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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.

Suggested Citation

  • 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.
  • Handle: RePEc:han:dpaper:dp-393
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    References listed on IDEAS

    as
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    Cited by:

    1. repec:eee:proeco:v:198:y:2018:i:c:p:25-37 is not listed on IDEAS
    2. 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.
    3. Anja Wolter & Stefan Helber, 2016. "Simultaneous production and maintenance planning for a single capacitated resource facing both a dynamic demand and intensive wear and tear," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 24(3), pages 489-513, September.
    4. 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.
    5. 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.
    6. Marcos Mansano Furlan & Maristela Oliveira Santos, 2017. "BFO: a hybrid bees algorithm for the multi-level capacitated lot-sizing problem," Journal of Intelligent Manufacturing, Springer, vol. 28(4), pages 929-944, April.
    7. Silvio Alexandre de Araujo & Bert De Reyck & Zeger Degraeve & Ioannis Fragkos & Raf Jans, 2015. "Period Decompositions for the Capacitated Lot Sizing Problem with Setup Times," INFORMS Journal on Computing, INFORMS, vol. 27(3), pages 431-448, August.
    8. 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.
    9. repec:spr:annopr:v:242:y:2016:i:2:d:10.1007_s10479-013-1526-x is not listed on IDEAS
    10. 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.
    11. Wei, Wenchao & Guimarães, Luis & Amorim, Pedro & Almada-Lobo, Bernardo, 2017. "Tactical production and distribution planning with dependency issues on the production process," Omega, Elsevier, vol. 67(C), pages 99-114.
    12. Chen, Haoxun, 2015. "Fix-and-optimize and variable neighborhood search approaches for multi-level capacitated lot sizing problems," Omega, Elsevier, vol. 56(C), pages 25-36.
    13. 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.
    14. Horst Tempelmeier & Karina Copil, 2016. "Capacitated lot sizing with parallel machines, sequence-dependent setups, and a common setup operator," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(4), pages 819-847, October.
    15. 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.
    16. 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.
    17. 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.
    18. Neves-Moreira, F. & Amorim, P. & Guimarães, L. & Almada-Lobo, B., 2016. "A long-haul freight transportation problem: Synchronizing resources to deliver requests passing through multiple transshipment locations," European Journal of Operational Research, Elsevier, vol. 248(2), pages 487-506.

    More about this item

    Keywords

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

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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