A Dynamic Lot-Sizing Problem with Backlogging for Minimum Replenishment Policy

최소공급량 정책을 위한 추후조달 롯사이징 문제

  • 황학진 (조선대학교 공과대학 산업공학과)
  • Received : 2009.07.10
  • Accepted : 2010.02.10
  • Published : 2010.03.01

Abstract

This paper considers a dynamic lot-sizing problem with backlogging under a minimum replenishment policy. For general concave production costs, we propose an O($T^5$) dynamic programming algorithm. If speculative motive is not allowed, in this case, a more efficient O($T^4$) algorithm is developed.

Keywords

References

  1. Chand, S. and Morton, T. E. (1986), Minimal Forecast Horizon Procedures for Dynamic Lot Size Models, Naval Research Logistics Quarterly, 33, 111-122. https://doi.org/10.1002/nav.3800330110
  2. Chung, C. S. and Lin, C. H. M. (1988), An O($T^2$) algorithm for the NI/G/NI/ND capacitated lot size problem, Management Science, 34, 420-426. https://doi.org/10.1287/mnsc.34.3.420
  3. Federgruen, A. and Tzur, M. (1991), A simple forward algorithm to solve general dynamic lot-sizing models with n periods in O(n log n) or O(n) Time. Management Science, 37, 909-925. https://doi.org/10.1287/mnsc.37.8.909
  4. Florian, M. and Klein, M. (1971), Deterministic Production Planning with Concave Costs and Capacity Constraints, Management Science, 18, 12-20. https://doi.org/10.1287/mnsc.18.1.12
  5. Hwang, H-C. (2009a) Inventory Replenishment and Inbound Shipment Scheduling under a Minimum Replenishment Policy, Transportation Science. 43, 244-264. https://doi.org/10.1287/trsc.1080.0237
  6. Hwang, H-C. (2009b), Economic Lot-Sizing for Integrated Production and Transportation, to appear in Operations Research.
  7. Lee, C-Y. (2004), Inventory production model : lot sizing versus just-in-time delivery, Operations Research Letters, 32, 581-590. https://doi.org/10.1016/j.orl.2003.12.008
  8. Van Hoesel, C. P. M. and Wagelmans, A. P. M. (1996), An O ($T^3$) algorithm for the economic lot-sizing problem with constant capacities, Management Science, 42, 142-150. https://doi.org/10.1287/mnsc.42.1.142
  9. Wagner, H. M. and Whitin, T. M. (1958), Dynamic version of the economic lot-size model, Management Science, 5, 89-96. https://doi.org/10.1287/mnsc.5.1.89
  10. Zangwill, W. I. (1966), A deterministic multi-period production scheduling model with backlogging, Management Science, 13, 105-119. https://doi.org/10.1287/mnsc.13.1.105