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Characterizing the Shapley value in fixed-route traveling salesman problems with appointments

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  • Duygu Yengin

Abstract

Starting from her home, a service provider visits several customers, following a predetermined route, and returns home after all customers are visited. The problem is to ?nd a fair allocation of the total cost of this tour among the customers served. A transferable-utility cooperative game can be associated with this cost allocation problem. We intro- duce a new class of games, which we refer as the fixed-route traveling salesman games with appointments. We characterize the Shapley Value in this class using a property which requires thttps://media.adelaide.edu.au/economics/litting into a set of sponsors.
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  • Duygu Yengin, 2012. "Characterizing the Shapley value in fixed-route traveling salesman problems with appointments," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 271-299, May.
    • Handle: RePEc:spr:jogath:v:41:y:2012:i:2:p:271-299
    DOI: 10.1007/s00182-011-0285-7
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    Cited by:

    1. Youngsub Chun & Nari Park & Duygu Yengin, 2015. "Coincidence of Cooperative Game Theoretic Solutions in the Appointment Problem," School of Economics and Public Policy Working Papers 2015-09, University of Adelaide, School of Economics and Public Policy.
    2. Arroyo, Federico, 2024. "Cost Allocation in Vehicle Routing Problems with Time Windows," Junior Management Science (JUMS), Junior Management Science e. V., vol. 9(1), pages 1241-1268.
    3. Kellner, Florian & Schneiderbauer, Miriam, 2019. "Further insights into the allocation of greenhouse gas emissions to shipments in road freight transportation: The pollution routing game," European Journal of Operational Research, Elsevier, vol. 278(1), pages 296-313.
    4. Florian Kellner, 2022. "Generating greenhouse gas cutting incentives when allocating carbon dioxide emissions to shipments in road freight transportation," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(3), pages 833-874, September.

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    More about this item

    Keywords

    Fixed-route traveling salesman games; Routing games; Appointment games; The Shapley value; The core; Transferable-utility games; Merging and splitting proofness; Networks; Cost allocation; C71;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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