.2003 1 12 6232 700609 44242 60 CNC Millinq Plcomax 60 9 28.5.2003 2.6.2003 5 13 6232 700609 44311 40 Manual machininq 3 17.5.2003 19.5.2003 2 14 6233 700609 44253 10 Rouqh millinq 1 16.5.2003 16.5.2003 0 15 6233 700609 44232 20 CNC Millinq Micron 2 16.5.2003 19.5.2003 3 16 6233 700609 44311 30 Manual machininq 1,5 19.5.2003 2.6.2003 14 17 6234 700609 44253 10 Rouqh millinq 3,75 14.5.2003 15.5.2003 1 18 6234 700609 44262 30 Plane/profile grlndinq 1.5 19.5.2003 30.5.2003 11 19 6234 700609 44232 20 CNC Millinq Micron 4.5 15.5.2003 19.5.2003 4 20 6235 700609 44253 10 Rouqh millinq 9 19.5.2003 19.5.2003 0 21 6235 700609 44232 20 CNC Milling Micron 6 19.5.2003 20.5.2003 1 22 6235 700609 44311 30 Manual machininq 2,5 20.5.2003 2.6.2003 13 23 6236 700609 44253 10 Rouqh millinq 4 16.5.2003 16.5.2003 0 24 6236 700609 44232 20 CNC Millinq Micron 5 16.5.2003 19.5.2003 3 25 6236 700609 44311 30 Manual machininq 2,5 19.5.2003 2.6.2003 14 26 6237 700609 44253 10 Rough milling 2,5 12.5.2003 12.5.2003 0 27 6237 700609 44261 30 Plane grinding 1 17.5.2003 3.6.2003 17 28 6237 700609 44232 20 CNC Millinq Micron 3,5 12.5.2003 17.5.2003 5 - r IH ' » ► sh.vu MEWMPm...... is Peadv NUM Fig. 12. Calculation of actual lead times offinished operational orders in interval from December 12, 2002 till August 22, 2005 provide quality parts and components. For the tool # 705429 some of these data are presented in Figure 14. In tool shop in ETI Ltd. they do an conglomeration of operations named preparing on manufacturing, which for this order contains: machine electronics (44142), design of tools (44143) and slitting (44211). This is actually not a real part of the tool, which can be shown in Figure 14, but it consumes time, so it is necessary to count it in by the sequence of operations. Steps 3 and 4: Random sampling and summing of vector element values of actual operational order lead times of individual manufacturing or assembly order of the planned order, and setup of vectors of expected lead times of manufacturing and assembly orders of the planned order for the tool # 705429 On the basis of defined sequence of machining on parts and components for the tool # 705429 made by MATLAB software, the vectors of expected lead Parts/components Sequence of operations Preparing 44142 ■■Itt43-1 44211 I Clamping plate 44244 4'. 44311 | Ejecting modul Plate 1 Final switch square 44253 | 44311 | Flange 44221 44232 | 44311 | Order 705429 44312 44311 I -1 Fig. 14. Type and sequence of operations required for manufacturing parts and components of the tool # 705429 o '3 o £ o OJ A o s= '(5 13 o o O 1 M d & OJ in ft -a p OJ OJ OJ £ ^ -d ft