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One-way and two-way cost allocation in hub network problems

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  • Bergantiños, Gustavo
  • Vidal-Puga, Juan

Abstract

We study hub problems where a set of nodes send and receive data from each other. In order to reduce costs, the nodes use a network with a given set of hubs. We address the cost sharing aspect by assuming that nodes are only interested in either sending or receiving data, but not both (one-way flow) or that nodes are interested in both sending and receiving data (two-way flow). In both cases, we study the non-emptiness of the core and the Shapley value of the corresponding cost game.

Suggested Citation

  • Bergantiños, Gustavo & Vidal-Puga, Juan, 2016. "One-way and two-way cost allocation in hub network problems," MPRA Paper 74875, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:74875
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    1. Alcalde-Unzu, Jorge & Gómez-Rúa, María & Molis, Elena, 2015. "Sharing the costs of cleaning a river: the Upstream Responsibility rule," Games and Economic Behavior, Elsevier, vol. 90(C), pages 134-150.
    2. Dutta, Bhaskar & Mishra, Debasis, 2012. "Minimum cost arborescences," Games and Economic Behavior, Elsevier, vol. 74(1), pages 120-143.
    3. Trudeau, Christian, 2014. "Minimum cost spanning tree problems with indifferent agents," Games and Economic Behavior, Elsevier, vol. 84(C), pages 137-151.
    4. Ivan Contreras & Moayad Tanash & Navneet Vidyarthi, 2017. "Exact and heuristic approaches for the cycle hub location problem," Annals of Operations Research, Springer, vol. 258(2), pages 655-677, November.
    5. Guardiola, Luis A. & Meca, Ana & Puerto, Justo, 2009. "Production-inventory games: A new class of totally balanced combinatorial optimization games," Games and Economic Behavior, Elsevier, vol. 65(1), pages 205-219, January.
    6. Aykin, Turgut, 1994. "Lagrangian relaxation based approaches to capacitated hub-and-spoke network design problem," European Journal of Operational Research, Elsevier, vol. 79(3), pages 501-523, December.
    7. Nader Azizi & Navneet Vidyarthi & Satyaveer S. Chauhan, 2018. "Modelling and analysis of hub-and-spoke networks under stochastic demand and congestion," Annals of Operations Research, Springer, vol. 264(1), pages 1-40, May.
    8. -, 1997. "International economic highlights 1996," Oficina de la CEPAL en Washington (Estudios e Investigaciones) 28965, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    9. Bogomolnaia, Anna & Moulin, Hervé, 2010. "Sharing a minimal cost spanning tree: Beyond the Folk solution," Games and Economic Behavior, Elsevier, vol. 69(2), pages 238-248, July.
    10. Moulin, Hervé, 2014. "Pricing traffic in a spanning network," Games and Economic Behavior, Elsevier, vol. 86(C), pages 475-490.
    11. Trudeau, Christian, 2012. "A new stable and more responsive cost sharing solution for minimum cost spanning tree problems," Games and Economic Behavior, Elsevier, vol. 75(1), pages 402-412.
    12. Bergantiños, G. & Gómez-Rúa, M. & Llorca, N. & Pulido, M. & Sánchez-Soriano, J., 2014. "A new rule for source connection problems," European Journal of Operational Research, Elsevier, vol. 234(3), pages 780-788.
    13. Matsubayashi, Nobuo & Umezawa, Masashi & Masuda, Yasushi & Nishino, Hisakazu, 2005. "A cost allocation problem arising in hub-spoke network systems," European Journal of Operational Research, Elsevier, vol. 160(3), pages 821-838, February.
    14. Darko Skorin-Kapov, 2001. "On Cost Allocation in Hub-Like Networks," Annals of Operations Research, Springer, vol. 106(1), pages 63-78, September.
    15. Lee McKnight & Joseph P. Bailey, 1997. "Global Internet Economics," Brazilian Electronic Journal of Economics, Department of Economics, Universidade Federal de Pernambuco, vol. 1(0), December.
    16. Bergantiños, Gustavo & Kar, Anirban, 2010. "On obligation rules for minimum cost spanning tree problems," Games and Economic Behavior, Elsevier, vol. 69(2), pages 224-237, July.
    17. Trudeau, Christian & Vidal-Puga, Juan, 2017. "On the set of extreme core allocations for minimal cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 169(C), pages 425-452.
    18. A.T. Ernst & M. Krishnamoorthy, 1999. "Solution algorithms for the capacitated single allocation hub location problem," Annals of Operations Research, Springer, vol. 86(0), pages 141-159, January.
    19. Perea, F. & Puerto, J. & Fernández, F.R., 2009. "Modeling cooperation on a class of distribution problems," European Journal of Operational Research, Elsevier, vol. 198(3), pages 726-733, November.
    20. Olivera Janković & Stefan Mišković & Zorica Stanimirović & Raca Todosijević, 2017. "Novel formulations and VNS-based heuristics for single and multiple allocation p-hub maximal covering problems," Annals of Operations Research, Springer, vol. 259(1), pages 191-216, December.
    21. Alumur, Sibel & Kara, Bahar Y., 2008. "Network hub location problems: The state of the art," European Journal of Operational Research, Elsevier, vol. 190(1), pages 1-21, October.
    22. Mohammad S. Roni & Sandra D. Eksioglu & Kara G. Cafferty & Jacob J. Jacobson, 2017. "A multi-objective, hub-and-spoke model to design and manage biofuel supply chains," Annals of Operations Research, Springer, vol. 249(1), pages 351-380, February.
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    More about this item

    Keywords

    hub network; cost allocation; core; Shapley value;
    All these keywords.

    JEL classification:

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

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