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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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    1. Tijs, S.H. & Meca, A. & Lopez, M.A., 2005. "Benefit sharing in holding situations," Other publications TiSEM 718b8e18-eb6f-407b-a9cd-e, Tilburg University, School of Economics and Management.
    2. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
    3. 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.
    4. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
    5. Ana Meca & Ignacio García-Jurado & Peter Borm, 2003. "Cooperation and competition in inventory games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(3), pages 481-493, August.
    6. Tijs, Stef & Meca, Ana & Lopez, Marco A., 2005. "Benefit sharing in holding situations," European Journal of Operational Research, Elsevier, vol. 162(1), pages 251-269, April.
    7. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
    8. Meca, Ana & Timmer, Judith & Garcia-Jurado, Ignacio & Borm, Peter, 2004. "Inventory games," European Journal of Operational Research, Elsevier, vol. 156(1), pages 127-139, July.
      • Meca-Martinez, A. & Timmer, J.B. & Garcia-Jurado, I. & Borm, P.E.M., 1999. "Inventory Games," Discussion Paper 1999-53, Tilburg University, Center for Economic Research.
      • Meca-Martinez, A. & Timmer, J.B. & Garcia-Jurado, I. & Borm, P.E.M., 1999. "Inventory Games," Other publications TiSEM 21f26b3f-7fae-4f19-908f-a, Tilburg University, School of Economics and Management.
      • Meca, A. & Timmer, J.B. & Garcia-Jurado, I. & Borm, P.E.M., 2004. "Inventory games," Other publications TiSEM 49368f2d-02fc-49c9-9d74-8, Tilburg University, School of Economics and Management.
    9. Ana Meca, 2007. "A core-allocation family for generalized holding cost games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(3), pages 499-517, June.
    10. Slikker, Marco & Fransoo, Jan & Wouters, Marc, 2005. "Cooperation between multiple news-vendors with transshipments," European Journal of Operational Research, Elsevier, vol. 167(2), pages 370-380, December.
    11. Rajeev Kohli & Heungsoo Park, 1989. "A Cooperative Game Theory Model of Quantity Discounts," Management Science, INFORMS, vol. 35(6), pages 693-707, June.
    12. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Muller, Alfred & Scarsini, Marco & Shaked, Moshe, 2002. "The Newsvendor Game Has a Nonempty Core," Games and Economic Behavior, Elsevier, vol. 38(1), pages 118-126, January.
    14. Gary D. Eppen, 1979. "Note--Effects of Centralization on Expected Costs in a Multi-Location Newsboy Problem," Management Science, INFORMS, vol. 25(5), pages 498-501, May.
    15. Ravi Anupindi & Yehuda Bassok & Eitan Zemel, 2001. "A General Framework for the Study of Decentralized Distribution Systems," Manufacturing & Service Operations Management, INFORMS, vol. 3(4), pages 349-368, February.
    16. van Gellekom, J. R. G. & Potters, J. A. M. & Reijnierse, J. H. & Engel, M. C. & Tijs, S. H., 2000. "Characterization of the Owen Set of Linear Production Processes," Games and Economic Behavior, Elsevier, vol. 32(1), pages 139-156, July.
    17. Hartman, Bruce C. & Dror, Moshe & Shaked, Moshe, 2000. "Cores of Inventory Centralization Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 26-49, April.
    18. Tijs, S.H. & van Gellekom, J.R.G. & Potters, J.A.M. & Reijnierse, J.H. & Engel, M.C., 2000. "Characterization of the Owen set of linear production processes," Other publications TiSEM bdf0c618-e9f1-496a-b977-0, Tilburg University, School of Economics and Management.
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    4. 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.
    5. 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.
    6. 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).
    7. 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.
    8. 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).
    9. J. Drechsel & A. Kimms, 2010. "The subcoalition-perfect core of cooperative games," Annals of Operations Research, Springer, vol. 181(1), pages 591-601, December.
    10. 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.
    11. 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.
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    13. Shoshana Anily & Moshe Haviv, 2010. "Cooperation in Service Systems," Operations Research, INFORMS, vol. 58(3), pages 660-673, June.
    14. 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.
    15. Zheng, Xiao-Xue & Liu, Zhi & Li, Kevin W. & Huang, Jun & Chen, Ji, 2019. "Cooperative game approaches to coordinating a three-echelon closed-loop supply chain with fairness concerns," International Journal of Production Economics, Elsevier, vol. 212(C), pages 92-110.
    16. Bernstein, Fernando & Gürhan Kök, A. & Meca, Ana, 2015. "Cooperation in assembly systems: The role of knowledge sharing networks," European Journal of Operational Research, Elsevier, vol. 240(1), pages 160-171.
    17. Luis Guardiola & Ana Meca & Justo Puerto, 2020. "Quid Pro Quo allocations in Production-Inventory games," Papers 2002.00953, arXiv.org.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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).
    23. 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.
    24. 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.
    25. 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).

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