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Transportation interval situations and related games

Author

Listed:
  • O. Palancı

    (Süleyman Demirel University)

  • S. Z. Alparslan Gök

    (Süleyman Demirel University)

  • M. O. Olgun

    (Süleyman Demirel University)

  • G.-W. Weber

    (Middle East Technical University)

Abstract

Basically, uncertainty is present in almost every real-world situation, it is influencing and questioning our decisions. In this paper, we analyze transportation interval games corresponding to transportation interval situations. In those situations, it may affect the optimal amount of goods and consequently whether and how much of a product is transported from a producer to a retailer. Firstly, we introduce the interval Shapley value of a game arising from a transportation situation under uncertainty. Secondly, a one-point solution concept by using a one-stage producere depending on the proportional, the constrained equal awards and the constrained equal losses rule is given. We prove that transportation interval games are interval balanced ( $$\mathcal {I}$$ I -balanced). Further, the nonemptiness of the interval core for the transportation interval games and some results on the relationship between the interval core and the dual interval optimal solutions of the underlying transportation situations are also provided. Moreover, we characterize the interval core using the square operator and addressing two scenarios such as pessimistic and optimistic.

Suggested Citation

  • O. Palancı & S. Z. Alparslan Gök & M. O. Olgun & G.-W. Weber, 2016. "Transportation interval situations and related games," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 119-136, January.
  • Handle: RePEc:spr:orspec:v:38:y:2016:i:1:d:10.1007_s00291-015-0422-y
    DOI: 10.1007/s00291-015-0422-y
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    References listed on IDEAS

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    2. R. Branzei & E. Gutiérrez & N. Llorca & J. Sánchez-Soriano, 2021. "Does it make sense to analyse a two-sided market as a multi-choice game?," Annals of Operations Research, Springer, vol. 301(1), pages 17-40, June.
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    4. Serap Ergün & Pınar Usta & Sırma Zeynep Alparslan Gök & Gerhard Wilhelm Weber, 2023. "A game theoretical approach to emergency logistics planning in natural disasters," Annals of Operations Research, Springer, vol. 324(1), pages 855-868, May.
    5. Alf Kimms & Herbert Kopfer, 2016. "Collaborative planning in transportation," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 1-2, January.
    6. Junnosuke Shino & Shinichi Ishihara & Shimpei Yamauchi, 2022. "Shapley Mapping and Its Axiomatizations in n -Person Cooperative Interval Games," Mathematics, MDPI, vol. 10(21), pages 1-14, October.
    7. Fialkoff, Marc R. & Omitaomu, Olufemi A. & Peterson, Steven K. & Tuttle, Mark A., 2017. "Using geographic information science to evaluate legal restrictions on freight transportation routing in disruptive scenarios," International Journal of Critical Infrastructure Protection, Elsevier, vol. 17(C), pages 60-74.
    8. Mostafa Pazoki & Hamed Samarghandi & Mehdi Behroozi, 2023. "Increasing Supply Chain Resiliency Through Equilibrium Pricing and Stipulating Transportation Quota Regulation," Papers 2308.00681, arXiv.org, revised Oct 2023.
    9. Meckling, Jonas & Nahm, Jonas, 2019. "The politics of technology bans: Industrial policy competition and green goals for the auto industry," Energy Policy, Elsevier, vol. 126(C), pages 470-479.
    10. Shinichi Ishihara & Junnosuke Shino, 2023. "Some Properties of Interval Shapley Values: An Axiomatic Analysis," Games, MDPI, vol. 14(3), pages 1-10, June.

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