Journal of Korean Institute of Industrial Engineers (대한산업공학회지)

Korean Institute of Industrial Engineers (대한산업공학회)
권호 표지

A Simulated Annealing Algorithm for the Capacitated Lot-sizing and Scheduling problem under Sequence-Dependent Setup Costs and Setup Times

순서에 종속된 준비 시간과 준비 비용을 고려한 로트사이징 문제의 시뮬레이티드 어닐링 해법

  • 정지영 (한국과학기술원 산업공학과) ;
  • 박성수 (한국과학기술원 산업공학과)
  • Published : 2006.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this research, the single machine capacitated lot-sizing and scheduling problem with sequence- dependent setup costs and setup times (CLSPSD) is considered. This problem is the extension of capacitated lot-sizing and scheduling problem (CLSP) with an additional assumption on sequence-dependent setup costs and setup times. The objective of the problem is minimizing the sum of production costs, inventory holding costs and setup costs satisfying customers' demands. It is known that the CLSPSD is NP-hard. In this paper, the MIP formulation is presented. To handle the problem more efficiently, a conceptual model is suggested, and one of the well-known meta-heuristics, the simulated annealing approach is applied. To illustrate the performance of this approach, various instances are tested and the results of this algorithm are compared with those of the CLPEX. Computational results show that this approach generates optimal or nearly optimal solutions.

Keywords

References

  1. Aras, O. A. and Swanson, L. A. (1982), A lot sizing and sequencing algorithm for dynamic demands upon a single facility, journal of Operations Management, 2(3), 177-185 https://doi.org/10.1016/0272-6963(82)90005-5
  2. Barany I., Van Roy, T. J., and Wolsey, L. (1984), Strong formulations for multi-item capacitated lot sizing, Management Science, 30(10), 1255-1261 https://doi.org/10.1287/mnsc.30.10.1255
  3. Diaby, M., Bahl, H. C., Karwan, M. H., and Ziont, S. (1992), Capacitated lot-sizing and scheduling by lagrangean relaxation, European Journal of Operational Research, 59, 444-458 https://doi.org/10.1016/0377-2217(92)90201-J
  4. Diwakar Gupta, Thorkell Magnusson (2005), The Capacitated lot-sizing and scheduling problem with sequence-dependent setup costs and setup times, Computers & Operations research, 32, 727-747 https://doi.org/10.1016/j.cor.2003.08.014
  5. Drexl, A., Kimms, A. (1997), Lot sizing and scheduling-Survey and extensions, European Journal of Operational Research, 99, 221-235 https://doi.org/10.1016/S0377-2217(97)00030-1
  6. Eppen, G. D. and Martin, R. K. (1987), Solving multi-item capacitated lot-sizing problem using variable redefinition, Operations Research, 35, 832-848 https://doi.org/10.1287/opre.35.6.832
  7. Garey, M. and Johnson, D. (1979), Computers and intractability: A guide to the theory of NP-completeness, Freeman and Co., San Francisco
  8. Haase, K. (1996), Capacitated lot -sizing withsequence-dependent setup costs, OR Specktrum, 18, 51-59 https://doi.org/10.1007/BF01539882
  9. Kirkpatrick, S., Gelatt, Jr. C. D., and Vecchi, M. P. (1983), Optimization by simulated annealing, Management Science, 220, 671-680
  10. Kuik, R. and Salomon, M. (1990), Multi-level lot-sizing problem: Evaluation of a simulated-annealing heuristic, European Journal of Operational Research, 45(1), 25-37 https://doi.org/10.1016/0377-2217(90)90153-3
  11. Mohan Gopalakrishnan, Ke Ding, Jean-Marie Bourijolly, and Srimathy Mohan (2001), A Tabu-Search Heuristic for the capapcitated lot-sizing problem with set-up carryover, Management science, 47(6), 851-863 https://doi.org/10.1287/mnsc.47.6.851.9813
  12. Ou Tang (2004), Simulated annealing in lot sizing problmes, Int. J. Production Economics, 88, 173-181 https://doi.org/10.1016/j.ijpe.2003.11.006
  13. Salomon M., Solomon M. M., Van Wassenhove L. N., Duman Y., and Duazere-Peres, S. (1997), Solving the discrete lot-sizing and scheduling problem with sequence-dependent setup costs and set-up times using the Travelling Salesman Problem with time windows, European Journal of Operational Research, 100(3), 494-513 https://doi.org/10.1016/S0377-2217(96)00020-3
  14. Sungmin Kang, Kavindra Malik, L. Joseph Thomas (1999), Lotsizing and scheduling on parallel machines with sequence-dependent setup costs, Management science, 45(2), 273-289 https://doi.org/10.1287/mnsc.45.2.273
  15. Trigeiro W. W., Thomas, L. J., and McClain, J. O. (1989), Capacitated lot sizing with setup times, Management Science, 35(3), 353-366 https://doi.org/10.1287/mnsc.35.3.353
  16. William J. Cook, William H. Cunningham, William R. Pulleyblank, Alexander Schrijver, Combinatorial Optimization