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The Heterogeneous Vehicle-Routing Game

Author

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  • Stefan Engevall

    (Department of Mathematics, Linköping Institute of Technology, 581 83 Linköping, Stockholm, Sweden)

  • Maud Göthe-Lundgren

    (Department of Mathematics, Linköping Institute of Technology, 581 83 Linköping, Stockholm, Sweden)

  • Peter Värbrand

    (Department of Science and Technology, Linköping Institute of Technology, 601 74 Norrköping, Stockholm, Sweden)

Abstract

In this paper, we study a cost-allocation problem that arises in a distribution-planning situation at the Logistics Department at Norsk Hydro Olje AB, Stockholm, Sweden. We consider the routes from one depot during one day. The total distribution cost for these routes is to be divided among the customers that are visited. This cost-allocation problem is formulated as a vehicle-routing game (VRG), allowing the use of vehicles with different capacities. Cost-allocation methods based on different concepts from cooperative game theory, such as the core and the nucleolus, are discussed. A procedure that can be used to investigate whether the core is empty or not is presented, as well as a procedure to compute the nucleolus. Computational results for the Norsk Hydro case are presented and discussed.

Suggested Citation

  • Stefan Engevall & Maud Göthe-Lundgren & Peter Värbrand, 2004. "The Heterogeneous Vehicle-Routing Game," Transportation Science, INFORMS, vol. 38(1), pages 71-85, February.
    • Handle: RePEc:inm:ortrsc:v:38:y:2004:i:1:p:71-85
    DOI: 10.1287/trsc.1030.0035
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    4. Gansterer, Margaretha & Hartl, Richard F., 2018. "Collaborative vehicle routing: A survey," European Journal of Operational Research, Elsevier, vol. 268(1), pages 1-12.
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    6. Hezarkhani, Behzad & Slikker, Marco & Van Woensel, Tom, 2019. "Gain-sharing in urban consolidation centers," European Journal of Operational Research, Elsevier, vol. 279(2), pages 380-392.
    7. Lindong Liu & Xiangtong Qi & Zhou Xu, 2016. "Computing Near-Optimal Stable Cost Allocations for Cooperative Games by Lagrangian Relaxation," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 687-702, November.
    8. Behzad Hezarkhani & Marco Slikker & Tom Woensel, 2016. "A competitive solution for cooperative truckload delivery," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 51-80, January.
    9. 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.
    10. Silvia Schwarze, 2016. "Pricing strategies for the site-dependent vehicle routing problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 137-173, January.
    11. Schlicher, Loe & Lurkin, Virginie, 2022. "Stable allocations for choice-based collaborative price setting," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1242-1254.
    12. 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.
    13. Joen Dahlberg & Stefan Engevall & Maud Göthe-Lundgren, 2018. "Consolidation in Urban Freight Transportation — Cost Allocation Models," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(04), pages 1-23, August.
    14. Hezarkhani, Behzad & Slikker, Marco & Van Woensel, Tom, 2018. "Collaborative replenishment in the presence of intermediaries," European Journal of Operational Research, Elsevier, vol. 266(1), pages 135-146.
    15. Cruijssen, Frans & Cools, Martine & Dullaert, W., 2007. "Horizontal cooperation in logistics: opportunities and impediments," Other publications TiSEM ab29fad8-1faf-422b-826e-0, Tilburg University, School of Economics and Management.
    16. Basso, Franco & Basso, Leonardo J. & Rönnqvist, Mikael & Weintraub, Andres, 2021. "Coalition formation in collaborative production and transportation with competing firms," European Journal of Operational Research, Elsevier, vol. 289(2), pages 569-581.
    17. Bouchery, Yann & Hezarkhani, Behzad & Stauffer, Gautier, 2022. "Coalition formation and cost sharing for truck platooning," Transportation Research Part B: Methodological, Elsevier, vol. 165(C), pages 15-34.
    18. 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.
    19. 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.
    20. Richa Agarwal & Özlem Ergun, 2010. "Network Design and Allocation Mechanisms for Carrier Alliances in Liner Shipping," Operations Research, INFORMS, vol. 58(6), pages 1726-1742, December.
    21. 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.
    22. Lu, Wei & Quadrifoglio, Luca, 2019. "Fair cost allocation for ridesharing services – modeling, mathematical programming and an algorithm to find the nucleolus," Transportation Research Part B: Methodological, Elsevier, vol. 121(C), pages 41-55.
    23. 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.
    24. Okan Örsan Özener & Özlem Ergun & Martin Savelsbergh, 2013. "Allocating Cost of Service to Customers in Inventory Routing," Operations Research, INFORMS, vol. 61(1), pages 112-125, February.
    25. Margaretha Gansterer & Richard F. Hartl, 2020. "Shared resources in collaborative vehicle routing," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 1-20, April.

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