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Exact solution approaches for bilevel lot-sizing

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  • Kis, Tamás
  • Kovács, András

Abstract

In this paper we propose exact solution methods for a bilevel uncapacitated lot-sizing problem with backlogs. This is an extension of the classical uncapacitated lot-sizing problem with backlogs, in which two autonomous and self-interested decision makers constitute a two-echelon supply chain. The leader buys items from the follower in order to meet external demand at lowest cost. The follower also tries to minimize its costs. Both parties may backlog. We study the leader’s problem, i.e., how to determine supply requests over time to minimize its costs in view of the possible actions of the follower. We develop two mixed-integer linear programming reformulations, as well as cutting planes to cut off feasible, but suboptimal solutions. We compare the reformulations on a series of benchmark instances.

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  • Kis, Tamás & Kovács, András, 2013. "Exact solution approaches for bilevel lot-sizing," European Journal of Operational Research, Elsevier, vol. 226(2), pages 237-245.
    • Handle: RePEc:eee:ejores:v:226:y:2013:i:2:p:237-245
    DOI: 10.1016/j.ejor.2012.11.023
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    1. Bard, Jonathan F, 1983. "Coordination of a multidivisional organization through two levels of management," Omega, Elsevier, vol. 11(5), pages 457-468.
    2. Lukac, Zrinka & Soric, Kristina & Rosenzweig, Visnja Vojvodic, 2008. "Production planning problem with sequence dependent setups as a bilevel programming problem," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1504-1512, June.
    3. POCHET, Yves & WOLSEY, Laurence A., 1988. "Lot-size models with backlogging: strong reformulations and cutting planes," LIDAM Reprints CORE 791, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. POCHET, Yves & WOLSEY, Laurence A., 2010. "Single item lot-sizing with non-decreasing capacities," LIDAM Reprints CORE 2145, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Hau Lee & Seungjin Whang, 1999. "Decentralized Multi-Echelon Supply Chains: Incentives and Information," Management Science, INFORMS, vol. 45(5), pages 633-640, May.
    6. 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.
    7. 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.
    8. Patrice Marcotte & Gilles Savard, 2005. "Bilevel Programming: A Combinatorial Perspective," Springer Books, in: David Avis & Alain Hertz & Odile Marcotte (ed.), Graph Theory and Combinatorial Optimization, chapter 0, pages 191-217, Springer.
    9. Willard I. Zangwill, 1969. "A Backlogging Model and a Multi-Echelon Model of a Dynamic Economic Lot Size Production System--A Network Approach," Management Science, INFORMS, vol. 15(9), pages 506-527, May.
    10. BARANY, Imre & VAN ROY, Tony J. & WOLSEY, Laurence A., 1984. "Strong formulations for multi-item capacitated lot sizing," LIDAM Reprints CORE 590, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Li, Xiuhui & Wang, Qinan, 2007. "Coordination mechanisms of supply chain systems," European Journal of Operational Research, Elsevier, vol. 179(1), pages 1-16, May.
    12. VAN VYVE, Mathieu, 2006. "Linear-programming extended formulations for the single-item lot-sizing problem with backlogging and constant capacity," LIDAM Reprints CORE 1855, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. BELVAUX, Gaetan & WOLSEY, Laurence A., 2001. "Modelling practical lot-sizing problems as mixed-integer programs," LIDAM Reprints CORE 1516, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. BARANY, Imre & VAN ROY, Tony & WOLSEY, Laurence A., 1984. "Uncapacitated lot-sizing: the convex hull of solutions," LIDAM Reprints CORE 605, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    15. Martin Albrecht, 2010. "Supply Chain Coordination Mechanisms," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02833-5, July.
    16. 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.
    17. MELO, Rafael A. & WOLSEY, Laurence A., 2010. "Uncapacitated two-level lot-sizing," LIDAM Reprints CORE 2235, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. Imre Barany & Tony J. Van Roy & Laurence A. Wolsey, 1984. "Strong Formulations for Multi-Item Capacitated Lot Sizing," Management Science, INFORMS, vol. 30(10), pages 1255-1261, October.
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    1. Kailash Lachhwani, 2021. "Solving the general fully neutrosophic multi-level multiobjective linear programming problems," OPSEARCH, Springer;Operational Research Society of India, vol. 58(4), pages 1192-1216, December.
    2. Egri, Péter & Kis, Tamás & Kovács, András & Váncza, József, 2014. "An inverse economic lot-sizing approach to eliciting supplier cost parameters," International Journal of Production Economics, Elsevier, vol. 149(C), pages 80-88.
    3. Rowshannahad, Mehdi & Absi, Nabil & Dauzère-Pérès, Stéphane & Cassini, Bernard, 2018. "Multi-item bi-level supply chain planning with multiple remanufacturing of reusable by-products," International Journal of Production Economics, Elsevier, vol. 198(C), pages 25-37.
    4. Milička, P. & Šůcha, P. & Vanhoucke, M. & Maenhout, B., 2022. "The bilevel optimisation of a multi-agent project scheduling and staffing problem," European Journal of Operational Research, Elsevier, vol. 296(1), pages 72-86.

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