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Coalition Formation and Cost Allocation for Joint Replenishment Systems

Author

Listed:
  • Zied Jemai

    (LGI - Laboratoire Génie Industriel - EA 2606 - CentraleSupélec)

  • Adel Elomri
  • Asma Ghaffari

    (LGI - Laboratoire Génie Industriel - EA 2606 - CentraleSupélec)

  • Yves Dallery

    (LGI - Laboratoire Génie Industriel - EA 2606 - CentraleSupélec)

Abstract

T his paper focuses on the issues of coalition formation and cost allocation in a joint replenishment system involving a set of independent and freely interacting retailers purchasing an item from one supplier to meet a deterministic demand. The papers dealing with this problem are mainly focused on supperadditive games, where the cost savings associated with a coalition increase with the number of players in the coalition. The most relevant question addressed then is how to allocate the savings to the players. In this paper, we propose to go further by dealing with a non-supperadditive game, where a set of independent retailers have the common understanding to share the cost savings according to the cost-based proportional rule. In this setting, the global cost optimization is no longer a relevant approach to identify appealing coalitions for any retailer. Here, we provide an iterative procedure to form the so-called efficient coalition structure and we show that this coalition structure has the nice properties of being (i) weakly stable in the sense of the coalition structure core and (ii) strongly stable under a given assumption. An exact fractional programming based solution is also given to generate such efficient coalitions.

Suggested Citation

  • Zied Jemai & Adel Elomri & Asma Ghaffari & Yves Dallery, 2012. "Coalition Formation and Cost Allocation for Joint Replenishment Systems," Post-Print hal-01672397, HAL.
    • Handle: RePEc:hal:journl:hal-01672397
    DOI: 10.1111/j.1937-5956.2012.01333.x
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    Citations

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    Cited by:

    1. Simai He & Jay Sethuraman & Xuan Wang & Jiawei Zhang, 2017. "A NonCooperative Approach to Cost Allocation in Joint Replenishment," Operations Research, INFORMS, vol. 65(6), pages 1562-1573, December.
    2. Körpeoğlu, Evren & Şen, Alper & Güler, Kemal, 2013. "Non-cooperative joint replenishment under asymmetric information," European Journal of Operational Research, Elsevier, vol. 227(3), pages 434-443.
    3. Kidd, Martin P. & Borm, Peter, 2021. "On Determining Leading Coalitions in Supply Chains: Methodology and Application," Discussion Paper 2021-009, Tilburg University, Center for Economic Research.
    4. Wang, Min & Zhao, Lindu & Herty, Michael, 2019. "Joint replenishment and carbon trading in fresh food supply chains," European Journal of Operational Research, Elsevier, vol. 277(2), pages 561-573.
    5. A. Saavedra-Nieves & I. García-Jurado & M. G. Fiestras-Janeiro, 2018. "On coalition formation in a non-convex multi-agent inventory problem," Annals of Operations Research, Springer, vol. 261(1), pages 255-273, February.
    6. Juan S. Borrero & Colin Gillen & Oleg A. Prokopyev, 2017. "Fractional 0–1 programming: applications and algorithms," Journal of Global Optimization, Springer, vol. 69(1), pages 255-282, September.
    7. Ben Jouida, Sihem & Guajardo, Mario & Klibi, Walid & Krichen, Saoussen, 2021. "Profit maximizing coalitions with shared capacities in distribution networks," European Journal of Operational Research, Elsevier, vol. 288(2), pages 480-495.
    8. Öner, Nihat & Kuyzu, Gültekin, 2021. "Core stable coalition selection in collaborative truckload transportation procurement," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 154(C).
    9. Mauricio Varas & Franco Basso & Paul Bosch & Juan Pablo Contreras & Raúl Pezoa, 2022. "A horizontal collaborative approach for planning the wine grape harvesting," Operational Research, Springer, vol. 22(5), pages 4965-4998, November.
    10. Ben Jouida, Sihem & Krichen, Saoussen & Klibi, Walid, 2017. "Coalition-formation problem for sourcing contract design in supply networks," European Journal of Operational Research, Elsevier, vol. 257(2), pages 539-558.
    11. Nguyen, Christine & Dessouky, Maged & Toriello, Alejandro, 2014. "Consolidation strategies for the delivery of perishable products," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 69(C), pages 108-121.

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