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Solving Multi-Item Lot-Sizing Problems Using Strong Cutting Planes

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Author Info

  • Yves Pochet

    (Center for Operations Research and Econometrics, Université Catholique de Louvain, 34 Voie du Roman Pays, 1348 Louvain-la-Neuve, Belgium)

  • Laurence A. Wolsey

    (Center for Operations Research and Econometrics, Université Catholique de Louvain, 34 Voie du Roman Pays, 1348 Louvain-la-Neuve, Belgium)

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    Abstract

    We consider two classes of multi-item lot-sizing problems. The first is a class of single stage problems involving joint machine capacity constraints and/or start up costs, and the second is a class of multistage problems with general product structure. The problems are solved as mixed integer programs based on (i) an appropriate choice of the initial problem formulation and (ii) the addition of cuts which are generated automatically by a mathematical programming system (MPSARX). Our results extend and complement those of Karmarkar and Schrage (1985), Afentakis and Gavish (1986), Eppen and Martin (1987) and Van Roy and Wolsey (1987). A major advantage of this approach is its robustness or flexibility. By using just a matrix generator and a mathematical programming system with automatic cut generation routines we can formulate and solve model variants without incurring the costs of adapting an algorithm.

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    File URL: http://dx.doi.org/10.1287/mnsc.37.1.53
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 37 (1991)
    Issue (Month): 1 (January)
    Pages: 53-67

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    Handle: RePEc:inm:ormnsc:v:37:y:1991:i:1:p:53-67

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    Related research

    Keywords: production planning; lot-sizing; mixed integer programming; cutting plane algorithms;

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    Cited by:
    1. Wu, Tao & Shi, Leyuan & Geunes, Joseph & AkartunalI, Kerem, 2011. "An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging," European Journal of Operational Research, Elsevier, vol. 214(2), pages 428-441, October.
    2. Atamturk, Alper & Munoz, Juan Carlos, 2002. "A Study of the Lot-Sizing Polytope," University of California Transportation Center, Working Papers qt6zz2g0z4, University of California Transportation Center.
    3. AkartunalI, Kerem & Miller, Andrew J., 2009. "A heuristic approach for big bucket multi-level production planning problems," European Journal of Operational Research, Elsevier, vol. 193(2), pages 396-411, March.
    4. VAN VYVE, Mathieu & POCHET, Yves, 2001. "A general heuristic or production planning problems," CORE Discussion Papers 2001056, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. 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.
    6. Helber, Stefan & Sahling, Florian, 2008. "A Fix-and-Optimize Approach for the Multi-Level Capacitated Lot Sizing Problems," Hannover Economic Papers (HEP) dp-393, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    7. Stadtler, Hartmut, 1996. "Mixed integer programming model formulations for dynamic multi-item multi-level capacitated lotsizing," European Journal of Operational Research, Elsevier, vol. 94(3), pages 561-581, November.
    8. Atamturk, Alper & Munoz, Juan Carlos, 2002. "A Study of the Lot-Sizing Polytope," University of California Transportation Center, Working Papers qt9gx170tx, University of California Transportation Center.
    9. VAN VYVE, Mathieu & WOLSEY, Laurence & YAMAN, Hande, 2012. "Relaxations for two-level multi-item lot-sizing problem," CORE Discussion Papers 2012031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. 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).
    11. Wolsey, Laurence A., 1995. "Progress with single-item lot-sizing," European Journal of Operational Research, Elsevier, vol. 86(3), pages 395-401, November.
    12. Rizk, Nafee & Martel, Alain & Ramudhin, Amar, 2006. "A Lagrangean relaxation algorithm for multi-item lot-sizing problems with joint piecewise linear resource costs," International Journal of Production Economics, Elsevier, vol. 102(2), pages 344-357, August.
    13. Kerem Akartunalı & Andrew Miller, 2012. "A computational analysis of lower bounds for big bucket production planning problems," Computational Optimization and Applications, Springer, vol. 53(3), pages 729-753, December.
    14. Jans, Raf & Degraeve, Zeger, 2007. "Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1855-1875, March.
    15. Wolsey, Laurence A., 1997. "MIP modelling of changeovers in production planning and scheduling problems," European Journal of Operational Research, Elsevier, vol. 99(1), pages 154-165, May.
    16. Drexl, Andreas & Haase, Knut, 1995. "Proportional lotsizing and scheduling," International Journal of Production Economics, Elsevier, vol. 40(1), pages 73-87, June.
    17. BELVAUX, Gaetan & WOLSEY, Laurence A., 2000. "Modelling practical lot-sizing problems as mixed integer programs," CORE Discussion Papers 2000009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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