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A computational analysis of lower bounds for big bucket production planning problems

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  • Kerem Akartunal─▒

    ()

  • Andrew Miller

    ()

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    Abstract

    In this paper, we analyze a variety of approaches to obtain lower bounds for multi-level production planning problems with big bucket capacities, i.e., problems in which multiple items compete for the same resources. We give an extensive survey of both known and new methods, and also establish relationships between some of these methods that, to our knowledge, have not been presented before. As will be highlighted, understanding the substructures of difficult problems provide crucial insights on why these problems are hard to solve, and this is addressed by a thorough analysis in the paper. We conclude with computational results on a variety of widely used test sets, and a discussion of future research. Copyright Springer Science+Business Media, LLC 2012

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    File URL: http://hdl.handle.net/10.1007/s10589-012-9465-z
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    Bibliographic Info

    Article provided by Springer in its journal Computational Optimization and Applications.

    Volume (Year): 53 (2012)
    Issue (Month): 3 (December)
    Pages: 729-753

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    Handle: RePEc:spr:coopap:v:53:y:2012:i:3:p:729-753

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    Web page: http://www.springer.com/math/journal/10589

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    Related research

    Keywords: Production planning; Lot-sizing; Integer programming; Strong formulations; Lagrangian relaxation;

    References

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    1. Willard I. Zangwill, 1969. "A Backlogging Model and a Multi-Echelon Model of a Dynamic Economic Lot Size Production System--A Network Approach," Management Science, INFORMS, vol. 15(9), pages 506-527, May.
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    3. William W. Trigeiro & L. Joseph Thomas & John O. McClain, 1989. "Capacitated Lot Sizing with Setup Times," Management Science, INFORMS, vol. 35(3), pages 353-366, March.
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    5. Alan S. Manne, 1958. "Programming of Economic Lot Sizes," Management Science, INFORMS, vol. 4(2), pages 115-135, January.
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    7. 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.
    8. Awi Federgruen & Michal Tzur, 1991. "A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in 0(n log n) or 0(n) Time," Management Science, INFORMS, vol. 37(8), pages 909-925, August.
    9. 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.
    10. 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.
    11. Gaetan Belvaux & Laurence A. Wolsey, 2001. "Modelling Practical Lot-Sizing Problems as Mixed-Integer Programs," Management Science, INFORMS, vol. 47(7), pages 993-1007, July.
    12. Gabriel R. Bitran & Hirofumi Matsuo, 1986. "The Multi-Item Capacitated Lot Size Problem: Error Bounds of Manne's Formulations," Management Science, INFORMS, vol. 32(3), pages 350-359, March.
    13. Stadtler, Hartmut, 2003. "Multilevel lot sizing with setup times and multiple constrained resources: Internally rolling schedules with lot-sizing windows," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 20204, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
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