Model of Integrated Production and Delivery Batch Scheduling Under JIT Environment to Minimize Inventory Cost

Transcription

1 Proceeding of the 2014 International Conference on Indutrial Engineering and Operation Management Bali, Indoneia, January 7 9, 2014 Model of Integrated Production and Delivery Batch Scheduling Under JIT Environment to Minimize Inventory Cot Endang Praetyaningih, Suprayogi, TMA Ari Samadhi and Abdul Hakim Halim Bandung Intitut of Technology Bandung, 40132, Indoneia Abtract Thi paper conider a batch cheduling problem of a JIT upplier and integrate production and delivery deciion. Part that have been equenced are to be proceed on a ingle machine, collected in a container, and ent to a cutomer in order to be received at a common due date. Scheduling involve the number of batche, batch ize, cheduling of the reulting batche, and the number of vehicle delivering the batche.the objective i to minimize inventory cot wherein the holding cot of in-proce part and completed part are ditinguihed. The holding cot i derived from the o-called actual flow time, defined a an interval time of part pent in the hop ince the tarting time for proceing a batch until it due date. The propoed problem i formulated a a non-linier programming olved by relaxing the variable of the number of batche to be a parameter. An algorithm i propoed to olve the model and teted by numerical experience. Thi reearch how that there i a ratio between in-proce part and completed part holding cot which affect the deciion of the number of batche and their ize. In addition, thi reearch how that the lower the in-proce part holding cot, the more advantageouly to tore part a WIP than a finihed product, and vie vera. The number of vehicle i determined from the number of the reulting batche. Keyword Integrated production and delivery, batch cheduling, actual flow time, ditinguihed holding cot of WIP and finihed product. 1. Introduction In the cae of a company that produce part on a production facility and then deliver the part to cutomer on a delivery facility, production and delivery are two ucceive function and interrelated. However, many companie manage thee both function eparately. Thi eparation could bring to a olution with a local optimum. In order to achieve the global optimum, thee two function need to be integrated (Chen, 2010b). Integration of production and delivery deciion can be een in the cae of production of the part that have been equenced, o-called equenced part (junbiki), by a JIT upplier. In the JIT environment, the product mut be received by the cutomer at the right time in the right quantitie. Thi equenced part will be aemblied to the cutomer' aembly line directly, and the product mut be received at the time will be aemblied in the right quantitie. Lead time between the order received by the upplier and product received by the cutomer i too hort to provide inventorie (Iyer, et al., 2009). In order to provide 100 percent ervice level with minimum cot, the deciion of production and delivery mut be integrated. In thi reearch, the equenced part proceed on a ingle machine, collected in a container, and ent to a cutomer in order to be received by the cutomer at a common due date. For the next dicuion, the term part will be ued to refer to the equenced part. Conidering each container a one production batch, then many production batche that are delivered together in one vehicle are conidered a a delivery batch, and the product are ent by a number of vehicle imultaneouly at a common due date. The combined chedule involve determining the number of batche and their ize, tarting time of proceing the reulting batche, and the number of vehicle. Reearch on integrated production and delivery ha been developed in recent decade. Chen (2010b) named it a IPODS (Integrated Production and Outbound Ditribution Scheduling). Typical model of IPODS combine machine cheduling (to proce the order) and vehicle cheduling (to end the order). The IPODS model i a problem of optimizing one or combination of time-baed, cot-baed and revenue-baed performance (Chen, 2010b). 2109

