Stochastic Programming Model for Discrete Lotsizing and Scheduling Problem on Parallel Machines
- 1 Global Logistics, Kao Corporation, Tokyo, Japan
- 2 Faculty of Business Administration, Toyo University, Tokyo, Japan
- 3 Faculty of Social Systems Science, Chiba Institute of Technology, Chiba, Japan
- 4 School of Creative Science and Engineering, Waseda University, Tokyo, Japan
Abstract
In recent years, it has been difficult for manufactures and suppliers to forecast demand from a market for a given product precisely. Therefore, it has become important for them to cope with fluctuations in demand. From this viewpoint, the problem of planning or scheduling in production systems can be regarded as a mathematical problem with stochastic elements. However, in many previous studies, such problems are formulated without stochastic factors, treating stochastic elements as deterministic variables or parameters. Stochastic programming incorporates such factors into the mathematical formulation. In the present paper, we consider a multi-product, discrete, lotsizing and scheduling problem on parallel machines with stochastic demands. Under certain assumptions, this problem can be formulated as a stochastic integer programming problem. We attempt to solve this problem by a scenario aggregation method proposed by Rockafellar and Wets. The results from computational experiments suggest that our approach is able to solve large-scale problems, and that, under the condition of uncertainty, incorporating stochastic elements into the model gives better results than formulating the problem as a deterministic model.
- J. R. Birge, “Stochastic Programming Computation and Applications,” INFORMS Journal on Computing, Vol. 9, No. 2, 1997, pp. 111-133. doi:10.1287/ijoc.9.2.111
- J. R. Birge and F. Louveaux, “Introduction to Stochastic Programming,” Springer-Verlag, Berlin, 1997.
- T. Shiina, “Stochastic Programming (in Japanese),” In: M. Kubo, A. Tamura and T. Matsui, Eds., ?y? S?ri-Keikaku Handbook, Asakura Syoten, Tokyo, 2002, pp. 710-769.
- R. T. Rockafellar and R. J.-B. Wets, “Scenarios and Policy Aggregation in Optimization under Uncertainty,” Mathematics of Operations Research, Vol. 16, No. 1, 1991, pp. 119-147. doi:10.1287/moor.16.1.119
- A. L? kketangen and D. L. Woodruff, “Progressive Hedging and Tabu Search Applied to Mixed Integer (0,1) Multistage Stochastic Programming,” Journal of Heuristics, Vol. 2, 1996, pp. 111-128.
- H. Meyr, “Simultaneous Lotsizing and Scheduling on Parallel Machines,” European Journal of Operational Research, Vol. 139, No. 2, 2002, pp. 277-292. doi:10.1016/S0377-2217(01)00373-3
- H. Arai, S. Morito and J. Imaizumi, “A Column Generation Approachfor Discrete Lotsizing and Scheduling Problem on Identical Parallel Machines,” Journal of Japan Industrial Management Association, Vol. 55, 2004, pp. 69-76.