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

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  • Helber, Stefan
  • Sahling, Florian

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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File URL: http://diskussionspapiere.wiwi.uni-hannover.de/pdf_bib/dp-393.pdf
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Bibliographic Info

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

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References

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  4. 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.
  5. 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.
  6. 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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  15. 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).
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  20. 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.
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  26. 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.
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Citations

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Cited by:
  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," Hannover Economic Papers (HEP) dp-400, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  2. 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.
  3. Florian Sahling, 2013. "A Column-Generation Approach for a Short-Term Production Planning Problem in Closed-Loop Supply Chains," BuR - Business Research, German Academic Association for Business Research, vol. 6(1), pages 55-75, May.
  4. 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.
  5. Stadtler, Hartmut & Sahling, Florian, 2013. "A lot-sizing and scheduling model for multi-stage flow lines with zero lead times," European Journal of Operational Research, Elsevier, vol. 225(3), pages 404-419.
  6. Lang, Jan Christian & Shen, Zuo-Jun Max, 2011. "Fix-and-optimize heuristics for capacitated lot-sizing with sequence-dependent setups and substitutions," European Journal of Operational Research, Elsevier, vol. 214(3), pages 595-605, November.
  7. Helber, Stefan & Böhme, Daniel & Oucherif, Farid & Lagershausen, Svenja & Kasper, Steffen, 2014. "A hierarchical facility layout planning approach for large and complex hospitals," Hannover Economic Papers (HEP) dp-527, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  8. Zhang, Zhi-Hai & Jiang, Hai & Pan, Xunzhang, 2012. "A Lagrangian relaxation based approach for the capacitated lot sizing problem in closed-loop supply chain," International Journal of Production Economics, Elsevier, vol. 140(1), pages 249-255.
  9. Wolter, Anja & Helber, Stefan, 2013. "Simultaneous Production and Maintenance Planning for a Single Capacitated Resource facing both a Dynamic Demand and Intensive Wear and Tear," Hannover Economic Papers (HEP) dp-522, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  10. Ferreira, Deisemara & Clark, Alistair R. & Almada-Lobo, Bernardo & Morabito, Reinaldo, 2012. "Single-stage formulations for synchronised two-stage lot sizing and scheduling in soft drink production," International Journal of Production Economics, Elsevier, vol. 136(2), pages 255-265.
  11. Xiao, Yiyong & Zhang, Renqian & Zhao, Qiuhong & Kaku, Ikou & Xu, Yuchun, 2014. "A variable neighborhood search with an effective local search for uncapacitated multilevel lot-sizing problems," European Journal of Operational Research, Elsevier, vol. 235(1), pages 102-114.

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