2 Many IPODS reearch with time-baed performance ha been conducted by Geimar et al. (2008) and Chen (2010a), while the cot-baed performance ha been addreed by Hall and Pott (2003 and 2005), Stecke and Zhao (2007), Zhong et al (2010), Chen and Pundoor (2009), Lee and Yoon (2010 ) and Armentano (2011), Yan et al. (2011). The IPODS reearch that combine cot-baed and time-baed performance ha been carried out by Chen and Vairaktaraki (2005), and Gharehyakheh and Tavakkoli-Moghaddam (2012). Much of cot-baed performance of IPODS reearch doe not ditinguih the WIP holding cot and the finihed product holding cot, but in practice thee two holding cot are different. The reearch on integration of production and delivery and ditinguihing between WIP holding cot and finihed product holding cot wa done by Lee and Yoon (2010). The holding cot are computed by multiplication of the holding cot per unit time and the flow time. Lee and Yoon (2010) aumed that all part available in the hop at the beginning time of the cheduling period imultaneouly. The reulting chedule i a combination of job cheduling in a production tage and batch cheduling in a delivery tage, without conidering the due date. Thi reearch develop Lee and Yoon (2010) model, and involve the deciion of combining production and delivery batch cheduling under JIT environment. The performance ued i the actual flow time propoed by Halim et. al. (1994) intead of the traditional flow time (ee Dobon et. al., 1987, and Dobon et. al., 1989). By thi performance, the arrival of batche in the hop hould not be at the beginning time of the cheduling period, but could be controlled to be at the tarting time of proceing the batch preciely. The objective i to minimize the total relevant cot. 2. The Actual Flow Time of Integrated Production and Delivery. The batch cheduling model dicued in thi paper i developed from the batch cheduling problem that have been dealt in Halim et al. (1994). To enure the due date i achieved, Halim et al. (1994) adopted backward cheduling by putting the firt cheduled batch i cloet to the due date and ue the actual flow time a a performance meaure. Halim et al. (1994) model did for the production tage only and conidered the delivery time be zero. 2.1 The actual flow time of production batch cheduling Halim et al. (1994) define the actual flow time, F a, a the time pent by material/job in the hop from tarting time of procee part (B) until it due date (d). The actual flow time, F a, of each part can be formulated a: F i a = d B i, i = 1,2,, (1) In the batch cheduling, the batch proceing time i calculated by multiplication of part proceing time and the batch ize. Figure 1 how the actual flow time for each batch in a chedule. If t, and Q, repectively, tand for the part proceing time, etup time per batch, and the batch ize, then the actual flow time per batch, can be formulated a follow: The total actual flow time for batche can be written a follow: i FL a i = ( + tq j ), i = 1,2,, (2) j=1 i F a = [ ( + tq j ) ] Q i j=1 (3) d B [] F a [] F a [2] --- B F a [2] [1] B [1] tq [] tq [2] tq [1] Figure 1. The actual flow time (Source: Halim et. al., 1994) 2110

3 Batch cheduling model that ditinguih in-proce part and completed part have been developed in Halim and Ohta (1994). In-proce part are waiting in the batch until all part of the batch have been proceed, while completed part are tored in the delivery tage until the tarting time of delivery. The actual flow time of part in both tage are hown in Figure 2, and can be formulated a below: i 1 F a 2 = { tq i } + [ { ( + tq j )} Q i ] (4) i=2 j=1 Actual flow time of inproce part in batch 2 tq[2] Actual flow time of completed part in batch 2 tq[1] d tq[] --- tq[2] tq[1] B B2 B1 F a 1 F a 2 F a Figure 2. The actual flow time of in-proce part and completed part for the production batch (Source: Halim and Ohta, 1994) 2.2 Actual flow time of integrated production and delivery batch cheduling Figure 3 how the actual flow time of integrated production and delivery. The due date i defined a the time when the product arrive at the cutomer location. Let b i the departure time of vehicle, and v 01 i the travel time. The total actual flow time of part in both tage i an addition of the actual flow time in production tage and in the delivery tage. The actual flow time in the production tage i equal to the Equation (3), while the actual flow time in the delivery tage i equal to the travel time. For a imultaneou delivery problem, the total actual flow time of batche can be formulated a: i F a = [ ( + tq j ) ] Q i + v 01 Q i j=1 (5) F a b d B [] F a [] F a [2] F a v B [2] F a [1] B [1] --- tq [] tq [2] tq [1] v 01 Production Delivery Figure 3. The actual flow time of integrated production and delivery The actual flow time of integrated production and delivery batch cheduling and ditinguihing between in-proce part and completed part i adopted from Equation (4), and hown in Figure 4. In a common due date problem, all vehicle departure imultaneouly. The departure time i equal to the completed time of the firt batch. Hence, all part of the firt batch available a in-proce part only. However, the availability of the other batche are differ from the firt batch. Let take the econd batch a an example (ee Figure 4). The actual flow time of in-proce part in the econd batch i an interval time between the arrival time of the batch until all part of the batch have proceed. After proceing, all part in the econd batch i tored a completed part and wait until the delivery 2111

