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

  • Helber, Stefan
  • Sahling, Florian

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 Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät in its series Hannover Economic Papers (HEP) with number dp-393.

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Length: 22 pages
Date of creation: Mar 2008
Date of revision:
Handle: RePEc:han:dpaper:dp-393
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  1. 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.
  2. Elena Katok & Holly S. Lewis & Terry P. Harrison, 1998. "Lot Sizing in General Assembly Systems with Setup Costs, Setup Times, and Multiple Constrained Resources," Management Science, INFORMS, vol. 44(6), pages 859-877, June.
  3. Stadtler, Hartmut, 1997. "Reformulations of the shortest route model for dynamic multi-item multi-level capacitated lotsizing," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 7096, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
  4. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
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  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. Wolsey, Laurence A., 1995. "Progress with single-item lot-sizing," European Journal of Operational Research, Elsevier, vol. 86(3), pages 395-401, November.
  8. Peter J. Billington & John O. McClain & L. Joseph Thomas, 1986. "Heuristics for Multilevel Lot-Sizing with a Bottleneck," Management Science, INFORMS, vol. 32(8), pages 989-1006, August.
  9. Terry P. Harrison & Holly S. Lewis, 1996. "Lot Sizing in Serial Assembly Systems with Multiple Constrained Resources," Management Science, INFORMS, vol. 42(1), pages 19-36, January.
  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. 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.
  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. 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.
  14. Peter J. Billington & John O. McClain & L. Joseph Thomas, 1983. "Mathematical Programming Approaches to Capacity-Constrained MRP Systems: Review, Formulation and Problem Reduction," Management Science, INFORMS, vol. 29(10), pages 1126-1141, October.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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).
  21. Ozdamar, Linet & Barbarosoglu, Gulay, 2000. "An integrated Lagrangean relaxation-simulated annealing approach to the multi-level multi-item capacitated lot sizing problem," International Journal of Production Economics, Elsevier, vol. 68(3), pages 319-331, December.
  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.
  23. Regina Berretta & Paulo M. França & Vinícius A. Armentano, 2005. "Metaheuristic Approaches For The Multilevel Resource-Constrained Lot-Sizing Problem With Setup And Lead Times," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 261-286.
  24. Marc Salomon & Leo G. Kroon & Roelof Kuik & Luk N. Van Wassenhove, 1991. "Some Extensions of the Discrete Lotsizing and Scheduling Problem," Management Science, INFORMS, vol. 37(7), pages 801-812, July.
  25. 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.
  26. 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).
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