IDEAS home Printed from https://ideas.repec.org/a/spr/eurjtl/v5y2016i4d10.1007_s13676-015-0087-3.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13676-015-0087-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13676-015-0087-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hugo P. Simão & Jeff Day & Abraham P. George & Ted Gifford & John Nienow & Warren B. Powell, 2009. "An Approximate Dynamic Programming Algorithm for Large-Scale Fleet Management: A Case Application," Transportation Science, INFORMS, vol. 43(2), pages 178-197, May.
    2. M A Krajewska & H Kopfer & G Laporte & S Ropke & G Zaccour, 2008. "Horizontal cooperation among freight carriers: request allocation and profit sharing," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(11), pages 1483-1491, November.
    3. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
    4. Nicola Secomandi & François Margot, 2009. "Reoptimization Approaches for the Vehicle-Routing Problem with Stochastic Demands," Operations Research, INFORMS, vol. 57(1), pages 214-230, February.
    5. Anton J. Kleywegt & Vijay S. Nori & Martin W. P. Savelsbergh, 2004. "Dynamic Programming Approximations for a Stochastic Inventory Routing Problem," Transportation Science, INFORMS, vol. 38(1), pages 42-70, February.
    6. Nicola Secomandi, 2001. "A Rollout Policy for the Vehicle Routing Problem with Stochastic Demands," Operations Research, INFORMS, vol. 49(5), pages 796-802, October.
    7. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Warren B. Powell, 2010. "Feature Article ---Merging AI and OR to Solve High-Dimensional Stochastic Optimization Problems Using Approximate Dynamic Programming," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 2-17, February.
    9. Okan Örsan Özener & Özlem Ergun & Martin Savelsbergh, 2011. "Lane-Exchange Mechanisms for Truckload Carrier Collaboration," Transportation Science, INFORMS, vol. 45(1), pages 1-17, February.
    10. Okan Örsan Özener & Özlem Ergun, 2008. "Allocating Costs in a Collaborative Transportation Procurement Network," Transportation Science, INFORMS, vol. 42(2), pages 146-165, May.
    11. Potters, J.A.M. & Curiel, I. & Tijs, S.H., 1992. "Traveling salesman games," Other publications TiSEM 0dd4cf3d-25fa-4179-80f6-6, Tilburg University, School of Economics and Management.
    12. Stefan Engevall & Maud Göthe-Lundgren & Peter Värbrand, 2004. "The Heterogeneous Vehicle-Routing Game," Transportation Science, INFORMS, vol. 38(1), pages 71-85, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Defryn, Christof & Sörensen, Kenneth & Dullaert, Wout, 2019. "Integrating partner objectives in horizontal logistics optimisation models," Omega, Elsevier, vol. 82(C), pages 1-12.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    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. Minyoung Yea & Seokhyun Chung & Taesu Cheong & Daeki Kim, 2018. "The Sharing of Benefits from a Logistics Alliance Based on a Hub-Spoke Network: A Cooperative Game Theoretic Approach," Sustainability, MDPI, vol. 10(6), pages 1-16, June.
    4. Gansterer, Margaretha & Hartl, Richard F., 2018. "Collaborative vehicle routing: A survey," European Journal of Operational Research, Elsevier, vol. 268(1), pages 1-12.
    5. 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.
    6. Jun Li & Xiaoqiang Cai & Yinlian Zeng, 2016. "Cost allocation for less-than-truckload collaboration among perishable product retailers," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 81-117, January.
    7. Zolfagharinia, Hossein & Haughton, Michael, 2018. "The importance of considering non-linear layover and delay costs for local truckers," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 109(C), pages 331-355.
    8. Kimms, A. & Kozeletskyi, I., 2016. "Core-based cost allocation in the cooperative traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 248(3), pages 910-916.
    9. Arslan, Okan & Archetti, Claudia & Jabali, Ola & Laporte, Gilbert & Grazia Speranza, Maria, 2020. "Minimum cost network design in strategic alliances," Omega, Elsevier, vol. 96(C).
    10. M. Fiestras-Janeiro & Ignacio García-Jurado & Manuel Mosquera, 2011. "Cooperative games and cost allocation problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 1-22, July.
    11. Lozano, S. & Moreno, P. & Adenso-Díaz, B. & Algaba, E., 2013. "Cooperative game theory approach to allocating benefits of horizontal cooperation," European Journal of Operational Research, Elsevier, vol. 229(2), pages 444-452.
    12. Stehbeck, Florian, 2019. "Designing and Scheduling Cost-Efficient Tours by Using the Concept of Truck Platooning," Junior Management Science (JUMS), Junior Management Science e. V., vol. 4(4), pages 566-634.
    13. Pillac, Victor & Gendreau, Michel & Guéret, Christelle & Medaglia, Andrés L., 2013. "A review of dynamic vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 225(1), pages 1-11.
    14. 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.
    15. Okan Örsan Özener & Özlem Ergun, 2008. "Allocating Costs in a Collaborative Transportation Procurement Network," Transportation Science, INFORMS, vol. 42(2), pages 146-165, May.
    16. Mathijs van Zon & Remy Spliet & Wilco van den Heuvel, 2021. "The Joint Network Vehicle Routing Game," Transportation Science, INFORMS, vol. 55(1), pages 179-195, 1-2.
    17. 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.
    18. 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.
    19. Yang, Fei & Dai, Ying & Ma, Zu-Jun, 2020. "A cooperative rich vehicle routing problem in the last-mile logistics industry in rural areas," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    20. van Zon, M. & Spliet, R. & van den Heuvel, W., 2021. "The effect of algorithm capabilities on cooperative games," Econometric Institute Research Papers EI2021-02, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:eurjtl:v:5:y:2016:i:4:d:10.1007_s13676-015-0087-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.