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Allocating costs in set covering problems

Author

Listed:
  • Bergantiños, Gustavo
  • Gómez-Rúa, María
  • Llorca, Natividad
  • Pulido, Manuel
  • Sánchez-Soriano, Joaquin
Abstract
This paper deals with the problem of allocating costs in set covering situations. In particular, we focus on set covering situations where the optimal covering is given in advance. Thus, we take into account only the facilities that have to be opened and look for rules distributing their cost. We define a cooperative game and study the core and the nucleolus. We also introduce two new rules: the equal split rule on facilities and the serial rule. We axiomatically characterize the core, the nucleolus, and the two rules. Finally, we study several monotonicity properties of the rules.

Suggested Citation

  • Bergantiños, Gustavo & Gómez-Rúa, María & Llorca, Natividad & Pulido, Manuel & Sánchez-Soriano, Joaquin, 2019. "Allocating costs in set covering problems," MPRA Paper 92659, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:92659
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    References listed on IDEAS

    as
    1. Gustavo Bergantiños & Silvia Lorenzo-Freire, 2008. "A characterization of optimistic weighted Shapley rules in minimum cost spanning tree problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(3), pages 523-538, June.
    2. Daniel Granot, 1987. "The Role of Cost Allocation in Locational Models," Operations Research, INFORMS, vol. 35(2), pages 234-248, April.
    3. Constantine Toregas & Ralph Swain & Charles ReVelle & Lawrence Bergman, 1971. "The Location of Emergency Service Facilities," Operations Research, INFORMS, vol. 19(6), pages 1363-1373, October.
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    5. Xiang-Yang Li & Zheng Sun & Weizhao Wang & Wei Lou, 2010. "Cost sharing and strategyproof mechanisms for set cover games," Journal of Combinatorial Optimization, Springer, vol. 20(3), pages 259-284, October.
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    7. Xiaotie Deng & Toshihide Ibaraki & Hiroshi Nagamochi, 1999. "Algorithmic Aspects of the Core of Combinatorial Optimization Games," Mathematics of Operations Research, INFORMS, vol. 24(3), pages 751-766, August.
    8. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-1037, September.
    9. Bergantinos, Gustavo & Vidal-Puga, Juan J., 2007. "A fair rule in minimum cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 326-352, November.
    10. Sanchez-Soriano, Joaquin, 2006. "Pairwise solutions and the core of transportation situations," European Journal of Operational Research, Elsevier, vol. 175(1), pages 101-110, November.
    11. 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).
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    13. Sanchez-Soriano, Joaquin, 2003. "The pairwise egalitarian solution," European Journal of Operational Research, Elsevier, vol. 150(1), pages 220-231, October.
    14. Bergantinos, Gustavo & Lorenzo-Freire, Silvia, 2008. ""Optimistic" weighted Shapley rules in minimum cost spanning tree problems," European Journal of Operational Research, Elsevier, vol. 185(1), pages 289-298, February.
    15. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    16. M. Fiestras-Janeiro & Ignacio García-Jurado & Manuel Mosquera, 2011. "Rejoinder on: 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 33-34, July.
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    19. 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.
    20. Justo Puerto & Ignacio Garcı´a-Jurado & Francisco R. Fernández, 2001. "On the core of a class of location games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(3), pages 373-385, December.
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    Cited by:

    1. Bergantiños, Gustavo & Moreno-Ternero, Juan D., 2022. "Monotonicity in sharing the revenues from broadcasting sports leagues," European Journal of Operational Research, Elsevier, vol. 297(1), pages 338-346.
    2. Rick K. Acosta & Encarnación Algaba & Joaquín Sánchez-Soriano, 2022. "Multi-issue bankruptcy problems with crossed claims," Annals of Operations Research, Springer, vol. 318(2), pages 749-772, November.
    3. Acosta-Vega, Rick K. & Algaba, Encarnación & Sánchez-Soriano, Joaquín, 2023. "Design of water quality policies based on proportionality in multi-issue problems with crossed claims," European Journal of Operational Research, Elsevier, vol. 311(2), pages 777-788.

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    More about this item

    Keywords

    set covering problems; cost sharing rules; cooperative games;
    All these keywords.

    JEL classification:

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

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