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The Capacitated Lot-Sizing Problem with Linked Lot Sizes

Author

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  • Christopher Suerie

    (Technische Universität Darmstadt, Institut fü r Betriebswirtschaftslehre, Fachgebiet Produktion & Supply Chain Management, HochschulstraÑ 1, D-64289 Darmstadt, Germany)

  • Hartmut Stadtler

    (Technische Universität Darmstadt, Institut fü r Betriebswirtschaftslehre, Fachgebiet Produktion & Supply Chain Management, HochschulstraÑ 1, D-64289 Darmstadt, Germany)

Abstract

In this paper a new mixed integer programming (MIP) model formulation and its incorporation into a time-oriented decomposition heuristic for the capacitated lot-sizing problem with linked lot sizes (CLSPL) is proposed. The solution approach is based on an extended model formulation and valid inequalities to yield a tight formulation. Extensive computational tests prove the capability of this approach and show a superior solution quality with respect to other solution algorithms published so far.

Suggested Citation

  • Christopher Suerie & Hartmut Stadtler, 2003. "The Capacitated Lot-Sizing Problem with Linked Lot Sizes," Management Science, INFORMS, vol. 49(8), pages 1039-1054, August.
    • Handle: RePEc:inm:ormnsc:v:49:y:2003:i:8:p:1039-1054
    DOI: 10.1287/mnsc.49.8.1039.16406
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    References listed on IDEAS

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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. Bruno, Giuseppe & Genovese, Andrea & Piccolo, Carmela, 2014. "The capacitated Lot Sizing model: A powerful tool for logistics decision making," International Journal of Production Economics, Elsevier, vol. 155(C), pages 380-390.
    3. Lee, Younsoo & Lee, Kyungsik, 2022. "New integer optimization models and an approximate dynamic programming algorithm for the lot-sizing and scheduling problem with sequence-dependent setups," European Journal of Operational Research, Elsevier, vol. 302(1), pages 230-243.
    4. Raf Jans, 2009. "Solving Lot-Sizing Problems on Parallel Identical Machines Using Symmetry-Breaking Constraints," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 123-136, February.
    5. Absi, Nabil & van den Heuvel, Wilco, 2019. "Worst case analysis of Relax and Fix heuristics for lot-sizing problems," European Journal of Operational Research, Elsevier, vol. 279(2), pages 449-458.
    6. Tempelmeier, Horst & Buschkühl, Lisbeth, 2008. "Dynamic multi-machine lotsizing and sequencing with simultaneous scheduling of a common setup resource," International Journal of Production Economics, Elsevier, vol. 113(1), pages 401-412, May.
    7. Jenny Carolina Saldana Cortés, 2011. "Programación semidefinida aplicada a problemas de cantidad económica de pedido," Documentos CEDE 8735, Universidad de los Andes, Facultad de Economía, CEDE.
    8. Masoumeh Mahdieh & Alistair Clark & Mehdi Bijari, 2018. "A novel flexible model for lot sizing and scheduling with non-triangular, period overlapping and carryover setups in different machine configurations," Flexible Services and Manufacturing Journal, Springer, vol. 30(4), pages 884-923, December.
    9. 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.
    10. Malte Meistering & Hartmut Stadtler, 2020. "Stabilized-cycle strategy for a multi-item, capacitated, hierarchical production planning problem in rolling schedules," Business Research, Springer;German Academic Association for Business Research, vol. 13(1), pages 3-38, April.
    11. Awi Federgruen & Joern Meissner & Michal Tzur, 2007. "Progressive Interval Heuristics for Multi-Item Capacitated Lot-Sizing Problems," Operations Research, INFORMS, vol. 55(3), pages 490-502, June.
    12. Wei, Mingyuan & Qi, Mingyao & Wu, Tao & Zhang, Canrong, 2019. "Distance and matching-induced search algorithm for the multi-level lot-sizing problem with substitutable bill of materials," European Journal of Operational Research, Elsevier, vol. 277(2), pages 521-541.
    13. Suerie, Christopher, 2006. "Modeling of period overlapping setup times," European Journal of Operational Research, Elsevier, vol. 174(2), pages 874-886, October.
    14. Yang Dong & Kefeng Xu & Sining Song, 2014. "Contracting for Quality in a Multiple-Level Global Supply Chain," Working Papers 0205mss, College of Business, University of Texas at San Antonio.
    15. Jans, R.F. & Degraeve, Z., 2005. "Modeling Industrial Lot Sizing Problems: A Review," ERIM Report Series Research in Management ERS-2005-049-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    16. Tao Wu & Leyuan Shi & Jie Song, 2012. "An MIP-based interval heuristic for the capacitated multi-level lot-sizing problem with setup times," Annals of Operations Research, Springer, vol. 196(1), pages 635-650, July.
    17. Yavuz, Mesut & Tufekci, Suleyman, 2006. "A bounded dynamic programming solution to the batching problem in mixed-model just-in-time manufacturing systems," International Journal of Production Economics, Elsevier, vol. 103(2), pages 841-862, October.
    18. Liang, Zhe & He, Yan & Wu, Tao & Zhang, Canrong, 2015. "An informative column generation and decomposition method for a production planning and facility location problem," International Journal of Production Economics, Elsevier, vol. 170(PA), pages 88-96.
    19. Briskorn, D., 2004. "A note on capacitated lot sizing with setup carry-over," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 582, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    20. Kampf, M. & Kochel, P., 2006. "Simulation-based sequencing and lot size optimisation for a production-and-inventory system with multiple items," International Journal of Production Economics, Elsevier, vol. 104(1), pages 191-200, November.
    21. Talla Nobibon, Fabrice & Leus, Roel & Nip, Kameng & Wang, Zhenbo, 2015. "Resource loading with time windows," European Journal of Operational Research, Elsevier, vol. 244(2), pages 404-416.
    22. Sahling, Florian & Hahn, Gerd J., 2019. "Dynamic lot sizing in biopharmaceutical manufacturing," International Journal of Production Economics, Elsevier, vol. 207(C), pages 96-106.
    23. Helber, Stefan & Sahling, Florian, 2010. "A fix-and-optimize approach for the multi-level capacitated lot sizing problem," International Journal of Production Economics, Elsevier, vol. 123(2), pages 247-256, February.
    24. Ríos-Solís, Yasmín Á & Ibarra-Rojas, Omar J. & Cabo, Marta & Possani, Edgar, 2020. "A heuristic based on mathematical programming for a lot-sizing and scheduling problem in mold-injection production," European Journal of Operational Research, Elsevier, vol. 284(3), pages 861-873.

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