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Solving a Multi-Level Capacitated Lot Sizing Problem with Multi-Period Setup Carry-Over via a Fix-and-Optimize Heuristic

  • Sahling, Florian
  • Buschkühl, Lisbeth
  • Tempelmeier, Horst
  • Helber, Stefan

This paper presents a new algorithm for the dynamic Multi-Level Capacitated Lot Sizing Problem with Setup Carry-Overs (MLCLSP-L). The MLCLSP-L is a big-bucket model that allows the production of any number of products within a period, but it incorporates partial sequencing of the production orders in the sense that the first and the last product produced in a period are determined by the model. We solve a model which is applicable to general bill-of-material structures and which includes minimum lead times of one period and multi-period setup carry-overs. Our algorithm solves a series of mixed-integer linear programs in an iterative so-called Fix-and-Optimize approach. In each instance of these mixed-integer linear programs a large number of binary setup variables is fixed whereas only a small subset of these variables is optimized, together with the complete set of the inventory and lot size variables. A numerical study shows that the algorithm provides high-quality results and that the computational effort is moderate.

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Paper provided by Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät in its series Hannover Economic Papers (HEP) with number dp-400.

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Length: 24 pages
Date of creation: Jun 2008
Date of revision:
Handle: RePEc:han:dpaper:dp-400
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  1. 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).
  2. 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.
  3. Mohan Gopalakrishnan & Ke Ding & Jean-Marie Bourjolly & Srimathy Mohan, 2001. "A Tabu-Search Heuristic for the Capacitated Lot-Sizing Problem with Set-up Carryover," Management Science, INFORMS, vol. 47(6), pages 851-863, June.
  4. 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.
  5. Wolsey, Laurence A., 1995. "Progress with single-item lot-sizing," European Journal of Operational Research, Elsevier, vol. 86(3), pages 395-401, November.
  6. 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.
  7. 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.
  8. Suerie, Christopher & Stadtler, Hartmut, 2003. "The Capacitated lot-sizing problem with linked lot sizes," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 20206, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
  9. 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.
  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. Christopher Suerie & Hartmut Stadtler, 2003. "The Capacitated Lot-Sizing Problem with Linked Lot Sizes," Management Science, INFORMS, vol. 49(8), pages 1039-1054, August.
  12. 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.
  13. 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.
  14. 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.
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