4 time. Thu, the actual flow time of completed part of the econd batch i defined a an interval time between completion time of the econd batch and the delivery time, which i equal to the actual flow time of the firt batch plu etup time. The total actual flow time of batche in the production tage and the delivery tage can be written a: i 1 F a 2 = { tq i } + [ { ( + tq j )} Q i ] + v 01 Q i i=2 j=1 The firt term and the econd term of Equation (6) how the actual flow time of in-proce part and completed part, while the third term how the actual flow time of delivered part that indicate the number of delivery. (6) Actual flow time of inproce part in batch 2 tq[2] Actual flow time of completed part in batch 2 tq[1] b d tq[] --- tq[2] tq[1] v 01 Production Delivery B B2 B1 F a 2 F a 1 F a k F a F a Figure 4. The actual flow time of in-proce part and completed part of integrated production and delivery 3. Problem definition Let there be n part of ingle item that are requeted at a common due date, d, and proceed on a ingle machine. The total number of part proceed i equal to demand rate. The part are moved in the container that called a batch. Conequently, the batch ize are limited by container capacity, c. Let aume that the etup activity doe not require material, o that the arrival time of the batche in the hop are enured at the ame with tarting time for proceing the batch, B i. It i alo aumed that the etup time of a batch, i, i not affected by the batch equence and the batch ize, Q i. All product mut be received by the cutomer at the due date, imultaneouly. Deliverie are done by a number of homogeneou vehicle, n v, which are able to carry k production batche. The availability of vehicle i not a contraint, becaue it i held by a third party. Travel time from upplier to cutomer, v 01, i aumed contant. The problem are how to batche all the requeted part o a minimize the total relevant cot, how to chedule the reulting batche, and how many vehicle are needed to deliver all batche. To enure that the due date i not violated, a backward cheduling i choen, i.e. cheduling by putting the firt cheduled batch cloet to the due date and move toward zero. The propoed problem i called the ingle machine-ufficient vehicle-common due date (SMSVCD). Figure 5 illutrate the SMSVCD problem. PRODUCTIO DELIVERY Batch-r Batch-2 Batch-1 Machine Batch Batch-k delivery-batch Cutomer production-batch Batch-r Figure 5. Illutration of SMSVCD problem 2112

5 The total relevant cot of SMSVCD problem i conit of the inventory cot in the production tage and in the delivery tage, and the delivery cot. The inventory cot i multiplication of the holding cot per unit time and the actual flow time. The delivery cot i proportional to the number of vehicle delivering the batche. There i a cot that i not effected by the actual flow time but mut be accounted in the relevant cot, that i the cot for procuring container. Let c f, c w, c c, c d and n c a the holding cot per unit time completed part, the holding cot per unit time in-proce part, the procurement cot per unit container, the delivery cot and the number of container, repectively. Suppoe that F i aw and F i af are the actual flow time of in-proce part and the actual flow time of completed part, repectively. The total relevant cot, TC, for SMSVCD problem can be formulated a: aw af TC = c w F i + c f F i + c c n c + c v n v (7) 4. Model Formulation and Solution 4.1 Model Formulation The following aumption are adopted in formulating SMSVCD problem: Part moved in container, and a container aumed a a batch Batch ize i real poitive value, Vehicle capacity i expreed in term of container, The number of container in each hipment i alway an integer, Completed time of the firt batch i the ame with the departure time of delivery, Travel time include the activity of loading and unloading, Vehicle availability i ufficient. Refering to Equation (6) and Equation (7), the SMSVCD problem can be preented a a non-linier programming a follow: Minimize Subject to: i 1 2 TC = c w { tq i } + c f [ { ( + tq j )} Q i ] + x i c c + c v k (8) i=2 j=1 ( 1) + tq i + v 01 d Q i = n (10) Q i c, i = 1, 2,, (11) i d v 01 B i (i 1) tq i = 0, i = 1, 2,, (12) k=1 0 if Q i = 0, i = 1,2,, x i = { (13) 1 if Q i > 0, i = 1,2,, 1, = integer (14) Q i, B i 0, i = 1, 2,, (15) (9) 2113

