Abstract
In this paper we consider a single machine multi-product lot scheduling problem in which defective items are produced in any production run of each product. In each cycle after the normal production of each product the machine is setup for the rework of the defectives of the same product and then the rework process starts. We assume that the setup time for the normal production process as well as the rework process is non-zero. Further we consider the waiting time cost of defectives for rework. This paper has two objectives. The first objective is to obtain the economic batch quantity (EBQ) for a single product. The second objective is to extend the result of the first objective to the multi-product case. Adopting the common cycle scheduling policy we obtain optimal batch sizes for each product such that the total cost of the system per unit time is minimized.
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Cook, W.D., Saipe, A.L. & Seiford, L.M. (1980). Production runs for multiple products: the full-capacity heuristic. Journal of Operations Research, 31: 405–412
Dobson, G. (1987). The economic lotscheduling problem: achieving feasibility using time varying lot-sizes. Journal of Operations Research, 35 (5): 764–771
Elmaghraby, S.F. (1978). The economic lot scheduling problem (ELSP): review and extensions. Management Science, 24 (6): 587–598
Gallego, G. & Shaw, D.X. (1997). Complexity of the ELSP with general cyclic schedules. IIE Transaction, 29: 109–113
Glass, C.A. (1992). Feasibility of scheduling lot sizes of these products on one machine. Management Science, 18 (10): 1482–1495
Goyal, S.K. & Gonashekharan, A. (1990). Effect of dynamic process quality control on the economic production. International Journal of Operations and Production Management, 10 (3): 69–77
Graves, S.C. (1979). On the deterministic demand multi-product single machine for scheduling problem. Management Science, 25: 276–280
Gunter, S.I. & Swanson, L.A. (1986). A heuristic for zero setup cost lot sizing and scheduling problems. In: ORSA-TIMS Conference, 27-28, October 1986, Miami, Florida, USA
Haessler, R.W. (1979). An improved extended basic period procedure for solving the economic lot scheduling problem. AIIE Transaction, 11: 336–340
Haji, R. & Mansuri, M. (1995). Optimum common cycle for scheduling a single machine multi-product system with a budgetary constraint. Production Planning & Control, 6 (2): 151–156
Haji, R., Rahmati Tavakol, A. & Haji, B. (2006). Economic production quantity with accumulated rework. In: 36th CIE Conference on Computers and Industrial Engineering, 4196–4203, Taiwan, China
Hanssman, F. (1962). Operation Research in Production and Inventory. John Wiley and Sons Inc., New York
Hayek, P.A. & Salameh, M.K. (2001). Production lot sizing with the reworking of imperfect quality item produced. Production Planning and Control, 12 (6): 584–590
Jamal, A.M.M., Sarker, B.R. & Mondel, S. (2004). Optimal manufacturing batch size with network process at a single-stage production system. Computers & Industrial Engineering, 47: 77–89
Johnson, L.A. & Montgomery, D.C. (1974). Operations Research in Production Planning and Inventory Control. John Wiley and Sons, New York
Jones, P.C. & Inmann, R.R. (1989). When is the economic lot scheduling problem easy? IIE Transactions, 21: 11–20
Lee, H.L. (1992). Lot sizing to reduce capacity utilization in production process with defective item, process corrections, and rework. Management Science, 38 (9): 1314–1328
Lee, H.L., Chandra, M.J. & Deleveaux, V. J. (1997). Optimal batch size and investment in multistage production systems with scrap. Production Planning and Control, 8 (6): 586–596
Lee, H.L. & Rosenblat, M.J. (1986). Economic production cycles with imperfect production processes. IIE Transactions, 18 (1): 48–55
Park, K.S. & Yun, D.K. (1988). A stepwise partial enumeration algorithm for the economic lot scheduling problem. IIE Transactions, 16 (4): 363–370
Roundy, R. (1988). Rounding off to powers of two in continuous relaxations of capacitated lot sizing problems. Technical Report, College of Engineering, Cornell University
Zipkin, P.H. (1988). Computing optimal lot sizes in the economic lot scheduling problem. Working Paper, Graduate School of Business, Columbia University
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The original version was presented on ICSSSM’06.
Rasoul Haji is currently a Professor of Industrial Engineering at Sharif University of Technology in Tehran, Iran. He received a B.Sc. degree from University of Tehran in Chemical Engineering in 1964. He also earned a M.Sc. degree from University of California-Berkeley in Industrial Engineering in 1967. In 1970 he received his Ph.D. degree from Berkeley in Industrial Engineering. He is the Editor-in-Chief of the Journal of Industrial and Systems Engineering and he is a member of Iran’s Academy of Science. He is recognized as a co-founder of the fundamental and important relation in queuing theory known as “Distributional Little’s Law”. His research interests include inventory control, stochastic processes, and queuing theory. He has published papers in different technical journals such as Journal of Applied Probability, SIAM Journal of Applied Math, European Journal of Operational Research, Computers & Industrial Engineering, Journal of Production Planning and Control, and Applied Mathematics & Computation.
Alireza Haji is currently an Associate Professor of Industrial Engineering at Sharif University of Technology in Tehran, Iran. He received a B.Sc. degree from Sharif University of Technology in Industrial Engineering in 1987. He also earned a M.Sc. degree from Sharif University of Technology in Industrial Engineering in 1992. In 2001 he received his Ph.D. degree from Sharif University of Technology in Industrial Engineering. His research interests include inventory management and control, production scheduling, stochastic processes, project management and project scheduling.
Mehdi Sajadifar is currently a PhD candidate of Industrial Engineering at Sharif University of Technology. He received a B.Sc. and a M.Sc. degree in Industrial Engineering from Sharif University of Technology in 1994 and 1996. His research interests include inventory management and control, production scheduling and stochastic processes.
Saeed Zolfaghari is currently an Associate Professor and the Director of the Industrial Engineering Program at the Department of Mechanical and Industrial Engineering, Ryerson University in Toronto. He is also an Adjunct Professor at the Department of Mechanical Engineering, University of Ottawa. He received his Ph.D. from the University of Ottawa in 1997. His research interests include meta-heuristics and computational intelligence, simulation of production and service systems, and applications of operation research to flexible manufacturing systems, logistics and transportation planning. He is a member of IIE, IEEE, INFORMS, CORS and Professional Engineers Ontario.
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Haji, R., Haji, A., Sajadifar, M. et al. Lot sizing with non-zero setup times for rework. J. Syst. Sci. Syst. Eng. 17, 230–240 (2008). https://doi.org/10.1007/s11518-008-5077-7
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DOI: https://doi.org/10.1007/s11518-008-5077-7