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Unitary Owen Points in Cooperative Lot-Sizing Models with Backlogging

Author

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  • Luis A. Guardiola

    (Departamento de Fundamentos del Análisis Económico, Universidad de Alicante, 03690 Alicante, Spain
    All the authors contributed equally to this work.)

  • Ana Meca

    (I.U. Centro de Investigación Operativa, Universidad Miguel Hernández, Edificio Torretamarit, Avda. de la Universidad s.n., 03202 Elche, Spain
    All the authors contributed equally to this work.)

  • Justo Puerto

    (Facultad de Matemáticas, Universidad de Sevilla, 41012 Sevilla, Spain
    All the authors contributed equally to this work.)

Abstract

This paper analyzes cost sharing in uncapacitated lot-sizing models with backlogging and heterogeneous costs. It is assumed that several firms participate in a consortium aiming at satisfying their demand over the planning horizon with minimal operating cost. Each individual firm has its own ordering channel and holding technology, but cooperation with other firms consists in sharing that information. Therefore, the firms that cooperate can use the best ordering channels and holding technology among members of the consortium. This mode of cooperation is stable. in that allocations of the overall operating cost exist, so that no group of agents benefit from leaving the consortium. Our contribution in the current paper is to present a new family of cost sharing allocations with good properties for enforcing cooperation: the unitary Owen points. Necessary and sufficient conditions are provided for the unitary Owen points to belong to the core of the cooperative game. In addition, we provide empirical evidence, through simulation, showing that, in randomly-generated situations, the above condition is fulfilled in 99% of the cases. Additionally, a relationship between lot-sizing games and a certain family of production-inventory games, through Owen’s points of the latter, is described. This interesting relationship enables easily constructing a variety of coalitionally stable allocations for cooperative lot-sizing models.

Suggested Citation

  • Luis A. Guardiola & Ana Meca & Justo Puerto, 2021. "Unitary Owen Points in Cooperative Lot-Sizing Models with Backlogging," Mathematics, MDPI, vol. 9(8), pages 1-19, April.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:869-:d:536488
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    References listed on IDEAS

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    1. F. R. Fernández & M. A. Hinojosa & J. Puerto, 2002. "Core Solutions in Vector-Valued Games," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 331-360, February.
    2. 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).
    3. Carvalho, Margarida & Pedroso, João Pedro & Telha, Claudio & Van Vyve, Mathieu, 2018. "Competitive uncapacitated lot-sizing game," International Journal of Production Economics, Elsevier, vol. 204(C), pages 148-159.
    4. Heuvel, Wilco van den & Borm, Peter & Hamers, Herbert, 2007. "Economic lot-sizing games," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1117-1130, January.
    5. Brahimi, Nadjib & Absi, Nabil & Dauzère-Pérès, Stéphane & Nordli, Atle, 2017. "Single-item dynamic lot-sizing problems: An updated survey," European Journal of Operational Research, Elsevier, vol. 263(3), pages 838-863.
    6. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    7. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
    8. Li, Hongyan & Meissner, Joern, 2011. "Competition under capacitated dynamic lot-sizing with capacity acquisition," International Journal of Production Economics, Elsevier, vol. 131(2), pages 535-544, June.
    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. Arie Tamir, 1992. "Technical Note—On the Complexity of Some Classes of Location Problems," Transportation Science, INFORMS, vol. 26(4), pages 352-354, November.
    11. Dimitris Zissis & George Ioannou & Apostolos Burnetas, 2020. "Coordinating Lot Sizing Decisions Under Bilateral Information Asymmetry," Production and Operations Management, Production and Operations Management Society, vol. 29(2), pages 371-387, February.
    12. Willard I. Zangwill, 1966. "A Deterministic Multi-Period Production Scheduling Model with Backlogging," Management Science, INFORMS, vol. 13(1), pages 105-119, September.
    13. Perea, Federico & Puerto, Justo & Fernández, Francisco R., 2012. "Avoiding unfairness of Owen allocations in linear production processes," European Journal of Operational Research, Elsevier, vol. 220(1), pages 125-131.
    14. Xin Chen & Jiawei Zhang, 2016. "Duality Approaches to Economic Lot-Sizing Games," Production and Operations Management, Production and Operations Management Society, vol. 25(7), pages 1203-1215, July.
    15. Guardiola, Luis A. & Meca, Ana & Puerto, Justo, 2009. "Production-inventory games: A new class of totally balanced combinatorial optimization games," Games and Economic Behavior, Elsevier, vol. 65(1), pages 205-219, January.
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