6 Contraint (9) how that all batche are proceed and hipped from time zero to the due date. Contraint (10) tate a material balance in the hop. Contraint (11) implie that the batch ize doe not exceed the container capacity. Contraint (12) enure that all batche will be arrived at the cutomer location at the due date. Contraint (13) i a binary variable, that i 0 if the batch ize i zero, and 1 otherwie. Contraint (14) how that the number of batche mut be an integer which greater than or equal to one. Contraint (15) how the non-negative contraint. 4.2 Solution Method The SMSVCD problem i olved by relaxing the deciion variable to be a parameter. Uing Mathcad 14, we can find Q i for certain value of uing Equation (8) to (15). Propoition 1. In the batch cheduling problem with batch ize i limited by the container capacity, c, the batch ize, Q i, are Q i c, and the number of batche,, i n c n, where n i the total proceed part. Proof. The container can not tore part exceeded it capacity, c. If the container i full of part, the requirement of container will be minimum. The minimum requirement of container i computed by dividing the total number of part proceed (n) and the container capacity (c). However, the number of container i an integer, o the minimum requirement of the container i rounding up of ( n c). Converely, if each container contain one part, the requirement of container will be maximum, o that the maximum of occur when = n. If one container i conidered a one batch, then the maximum batch ize (Q i ) i c, the minimum number of batche i n c and the maximum number of batche i n. Determining of the optimal olution of SMSVCD problem i tarted at minimum according to Propoition 1 to find the total cot and the batch ize a the initial olution. Computation followed by increaing by 1 and it olution were compared with the previou olution. Thi proce i topped when the olution of TC at the lat larger than the previou, or the value of exceeded maximum. Propoition 2. In the integration of production and delivery problem and the vehicle capacity i expreed by k production batche, the minimum requirement of the vehicle delivering the batche for production batche are /k. Proof. The vehicle can not load the production batche exceeded it capacity, i.e. k batche. If the vehicle i loaded at the full capacity, the requirement of vehicle will be minimum. Thu, the minimum requirement of vehicle i computed by dividing the number of batche and the vehicle capacity, or (/k). However, the number of vehicle i an integer, o the minimum requirement of vehicle i rounding up of (/k), and tated a /k. Refering to Propoition 1 and Propoition 2, an algorithm i propoed to olve the SMSVCD problem. Algorithm SMSVCD Step 1. Set predetermined value of parameter n,, t, v 01, d, c w, c f, c c, c v, c, and k, Step 2. Uing Propoition 1, compute minimum, Step 3. Solve Equation (8) to (15) with minimum to determine TC and optimal batch ize (Q i ). Set the current olution TC a the bet olution (Z ) and batch ize a (Q i ). Step 4. Increae the number of batch, = + 1, then olve Equation (8) to (15) with to find TC and batch ize (Q i ). Set the value of the total cot a Z' and the batch ize a Q i. Step 5. If Z < Z, then et Z = Z, and Q i * = Q i, go to Step 6. Otherwie, et optimum =, go to Step 7. Step 6. If > makimum, then optimum =, go to Step 7. Otherwie, et optimum =, go to Step 4. Step 7. Uing Equation (12), compute B i, and according to Propoitoon 2, compute the number of vehicle, n v. Step 8. Stop 2114

7 5. umerical Experience and Analyi In order to how the behavior of the olution, everal numerical problem are preented here. The firt numerical experience i done to demontrate how the propoed algorithm olve the problem in one value of the parameter. The reult of the experience hown in Table 1. Table 1 how that the propoed algorithm able to olve the SMSVCD problem. By taking one value for all parameter hown in Table 1, it i found that the minimum total cot occur when the number of batche i 5, or optimum i 5, the number of vehicle i 2 with imultaneou departure at 90. Figure 6 how the Gantt Chart of SMSVCD problem. Table 1: The batch ize in everal number of batche () n = 90; = 2; t = 0,5; d = 100 ; v 01 = 10; c f = 