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Production-inventory games: A new class of totally balanced combinatorial optimization games

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  • Guardiola, Luis A.
  • Meca, Ana
  • Puerto, Justo

Abstract

In this paper we introduce a new class of cooperative games that arise from production-inventory problems. Several agents have to cover their demand over a finite time horizon and shortages are allowed. Each agent has its own unit production, inventory-holding and backlogging cost. Cooperation among agents is given by sharing production processes and warehouse facilities: agents in a coalition produce with the cheapest production cost and store with the cheapest inventory cost. We prove that the resulting cooperative game is totally balanced and the Owen set reduces to a singleton: the Owen point. Based on this type of allocation we find a population monotonic allocation scheme for this class of games. Finally, we point out the relationship of the Owen point with other well-known allocation rules such as the nucleolus and the Shapley value.

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  • 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.
    • Handle: RePEc:eee:gamebe:v:65:y:2009:i:1:p:205-219
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    4. LAMAS, ALEJANDRO & CHEVALIER, Philippe, 2013. "Jumping the hurdles for collaboration: fairness in operations pooling in the absence of transfer payments," LIDAM Discussion Papers CORE 2013073, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. G. Bergantiños & J. Vidal-Puga, 2020. "One-way and two-way cost allocation in hub network problems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(1), pages 199-234, March.
    6. Fiestras-Janeiro, M.G. & García-Jurado, I. & Meca, A. & Mosquera, M.A., 2011. "Cooperative game theory and inventory management," European Journal of Operational Research, Elsevier, vol. 210(3), pages 459-466, May.
    7. Luis Guardiola & Ana Meca & Justo Puerto, 2020. "Quid Pro Quo allocations in Production-Inventory games," Papers 2002.00953, arXiv.org.
    8. Li, Jun & Feng, Hairong & Zeng, Yinlian, 2014. "Inventory games with permissible delay in payments," European Journal of Operational Research, Elsevier, vol. 234(3), pages 694-700.
    9. Corberán, Ángel & Landete, Mercedes & Peiró, Juanjo & Saldanha-da-Gama, Francisco, 2020. "The facility location problem with capacity transfers," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 138(C).
    10. Luis A. Guardiola & Ana Meca & Justo Puerto, 2022. "The effect of consolidated periods in heterogeneous lot-sizing games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 380-404, July.
    11. Zheng, Xiao-Xue & Li, Deng-Feng & Liu, Zhi & Jia, Fu & Sheu, Jiuh-Biing, 2019. "Coordinating a closed-loop supply chain with fairness concerns through variable-weighted Shapley values," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 126(C), pages 227-253.
    12. Guardiola, Luis A. & Meca, Ana & Puerto, Justo, 2023. "Allocating the surplus induced by cooperation in distribution chains with multiple suppliers and retailers," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    13. Hezarkhani, Behzad & Slikker, Marco & Van Woensel, Tom, 2018. "Collaborative replenishment in the presence of intermediaries," European Journal of Operational Research, Elsevier, vol. 266(1), pages 135-146.
    14. 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.
    15. J. Drechsel & A. Kimms, 2010. "The subcoalition-perfect core of cooperative games," Annals of Operations Research, Springer, vol. 181(1), pages 591-601, December.
    16. Lu, Liang & Qi, Xiangtong & Liu, Zhixin, 2014. "On the cooperation of recycling operations," European Journal of Operational Research, Elsevier, vol. 233(2), pages 349-358.
    17. Hamers, H.J.M. & Miquel, S. & Norde, H.W., 2011. "Monotonic Stable Solutions for Minimum Coloring Games," Other publications TiSEM efae8d09-83e6-4fe4-9623-e, Tilburg University, School of Economics and Management.
    18. Feng, Hairong & Zeng, Yinlian & Cai, Xiaoqiang & Qian, Qian & Zhou, Yongwu, 2021. "Altruistic profit allocation rules for joint replenishment with carbon cap-and-trade policy," European Journal of Operational Research, Elsevier, vol. 290(3), pages 956-967.
    19. Luis A. Guardiola & Ana Meca & Justo Puerto, 2021. "Enforcing fair cooperation in production-inventory settings with heterogeneous agents," Annals of Operations Research, Springer, vol. 305(1), pages 59-80, October.
    20. Gansterer, Margaretha & Födermayr, Patrick & Hartl, Richard F., 2021. "The capacitated multi-level lot-sizing problem with distributed agents," International Journal of Production Economics, Elsevier, vol. 235(C).
    21. M Dror & B C Hartman, 2011. "Survey of cooperative inventory games and extensions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 565-580, April.
    22. Xin Chen & Zhisong Chen, 2013. "Cost allocation of capacity investment games," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(6), pages 512-523, September.
    23. Hamers, H.J.M. & Miquel, S. & Norde, H.W., 2011. "Monotonic Stable Solutions for Minimum Coloring Games," Discussion Paper 2011-016, Tilburg University, Center for Economic Research.
    24. Shoshana Anily & Moshe Haviv, 2010. "Cooperation in Service Systems," Operations Research, INFORMS, vol. 58(3), pages 660-673, June.
    25. Günter Fandel & Jan Trockel, 2016. "Investment and lot size planning in a supply chain: coordinating a just-in-time-delivery with a Harris- or a Wagner/Whitin-solution," Journal of Business Economics, Springer, vol. 86(1), pages 173-195, January.

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