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Modelling practical lot-sizing problems as mixed integer programs

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  • BELVAUX, Gaetan
  • WOLSEY, Laurence A.
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    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 are described that contain one or more of these special features, and some indicative computational results are presented. Finally to show the variety of techniques that are needed, 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.

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    Bibliographic Info

    Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2000009.

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    Date of creation: 01 Feb 2000
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    Handle: RePEc:cor:louvco:2000009

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    Related research

    Keywords: Lot-sizing; Production Planning; Mixed Integer Programming; Valid Inequalities; Reformulation.;

    References

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    1. François Vanderbeck, 1998. "Lot-Sizing with Start-Up Times," Management Science, INFORMS, vol. 44(10), pages 1409-1425, October.
    2. Andrew J. Clark & Herbert Scarf, 2004. "Optimal Policies for a Multi-Echelon Inventory Problem," Management Science, INFORMS, vol. 50(12_supple), pages 1782-1790, December.
    3. Imre Barany & Tony J. Van Roy & Laurence A. Wolsey, 1984. "Strong Formulations for Multi-Item Capacitated Lot Sizing," Management Science, INFORMS, vol. 30(10), pages 1255-1261, October.
    4. repec:fth:louvco:9849 is not listed on IDEAS
    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. 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.
    7. 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.
    8. 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.
    9. BELVAUX, Gaetan & WOLSEY, Laurence A., 1998. "Lot-sizing problems: modelling issues and a specialized branch-and-cut system BC-PROD," CORE Discussion Papers 1998049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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