20; c w = 15; c c = 25; c v = 100; k = 3; c = 20 Q i TC B i b n v 5 {20; 20; 20; 19; 11} 51,470 {80; 68; 56; 44.5; 37} {90} 2 6 {20; 20; 20; 18; 10; 2} 51,480 {80; 68; 56; 45; 38; 35} {90} 2 Produki Pengiriman Q[5] = 11 tq[5] = 5.5 Q [4] = 19 tq [4] = 9.5 Q [3] = 20 tq [3] = 10 Q [2] = 20 tq [2] = 10 Q [1] = 20 tq [1] = 10 v 01 = 10 B [5] = 37 B [4] = 44.5 B [3] = 56 B [2] = 68 B [1] = d=100 Actual Flow Time Figure 6. Gantt Chart of SMSVCD problem The econd numerical experience i intended to find how the change of in-proce part holding cot will affect the deciion of the number of batche and their ize. The change of in-proce part holding cot i expreed by the ratio of (c w c f ), wherea the other parameter were not change. Computation are conducted for everal value of, and the reult of the experience are hown in Table 2. Table 2: The batch ize in everal number of batche () and (c w c f ) n = 90; = 2; t = 0,5; d = 100 ; v 01 = 10; c c = 25; c v = 100; k = 1; c = 20 c w = 5 = 6 =7 c f Q i TC Q i TC TC 0,6 {20; 20; 20; 20; 10} 48,930 {20; 20; 20; 20; 10; 0} 48,930 0,65 {20; 20; 20; 20; 10} 49,780 {20; 20; 20; 20; 10; 0} 49,780 0,7 {20; 20; 20; 20; 10} 50,620 {20; 20; 20; 20; 10; 0} 50,620 0,75 {20; 20; 20; 19; 11} 51,470 {20; 20; 20; 18; 10; 2} 51,480 51,580 0,8 {20; 20; 20; 18.3; 11.7} 52,310 {20; 20; 20; 16.7; 10; 3.3} 52,280 52,380 0,85 {20; 20; 20; 17.9; 12.1} 53,140 {20; 20; 20; 15.7; 10; 4.3} 53,070 53,170 Table 2 how that for = 5 and = 6 and the value of (c w c f ) le than or equal to 0,7, the batch ize for the batch number 1 until number (-1) are equal with the container capacity, while the lat batch i equal with the remaining part. However, if (c w c f ) greater than or equal to 0.75, the minimum total cot will be achieved when the lat everal batche will hare the remaining part. It mean that in the in-proce part holding cot much lower than 2115

8 the completed part holding cot, there i a tendency to tore part a in-proce part than a completed part, and vice vera. The reaoning can be decribed a follow: the bigger the batch ize, the longer the actual flow time of in-proce part in it batch. Refering to the objective function a hown by Equation (8), the longer of actual flow time of inproce part will increae the inventory cot of in-proce part. Thi numerical experience how that there i a raio of (c w c f ) affecting the deciion of the number of batche and their ize. Thi value i called a changing point. If (c w c f ) le than the changing point, the batch ize of the firt batch until the batch number (-1) will be maximum, and the batch ize of the the lat batch i equal to the remaining part. Howefer, if (c w c f ) i greater than the changing point, the deciion of batch ize will tend to avoid fulfillment in the lat everal batche. 6. Concluion The integrated production and delivery batch cheduling problem ditinguihing the holding cot of the in-proce part and the completed part i affected by everal variable deciion, e.g. the number of batche (), the batch ize (Q), cheduling of the reulting batche and the number of vehicle delivering the batche (n v ). The problem can be formulated a a non-linier programming model. Refering to the numerical experience, it can be concluded that there i a ratio between the holding cot of in-proce part and completed part which affect the deciion of the number of batche and their ize. In addition, the lower the in-proce part holding cot, the more advantageouly to tore part a a WIP than a a finihed product, and vie vera. The number of vehicle i determined from the number of reulting batche. Reference Armentano, V.A., Shiguemoto, A.L., and Lokketangen, A Tabu earch with path relinking for an integrated production-ditribution problem, Computer and Operation Reearch, 38 (8), Chen, J-S., Integration of job cheduling with delivery vehicle routing, Information Technology Journal, 9 (6), , 2010a. Chen, Z-L., Integrated production and outbound ditribution cheduling: Review and Extention, Operation Reearch, 58 (1), , 2010b. Chen, Z-L, and Vairaktaraki, G.L., Integrated cheduling of production and ditribution operation, Management Science, 51 (4), , Chen, Z-L and Pundoor, G., Integrated order cheduling and packing, Production and Operation Management, 18 (6), , Dobon, G., Karmarkar., U.S., and Rummel., J., L., Batching to minimize flow time on one machine, Management Science, 33 (6), , 1987 Dobon, G., Karmarkar., U.S., and Rummel., J., L., Batching to minimize flow time on parallel heterogeneou machine, Management Science, 35 (5), , Ertogral, K., Wu, S.D., and