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Allocating costs in set covering problems

Author

Listed:
  • Bergantiños, Gustavo
  • Gómez-Rúa, María
  • Llorca, Natividad
  • Pulido, Manuel
  • Sánchez-Soriano, Joaquín

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, Joaquín, 2020. "Allocating costs in set covering problems," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1074-1087.
    • Handle: RePEc:eee:ejores:v:284:y:2020:i:3:p:1074-1087
    DOI: 10.1016/j.ejor.2020.01.031
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    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.
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    Cited by:

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    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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