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Modelling Practical Lot-Sizing Problems as Mixed-Integer Programs

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  • 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)

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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 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.

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    File URL: http://dx.doi.org/10.1287/mnsc.47.7.993.9800
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 47 (2001)
    Issue (Month): 7 (July)
    Pages: 993-1007

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    Handle: RePEc:inm:ormnsc:v:47:y:2001:i:7:p:993-1007

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

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    Cited by:
    1. Camargo, Victor C.B. & Toledo, Franklina M.B. & Almada-Lobo, Bernardo, 2014. "HOPS – Hamming-Oriented Partition Search for production planning in the spinning industry," European Journal of Operational Research, Elsevier, vol. 234(1), pages 266-277.
    2. 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.
    3. Stadtler, Hartmut, 2011. "Multi-level single machine lot-sizing and scheduling with zero lead times," European Journal of Operational Research, Elsevier, vol. 209(3), pages 241-252, March.
    4. 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.
    5. 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.
    6. Newman, Alexandra M. & Kuchta, Mark, 2007. "Using aggregation to optimize long-term production planning at an underground mine," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1205-1218, January.
    7. 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.
    8. Akbalik, Ayse & Penz, Bernard, 2009. "Exact methods for single-item capacitated lot sizing problem with alternative machines and piece-wise linear production costs," International Journal of Production Economics, Elsevier, vol. 119(2), pages 367-379, June.
    9. 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.
    10. Karimi, B. & Fatemi Ghomi, S. M. T. & Wilson, J. M., 2003. "The capacitated lot sizing problem: a review of models and algorithms," Omega, Elsevier, vol. 31(5), pages 365-378, October.
    11. Helber, Stefan & Sahling, Florian, 2010. "A fix-and-optimize approach for the multi-level capacitated lot sizing problem," International Journal of Production Economics, Elsevier, vol. 123(2), pages 247-256, February.
    12. 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.
    13. Degraeve, Z. & Jans, R.F., 2003. "A New Dantzig-Wolfe Reformulation And Branch-And-Price Algorithm For The Capacitated Lot Sizing Problem With Set Up Times," ERIM Report Series Research in Management ERS-2003-010-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.
    14. Jans, R.F., 2006. "Solving Lotsizing Problems on Parallel Identical Machines Using Symmetry Breaking Constraints," ERIM Report Series Research in Management ERS-2006-051-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.
    15. Awi Federgruen & Joern Meissner & Michal Tzur, 2002. "Progressive Interval Heuristics for Multi-Item Capacitated Lot-Sizing Problems," Working Papers MRG/0001, Department of Management Science, Lancaster University, revised Nov 2004.
    16. Jenny Carolina Saldaña Cortés, 2011. "Programación semidefinida aplicada a problemas de cantidad económica de pedido," DOCUMENTOS CEDE 008735, UNIVERSIDAD DE LOS ANDES-CEDE.
    17. Skintzi, Georgia & Ioannou, George & Prastacos, Gregory, 2008. "Investigating warehousing policies," International Journal of Production Economics, Elsevier, vol. 112(2), pages 955-970, April.
    18. Egri, Péter & Kis, Tamás & Kovács, András & Váncza, József, 2014. "An inverse economic lot-sizing approach to eliciting supplier cost parameters," International Journal of Production Economics, Elsevier, vol. 149(C), pages 80-88.
    19. Kovcs, Andrs & Brown, Kenneth N. & Tarim, S. Armagan, 2009. "An efficient MIP model for the capacitated lot-sizing and scheduling problem with sequence-dependent setups," International Journal of Production Economics, Elsevier, vol. 118(1), pages 282-291, March.
    20. Kis, Tamás & Kovács, András, 2013. "Exact solution approaches for bilevel lot-sizing," European Journal of Operational Research, Elsevier, vol. 226(2), pages 237-245.
    21. Haugen, Kjetil K. & Olstad, Asmund & Pettersen, Bard I., 2007. "The profit maximizing capacitated lot-size (PCLSP) problem," European Journal of Operational Research, Elsevier, vol. 176(1), pages 165-176, January.
    22. 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.

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