Burke, L.I., Coordination production and tranportation cheduling in the upply chain, Technical Report #98T-010, Department of Indutrial and Manufacturing Sytem Engineering, Lehigh Univerity, Geimar, H.., Laporte, G., Lei, L., and Srikandarajah, C., The integrated production and tranportation cheduling problem for a product with a hort lifepan, Inform Journal on Computing, 20(1), 21-33, Gharehyakheh, A. and Tavakkoli-Moghaddam, R., A fuzzy olution approach for a multi-objective integrated production-ditribution model with multi product and multi period under uncertainty, Management Science Letter, 2, pp , 2012 Halim, A.H., Miyazaki, S., and Ohta, H., Batch-cheduling problem to minimize actual flow time of part through the hop under JIT environment, European Journal of Operational Reearch, 72, pp , Halim, A.H. and Ohta, H., Batch-cheduling problem to minimize inventory cot in the hop with both receiving and delivery jut in time, International Journal Production Economic, 33, , Hall,.G., and Pott, C.., Supply chain cheduling: batching and delivery, Operation Reearch, 51(4), , Hall,.G., and Pott, C.., The coordination of cheduling and batch cheduling deliverie, Annal of Operation Reearch, 135, 41-64,

9 Pan, J.C.H, Wu, C.l, Huang, H.C., and Su, C.S., Coordinating cheduling with batch deliverie in a two-machine flow hop, Int. J. Adv. Manuf. Tech., 40, , Iyer, A.V., Sehadri, S., and Vaher, R., Toyota Supply Chain Management, A Strategic Approach to the Principle of Toyota Renowned Sytem, Mc Graw Hill, ew York, Lee, I.S. and Yoon, S.H., Coordinated cheduling of production and delivery tage with tage-dependent inventory holding cot, Omega, 38, , Stecke, K.E. and Zhao, X., Production and tranportation integration for a make-to-order manufacturing company with a commit-to-delivery buine model, Manufacturing & Service Operation Management, 9 (2), , Yan, C., Banerjee, A., and Yang, L., An integrated production-ditribution model for a deteriorating inventory item, International Journal of Production Economic, 133, , Zhong, W., Chen, Z.L., and Chen, M., Integrated production and ditribution cheduling with committed delivery date, Operation Reearch Letter, 38, , Biography Endang Praetyaningih i currently completing her Doctorate degree in Indutrial Engineering at the Graduate Program on Indutrial Engineering and Management, Faculty of Indutrial Technology, Intitut Teknologi Bandung (ITB), Bandung, Indoneia. She i a lecturer in Univerita Ilam Bandung, Bandung, Indoneia. She recieved her BS degree from the Chemical Engineering Department, Univerita Gadjah Mada (UGM), Yogyakarta, Indoneia, and her MS degree from Indutrial Engineering, ITB. Her reearch interet are in Production Scheduling, JIT Sytem, and Production Sytem. Her addre i endangpra@gmail.com. Suprayogi i an Aociate Profeor in Faculty of Indutrial Technology, Intitut Teknologi Bandung (ITB), Bandung, Indoneia. He received hi BS and MS degree in Indutrial Engineering from ITB and hi Ph.D degree in Ocean and Environmental Engineering from the Univerity of Tokyo. Hi reearch interet are in operation reearch, maritime logitic, and tranportation and ditribution ytem. Hi addre i <yogi@mail.ti.itb.ac.id> TMA Ari Samadhi i an Aociate Profeor in Faculty of Indutrial Technology, Intitut Teknologi Bandung (ITB), Bandung, Indoneia. He received hi BS degree in Indutrial Engineering from ITB and hi MS and Ph.D degree in Manufacturing Engineering, from Univerity of ew South Wale, Sydney, Autralia. Hi reearch interet are in Production etwork, Lean Manufacturing, and Knowledge Management. He publihed hi paper in International Journal of Production and Operation Management and International Journal of Computer Integrated Manufacturing Sytem. Hi addre i aamadhi@mail.ti.itb.ac.id. Abdul Hakim Halim i a Profeor of Indutrial Engineering at Indutrial Engineering Department, Intitut Teknologi Bandung (ITB), Bandung, Indoneia. He received hi BS and MS degree in Indutrial Engineering from ITB and hi PhD from the Indutrial Engineering Department, Oaka Perfecture Univerity, Oaka, Japan. Hi reearch interet are in production cheduling, inventory control, FMS and JIT ytem. He publihed hi paper in International Journal of Production Reearch, International Journal of Production Economic, European Journal of Operational Reearch, and Production Planning and Control, a well a in Journal of Japan Indutrial Management Aociation (JIMA) written in Japanee and everal national journal on production ytem written in Indoneia. Hi addre i ahakimhalim@ti.itb.ac.id. 2117