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Shapley value-based cost allocation in the cooperative traveling salesman problem under rolling horizon planning

Author

Listed:
  • A. Kimms

    (University of Duisburg–Essen)

  • I. Kozeletskyi

    (University of Duisburg–Essen)

Abstract

This paper examines cooperation among salesmen from a game-theoretic perspective for the case of the traveling salesman problem with rolling horizon. The rolling horizon planning is modeled using stochastic demands. The goal is to determine a cost allocation for this problem using the Shapley value. The game-theoretic formulation of the problem is provided and structural properties are investigated. To compute the value of the characteristic function of this game, an optimization problem formulated as a stochastic dynamic program is introduced. Due to high computational effort of stochastic dynamic programming and calculation of the Shapley value, a tailor-made solution procedure is developed. This procedure combines methods of approximate dynamic programming to find an approximate value of the characteristic function and an estimation algorithm for the Shapley value. The developed computational study tests the computational performance of the solution procedure.

Suggested Citation

  • A. Kimms & I. Kozeletskyi, 2016. "Shapley value-based cost allocation in the cooperative traveling salesman problem under rolling horizon planning," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 5(4), pages 371-392, December.
    • Handle: RePEc:spr:eurjtl:v:5:y:2016:i:4:d:10.1007_s13676-015-0087-3
    DOI: 10.1007/s13676-015-0087-3
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    Cited by:

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    2. García-Martínez, Jose A. & Mayor-Serra, Antonio J. & Meca, Ana, 2020. "Efficient Effort Equilibrium in Cooperation with Pairwise Cost Reduction," MPRA Paper 105604, University Library of Munich, Germany.
    3. Gezahegn, T.W. & Maertens, M., 2018. "Economic Incentives for Collective Action in Agriculture: Evidence from Agricultural Co-operatives in Tigray, North Ethiopia," 2018 Conference, July 28-August 2, 2018, Vancouver, British Columbia 277137, International Association of Agricultural Economists.
    4. Cleophas, Catherine & Cottrill, Caitlin & Ehmke, Jan Fabian & Tierney, Kevin, 2019. "Collaborative urban transportation: Recent advances in theory and practice," European Journal of Operational Research, Elsevier, vol. 273(3), pages 801-816.
    5. Margaretha Gansterer & Richard F. Hartl, 2021. "The Prisoners’ Dilemma in collaborative carriers’ request selection," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(1), pages 73-87, March.
    6. Margaretha Gansterer & Richard F. Hartl & Sarah Wieser, 2021. "Assignment constraints in shared transportation services," Annals of Operations Research, Springer, vol. 305(1), pages 513-539, October.
    7. Yanjun Shi & Na Lin & Qiaomei Han & Tongliang Zhang & Weiming Shen, 2020. "A Method for Transportation Planning and Profit Sharing in Collaborative Multi-Carrier Vehicle Routing," Mathematics, MDPI, vol. 8(10), pages 1-23, October.
    8. García-Martínez, Jose A. & Mayor-Serra, Antonio J. & Meca, Ana, 2023. "Efficient effort equilibrium in cooperation with pairwise cost reduction," Omega, Elsevier, vol. 121(C).
    9. Gansterer, Margaretha & Hartl, Richard F., 2018. "Collaborative vehicle routing: A survey," European Journal of Operational Research, Elsevier, vol. 268(1), pages 1-12.
    10. Alix Vargas & Shushma Patel & Dilip Patel, 2018. "Towards a Business Model Framework to Increase Collaboration in the Freight Industry," Logistics, MDPI, vol. 2(4), pages 1-32, October.

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