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Uncapacitated Lot-Sizing Problems with Start-Up Costs

Author

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  • Laurence A. Wolsey

    (Université Catholique de Louvain, Louvain-la-Neuve, Belgium)

Abstract

We consider the uncapacitated economic lot-sizing problem with start-up costs as a mixed integer program. A family of strong valid inequalities is derived for the class as well as a polynomial separation algorithm. It is then shown how equivalent, or possibly stronger, formulations are obtained by the introduction of auxiliary variables. Finally, some limited computational results for a single item model and a multi-item model with changeover costs are reported.

Suggested Citation

  • Laurence A. Wolsey, 1989. "Uncapacitated Lot-Sizing Problems with Start-Up Costs," Operations Research, INFORMS, vol. 37(5), pages 741-747, October.
    • Handle: RePEc:inm:oropre:v:37:y:1989:i:5:p:741-747
    DOI: 10.1287/opre.37.5.741
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    Citations

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    Cited by:

    1. 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.
    2. Silvio Alexandre de Araujo & Bert De Reyck & Zeger Degraeve & Ioannis Fragkos & Raf Jans, 2015. "Period Decompositions for the Capacitated Lot Sizing Problem with Setup Times," INFORMS Journal on Computing, INFORMS, vol. 27(3), pages 431-448, August.
    3. Brahimi, Nadjib & Absi, Nabil & Dauzère-Pérès, Stéphane & Nordli, Atle, 2017. "Single-item dynamic lot-sizing problems: An updated survey," European Journal of Operational Research, Elsevier, vol. 263(3), pages 838-863.
    4. Laurence A. Wolsey, 2002. "Solving Multi-Item Lot-Sizing Problems with an MIP Solver Using Classification and Reformulation," Management Science, INFORMS, vol. 48(12), pages 1587-1602, December.
    5. Thomas L. Magnanti & Trilochan Sastry, 2002. "Facets and Reformulations for Solving Production Planning With Changeover Costs," Operations Research, INFORMS, vol. 50(4), pages 708-719, August.
    6. Christopher Suerie & Hartmut Stadtler, 2003. "The Capacitated Lot-Sizing Problem with Linked Lot Sizes," Management Science, INFORMS, vol. 49(8), pages 1039-1054, August.
    7. Jans, R.F. & Degraeve, Z., 2005. "Modeling Industrial Lot Sizing Problems: A Review," ERIM Report Series Research in Management ERS-2005-049-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    8. BELVAUX, Gaetan & WOLSEY, Laurence A., 1998. "Lot-sizing problems: modelling issues and a specialized branch-and-cut system BC-PROD," LIDAM Discussion Papers CORE 1998049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Soric, Kristina, 2000. "A cutting plane algorithm for a single machine scheduling problem," European Journal of Operational Research, Elsevier, vol. 127(2), pages 383-393, December.
    10. Drexl, Andreas & Haase, Knut, 1992. "A new type of model for multi-item capacitated dynamic lotsizing and scheduling," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 286, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    11. Kaczmarczyk, Waldemar, 2020. "Valid inequalities for proportional lot-sizing and scheduling problem with fictitious microperiods," International Journal of Production Economics, Elsevier, vol. 219(C), pages 236-247.
    12. 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.

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