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A Fix-and-Optimize Approach for the Multi-Level Capacitated Lot Sizing Problems

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Author Info
Helber, Stefan
Sahling, Florian

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Abstract

This paper presents an optimization-based solution approach for the dynamic multi-level capacitated lot sizing problem (MLCLSP) with positive lead times. The key idea is to solve a series of mixed-integer programs in an iterative fix-and-optimize algorithm. Each of these programs is optimized over all real-valued variables, but only a small subset of binary setup variables. The remaining binary setup variables are tentatively fixed to values determined in previous iterations. The resulting algorithm is transparent, flexible, accurate and relatively fast. Its solution quality outperforms those of the approaches by Tempelmeier/Derstroff and by Stadtler.

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Paper provided by Universität Hannover, Wirtschaftswissenschaftliche Fakultät in its series Diskussionspapiere der Wirtschaftswissenschaftlichen Fakultät der Universität Hannover with number dp-393.

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Length: 22 pages
Date of creation: Mar 2008
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Handle: RePEc:han:dpaper:dp-393

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Related research
Keywords: multi-level lot sizing; MLCLSP; lead times; Fix-and-Optimize heuristic.;

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Tempelmeier, Horst, 2006. "Supply chain inventory optimization with two customer classes in discrete time," European Journal of Operational Research, Elsevier, vol. 174(1), pages 600-621, October. [Downloadable!] (restricted)
  2. Maes, Johan & McClain, John O. & Van Wassenhove, Luk N., 1991. "Multilevel capacitated lotsizing complexity and LP-based heuristics," European Journal of Operational Research, Elsevier, vol. 53(2), pages 131-148, July. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. Drexl, A. & Kimms, A., 1997. "Lot sizing and scheduling -- Survey and extensions," European Journal of Operational Research, Elsevier, vol. 99(2), pages 221-235, June. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
  6. Katok, Elena & Holly S. Lewis & Terry P. Harrison, 1995. "Lot Sizing in General Assembly Systems with Setup Costs, Setup Times and Multiple Constrained Resources," Discussion Paper Serie B 346, University of Bonn, Germany.
  7. Tempelmeier, Horst & Helber, Stefan, 1994. "A heuristic for dynamic multi-item multi-level capacitated lotsizing for general product structures," European Journal of Operational Research, Elsevier, vol. 75(2), pages 296-311, June. [Downloadable!] (restricted)
  8. Kuik, Roelof & Salomon, Marc & van Wassenhove, Luk N., 1994. "Batching decisions: structure and models," European Journal of Operational Research, Elsevier, vol. 75(2), pages 243-263, June. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
  11. Wolsey, Laurence A., 1995. "Progress with single-item lot-sizing," European Journal of Operational Research, Elsevier, vol. 86(3), pages 395-401, November. [Downloadable!] (restricted)
  12. Berretta, Regina & Rodrigues, Luiz Fernando, 2004. "A memetic algorithm for a multistage capacitated lot-sizing problem," International Journal of Production Economics, Elsevier, vol. 87(1), pages 67-81, January. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Sahling, Florian & Buschkühl, Lisbeth & Tempelmeier, Horst & Helber, Stefan, 2008. "Solving a Multi-Level Capacitated Lot Sizing Problem with Multi-Period Setup Carry-Over via a Fix-and-Optimize Heuristic," Diskussionspapiere der Wirtschaftswissenschaftlichen Fakultät der Universität Hannover dp-400, Universität Hannover, Wirtschaftswissenschaftliche Fakultät. [Downloadable!]
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