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Equal Surplus Sharing in Grey Inventory Games

Author

Listed:
  • Halil İbrahim Dönmez
  • Mehmet Onur Olgun
  • Sırma Zeynep Alparslan Gök

Abstract

This study introduces a model where inventory costs are represented as grey numbers, rather than traditional crisp or stochastic values. Utilizing grey calculus, game-theoretic solutions are reinterpreted to address interval uncertainty within cooperative grey inventory games. Grey equal distribution rules are established for fair cost allocation. The model parameters are determined to construct a grey inventory game, which is applied to three shotgun companies in Türkiye. The calculated grey inventory costs and different game-theoretic solutions are presented. This study extends solutions like the Banzhaf value, _CIS_-value, _ENSC_-value, and _ED_-solution by incorporating interval uncertainty.

Suggested Citation

  • Halil İbrahim Dönmez & Mehmet Onur Olgun & Sırma Zeynep Alparslan Gök, 2024. "Equal Surplus Sharing in Grey Inventory Games," Alphanumeric Journal, Bahadir Fatih Yildirim, vol. 12(3), pages 215-226, December.
    • Handle: RePEc:anm:alpnmr:v:12:y:2024:i:3:p:215-226
    DOI: https://doi.org/10.17093/alphanumeric.1492875
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    References listed on IDEAS

    as
    1. Mehmet Onur Olgun & Erdal Aydemir, 2021. "A new cooperative depot sharing approach for inventory routing problem," Annals of Operations Research, Springer, vol. 307(1), pages 417-441, December.
    2. Patrick Legros, 1986. "Allocating joint costs by means of the nucleolus," ULB Institutional Repository 2013/7050, ULB -- Universite Libre de Bruxelles.
    3. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Cooperative game theory; Equal surplus sharing rules; Grey Numbers; Inventory Management;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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