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Tight Mip Formulation for Multi-Item Discrete Lot-Sizing Problems

Author

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  • Andrew J. Miller

    (Department of Industrial Engineering, University of Wisconsin at Madison, Madison, Wisconsin 53706)

  • Laurence A. Wolsey

    (CORE and INMA, Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium)

Abstract

This paper discusses mixed-integer programming formulations of variants of the discrete lot-sizing problem. Our approach is to identify simple mixed-integer sets within these models and to apply tight formulations for these sets. This allows us to define integral linear programming formulations for the discrete lot-sizing problem in which backlogging and/or safety stocks are present, and to give extended formulations for other cases. The results help significantly to solve test cases arising from an industrial application motivating this research.

Suggested Citation

  • Andrew J. Miller & Laurence A. Wolsey, 2003. "Tight Mip Formulation for Multi-Item Discrete Lot-Sizing Problems," Operations Research, INFORMS, vol. 51(4), pages 557-565, August.
    • Handle: RePEc:inm:oropre:v:51:y:2003:i:4:p:557-565
    DOI: 10.1287/opre.51.4.557.16094
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    References listed on IDEAS

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    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.
    2. Pochet, Y. & Wolsey, L. A., 1994. "Polyhedra for lot-sizing with Wagner-Whitin costs," LIDAM Reprints CORE 1129, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Fleischmann, Bernhard, 1990. "The discrete lot-sizing and scheduling problem," European Journal of Operational Research, Elsevier, vol. 44(3), pages 337-348, February.
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    Cited by:

    1. Karina Copil & Martin Wörbelauer & Herbert Meyr & Horst Tempelmeier, 2017. "Simultaneous lotsizing and scheduling problems: a classification and review of models," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(1), pages 1-64, January.
    2. Francesco Gaglioppa & Lisa A. Miller & Saif Benjaafar, 2008. "Multitask and Multistage Production Planning and Scheduling for Process Industries," Operations Research, INFORMS, vol. 56(4), pages 1010-1025, August.
    3. Roger Rocha & Ignacio Grossmann & Marcus Poggi de Aragão, 2013. "Cascading Knapsack Inequalities: reformulation of a crude oil distribution problem," Annals of Operations Research, Springer, vol. 203(1), pages 217-234, March.
    4. Mathieu Van Vyve, 2007. "Algorithms for Single-Item Lot-Sizing Problems with Constant Batch Size," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 594-613, August.
    5. Moo-Sung Sohn & Jiwoong Choi & Hoseog Kang & In-Chan Choi, 2017. "Multiobjective Production Planning at LG Display," Interfaces, INFORMS, vol. 47(4), pages 279-291, August.
    6. Lee, Younsoo & Lee, Kyungsik, 2020. "Lot-sizing and scheduling in flat-panel display manufacturing process," Omega, Elsevier, vol. 93(C).
    7. Yaman, Hande & Sen, Alper, 2008. "Manufacturer's mixed pallet design problem," European Journal of Operational Research, Elsevier, vol. 186(2), pages 826-840, April.

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