Skip to main content
SpringerLink
Log in

Cost Allocation for Horizontal Carrier Coalitions Based on Approximated Shapley Values

  • Conference paper
  • First Online:
Book cover Operations Research Proceedings 2015

Part of the book series: Operations Research Proceedings ((ORP))

Abstract

To improve competitiveness, small and mid-sized carriers ally in horizontal carrier coalitions for request exchange. A crucial aspect for the long-term viability and stability of coalitions is a fair cost allocation among the agents. Despite of the long computing time, the well-known Shapley value has been used as a scheme for cost allocation. The contribution of this paper lies on the development of a suitable sampling procedure that approximates the Shapley value applied to cost allocations for the collaborative traveling salesman problem with time windows. A computational study identifies the deviation of the values generated by the proposed sampling procedures from the actual Shapley value.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Notes

  1. 1.

    http://www.logistik.uni-bremen.de/english/instances/.

References

  1. Aziz H., Cahan C., Gretton C., Kilby P., Mattei N., Walsh: A study of Proxies for Shapley Allocations of Transport Costs. arXiv preprint (2014). arXiv:1408.4901

  2. Castro, J., Gomez, D., Tejada, J.: Polynomial calculation of the Shapley value based on sampling. Comput. Oper. Res. 36, 1726–1730 (2009)

    Article  Google Scholar 

  3. Cruijssen, F., Cools, M., Dullaert, W.: Horizontal cooperation in logistics: opportunities and impediments. Transp. Res. Part E Log. Transp. Rev. 43, 129–142 (2007)

    Article  Google Scholar 

  4. Frisk, M., Göthe-Lundgren, M., Jörnsten, K., Rönnqvist, M.: Cost allocation in collaborative forest transportation. Eur. J. Oper. Res. 205, 448–458 (2010)

    Article  Google Scholar 

  5. Krajewska, M., Kopfer, H., Laporte, G., Ropke, S., Zaccour, G.: Horizontal cooperation among freight carriers: request allocation and profit sharing. J. Oper. Res. Soc. 59, 1483–1491 (2008)

    Article  Google Scholar 

  6. Mann, I., Shapley, L.: Values of large games IV: Evaluating the electoral college by Monte Carlo techniques. Technical report, The RAND Corporation, Santa Monica, CA, USA (1960)

    Google Scholar 

  7. Shapley, L.: A value for n-person games. In: Kuhn, H., Tucker, A. (eds.) Contributions to the Theory of Games II 28, pp. 307–317. Princeton University Press, Princenton (1957)

    Google Scholar 

  8. Verdonck, L., Caris, A., Ramaekers, K., Janssens, G.K.: Collaborative logistics from the perspective of road transportation companies. Transp. Rev. 33, 700–719 (2013)

    Article  Google Scholar 

Download references

Acknowledgements

The research was supported by the German Research Foundation (DFG) as part of the project “Kooperierende Rundreiseplanung bei rollierender Planung”.

Author information

Authors and Affiliations

  1. Chair of Logistics, University of Bremen, Wilhelm-Herbst-Str. 5, 28359, Bremen, Germany

    Kristian Schopka & Herbert Kopfer

Authors
  1. Kristian Schopka
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Herbert Kopfer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kristian Schopka .

Editor information

Editors and Affiliations

  1. Department of Business Administration, University of Vienna, Vienna, Austria

    Karl Franz Dörner

  2. Decision Sciences and Statistics (IDS) Department, ESSEC Business School of Paris, Cergy Pontoise Cedex, France

    Ivana Ljubic

  3. Department of Statistics and Operations Research, University of Vienna, Vienna, Austria

    Georg Pflug

  4. Operations Research and Control Systems, TU Wien, Vienna, Austria

    Gernot Tragler

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this paper

Cite this paper

Schopka, K., Kopfer, H. (2017). Cost Allocation for Horizontal Carrier Coalitions Based on Approximated Shapley Values. In: Dörner, K., Ljubic, I., Pflug, G., Tragler, G. (eds) Operations Research Proceedings 2015. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-42902-1_18

Download citation

Publish with us

Policies and ethics

Search

Navigation