Abstract
The main goal of just-in-time production planing is the reduction of the in-process inventory level. This goal may be achieved by completing the items as close to their further processing (or shipment) dates as possible. In the mass production environment, it is too costly to define and control due dates for individual items. Instead, the model proposed in Toyota is applied that assumes monitoring the actual product rate of particular products. The objective is to construct schedules with minimum deviation from an ideal product rate. In the approach aimed at minimization of the Product Rate Variation, the control process concentrates on product types, not individual items. In this chapter, we discuss the PRV model and scheduling algorithms developed to solve this problem with two types of objectives: to minimize the total or maximum deviation from the ideal product rate. We present algorithms proposed in the context of the just-in-time production scheduling as well as in other areas, adopted later to solve the PRV problem. One of the most interesting problems discussed in this context is the apportionment problem. Originally, the PRV problem was defined as a single machine scheduling problem. We show that some algorithms can be generalized to solve the parallel-machine scheduling problem as well.
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References
Balinski, M., Ramirez, V.: Parametric methods of apportionment, rounding and production. Mathematical Social Sciences 37(2), 107–122 (1999)
Balinski, M., Shahidi, N.: A simple approach to the product rate variation problem via axiomatics. Operations Research Letters 22(4-5), 129–135 (1998)
Balinski, M., Young, H.: The quota method of apportionment. The American Mathematical Monthly 82(7), 701–730 (1975)
Balinski, M., Young, H.: Fair Representation: Meeting the Ideal of One Man, One Vote. Yale University Press (1982)
Bautista, J., Companys, R., Corominas, A.: A note on the relation between the product rate variation (prv) problem and the apportionment problem. Journal of the Operational Research Society 47(11), 1410–1414 (1996)
Brauner, N., Crama, Y.: The maximum deviation just-in-time scheduling problem. Discrete Applied Mathematics 134, 25–50 (2004)
Garey, M.R., Tarjan, R.E., Wilfong, G.T.: One-processor scheduling with symmetric earliness and tardiness penalties. Mathematics of Operations Research 13, 330–348 (1988)
Inman, R.R., Bulfin, R.L.: Sequencing jit mixed-model assembly lines. Management Science 37, 901–904 (1991)
Józefowska, J.: Models and Algorithms for Computer and Manufacturing Systems. Springer, New York (2007)
Józefowska, J., Józefowski, L., Kubiak, W.: Characterization of just in time sequencing via apportionment. In: H. Yan, G. Yin, Q. Zhang (eds.) Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems, International Series in Operations Research & Management Science, vol. 94, pp. 175–200. Springer US (2006)
Józefowska, J., Józefowski, L., Kubiak, W.: Apportionment methods and the liu-layland problem. European Journal of Operational Research 193(3), 857–864 (2009)
Józefowska, J., Józefowski, L., Kubiak, W.: Dynamic divisor-based resource scheduling algorithm. In: Proceedings of the 12th International Workshop on Project Management and Scheduling. Tours, France (2010)
Kubiak, W.: Proportional Optimization and Fairness, International Series in Operations Research & Management Science, vol. 127. Springer, New York (2009)
Kubiak, W., Sethi, S.: A note on “level schedules for mixed-model assembly lines in just-in-time production systems”. Management Science 37(1), 121–122 (1991)
Kubiak, W., Sethi, S.P.: Optimal just-in-time schedules for flexible transfer lines. International Journal of Flexible Manufacturing Systems 6, 137–154 (1994)
Miltenburg, J.: Level schedules for mixed-model assembly lines in just-in-time production systems. Management Science 35(2), 192–207 (1989)
Monden, Y.: Toyota Production Systems. Industrial Engineering and Management Press, Norcross (1983)
Okamura, K., Yamashina, H.: A heuristic algorithm for the assembly line model-mix sequencing problem to minimize the risk of stopping the conveyor. Journal of Production Research 17(3), 233–247 (1979)
Steiner, G., Yeomans, S.: Level schedules for mixed-model, just-in-time processes. Management Science 39, 728–735 (1993)
Still, J.W.: A class of new methods for congressional apportionment. SIAM Journal on Applied Mathematics 37(2), 401–418 (1979)
Tijdeman, R.: The chairman assignment problem. Discrete Mathematics 32(3), 323–330 (1980)
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Józefowska, J. (2012). Just-in-Time Scheduling in Modern Mass Production Environment. In: Ríos-Mercado, R., Ríos-Solís, Y. (eds) Just-in-Time Systems. Springer Optimization and Its Applications(), vol 60. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1123-9_8
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DOI: https://doi.org/10.1007/978-1-4614-1123-9_8
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