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Modelling Practical Lot-Sizing Problems as Mixed-Integer Programs

Author

Listed:
  • Gaetan Belvaux

    () (Cockerill-Sambre, Flémalle Work carried out at CORE, Université Catholique de Louvain)

  • Laurence A. Wolsey

    () (CORE and INMA, Université Catholique de Louvain, Voie du Roman Pays 34, 1348 Louvain-la-Neuve, Belgium)

Abstract

In spite of the remarkable improvements in the quality of general purpose mixed-integer programming software, the effective solution of a variety of lot-sizing problems depends crucially on the development of tight formulations for the special problem features occurring in practice. After reviewing some of the basic preprocessing techniques for handling safety stocks and multilevel problems, we discuss a variety of aspects arising particularly in small and large bucket (time period) models such as start-ups, changeovers, minimum batch sizes, choice of one or two set-ups per period, etc. A set of applications is described that contains one or more of these special features, and some indicative computational results are presented. Finally, to show another technique that is useful, a slightly different (supply chain) application is presented, for which the a priori addition of some simple mixed-integer inequalities, based on aggregation, leads to important improvements in the results.

Suggested Citation

  • Gaetan Belvaux & Laurence A. Wolsey, 2001. "Modelling Practical Lot-Sizing Problems as Mixed-Integer Programs," Management Science, INFORMS, vol. 47(7), pages 993-1007, July.
  • Handle: RePEc:inm:ormnsc:v:47:y:2001:i:7:p:993-1007
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    File URL: http://dx.doi.org/10.1287/mnsc.47.7.993.9800
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    References listed on IDEAS

    as
    1. Fleischmann, Bernhard, 1994. "The discrete lot-sizing and scheduling problem with sequence-dependent setup costs," European Journal of Operational Research, Elsevier, vol. 75(2), pages 395-404, June.
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    3. Yves Pochet & Laurence A. Wolsey, 1991. "Solving Multi-Item Lot-Sizing Problems Using Strong Cutting Planes," Management Science, INFORMS, vol. 37(1), pages 53-67, January.
    4. Cattrysse, Dirk & Maes, Johan & Van Wassenhove, Luk N., 1990. "Set partitioning and column generation heuristics for capacitated dynamic lotsizing," European Journal of Operational Research, Elsevier, vol. 46(1), pages 38-47, May.
    5. Horst Tempelmeier & Matthias Derstroff, 1996. "A Lagrangean-Based Heuristic for Dynamic Multilevel Multiitem Constrained Lotsizing with Setup Times," Management Science, INFORMS, vol. 42(5), pages 738-757, May.
    6. Dirk Cattrysse & Marc Salomon & Roelof Kuik & Luk N. Van Wassenhove, 1993. "A Dual Ascent and Column Generation Heuristic for the Discrete Lotsizing and Scheduling Problem with Setup Times," Management Science, INFORMS, vol. 39(4), pages 477-486, April.
    7. François Vanderbeck, 1998. "Lot-Sizing with Start-Up Times," Management Science, INFORMS, vol. 44(10), pages 1409-1425, October.
    8. Andrew J. Clark & Herbert Scarf, 2004. "Optimal Policies for a Multi-Echelon Inventory Problem," Management Science, INFORMS, pages 1782-1790.
    9. Moustapha Diaby & Harish C. Bahl & Mark H. Karwan & Stanley Zionts, 1992. "A Lagrangean Relaxation Approach for Very-Large-Scale Capacitated Lot-Sizing," Management Science, INFORMS, vol. 38(9), pages 1329-1340, September.
    10. Sungmin Kang & Kavindra Malik & L. Joseph Thomas, 1999. "Lotsizing and Scheduling on Parallel Machines with Sequence-Dependent Setup Costs," Management Science, INFORMS, vol. 45(2), pages 273-289, February.
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