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An Algorithm for the Dynamic Lot-Size Problem with Time-Varying Production Capacity Constraints

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Author Info

  • Kenneth R. Baker

    (Duke University)

  • Paul Dixon

    (University of Waterloo)

  • Michael J. Magazine

    (University of Waterloo)

  • Edward A. Silver

    (University of Waterloo)

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    Abstract

    We consider the situation of a single item having a deterministic, time-varying demand pattern. Production lot sizes, so as to minimize the total of setup and carrying costs, are to be determined subject to production capacity restrictions that can vary with time. Two important theorems concerning properties of the optimal solution are exploited in developing a tree search algorithm. In addition, other properties are utilized to reduce the amount of search necessary. Results of extensive tests are presented and discussed.

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    File URL: http://dx.doi.org/10.1287/mnsc.24.16.1710
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 24 (1978)
    Issue (Month): 16 (December)
    Pages: 1710-1720

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    Handle: RePEc:inm:ormnsc:v:24:y:1978:i:16:p:1710-1720

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    Related research

    Keywords: dynamic programming: deterministic; discrete time; inventory/production: deterministic models; production scheduling;

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    Cited by:
    1. Stan van Hoesel & H. Edwin Romeijn & Dolores Romero Morales & Albert P.M. Wagelmans, 2002. "Polynomial Time Algorithms for Some Multi-Level Lot-Sizing Problems with Production Capacities," Tinbergen Institute Discussion Papers 02-066/4, Tinbergen Institute.
    2. Elhafsi, Mohsen, 2002. "A production planning model for an unreliable production facility: Case of finite horizon and single demand," European Journal of Operational Research, Elsevier, vol. 143(1), pages 94-114, November.
    3. Safer, Hershel M. & Orlin, James B., 1953-, 1995. "Fast approximation schemes for multi-criteria flow, knapsack, and scheduling problems," Working papers 3757-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    4. Hongyan Li & Joern Meissner, 2006. "Competition under Dynamic Lot Sizing Costs with Capacity Acquisition," Working Papers MRG/0006, Department of Management Science, Lancaster University, revised Apr 2010.
    5. Liu, X. & Tu, Yl., 2008. "Production planning with limited inventory capacity and allowed stockout," International Journal of Production Economics, Elsevier, vol. 111(1), pages 180-191, January.
    6. van Hoesel, C.P.M. & Wagelmans, A.P.M., 1997. "Fully Polynomial Approximation Schemes for Single-Item Capacitated Economic Lot-Sizing Problems," Econometric Institute Research Papers EI 9735/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    7. Stan van Hoesel & H. Edwin Romeijn & Dolores Romero Morales & Albert P.M. Wagelmans, 2002. "Polynomial Time Algorithms for Some Multi-Level Lot-Sizing Problems with Production Capacities," Tinbergen Institute Discussion Papers 02-066/4, Tinbergen Institute.
    8. Bitran, Gabriel R. & Yanasse, Horacio H., 1981. "Computational complexity of the capacitated lot size problem," Working papers 1271-81., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    9. Jenny Carolina Saldaña Cortés, 2011. "Programación semidefinida aplicada a problemas de cantidad económica de pedido," DOCUMENTOS CEDE 008735, UNIVERSIDAD DE LOS ANDES-CEDE.
    10. Song, Yuyue & Chan, Gin Hor, 2005. "Single item lot-sizing problems with backlogging on a single machine at a finite production rate," European Journal of Operational Research, Elsevier, vol. 161(1), pages 191-202, February.
    11. Brahimi, Nadjib & Dauzere-Peres, Stephane & Najid, Najib M. & Nordli, Atle, 2006. "Single item lot sizing problems," European Journal of Operational Research, Elsevier, vol. 168(1), pages 1-16, January.

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