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On Analyzing Cost Allocation Problems: Cooperation Building Structures and Order Problem Representations

Author

Listed:
  • John Kleppe

    (Department of Econometrics and Operations Research, School of Economics and Management, Tilburg University, P. O. Box 90153, 5000 LE Tilburg, The Netherlands)

  • Peter Borm

    (Department of Econometrics and Operations Research, School of Economics and Management, Tilburg University, P. O. Box 90153, 5000 LE Tilburg, The Netherlands)

  • Ruud Hendrickx

    (Department of Econometrics and Operations Research, School of Economics and Management, Tilburg University, P. O. Box 90153, 5000 LE Tilburg, The Netherlands)

  • Hans Reijnierse

    (Department of Econometrics and Operations Research, School of Economics and Management, Tilburg University, P. O. Box 90153, 5000 LE Tilburg, The Netherlands)

Abstract

To analyze cost allocation problems, this paper identifies associated cooperation building structures, with joint cost functions, and corresponding efficient order problem representations, with individualized cost functions. This paper presents an approach that, when applicable, offers a way not only to adequately model a cost allocation problem by means of a cooperative cost game, but also to construct a core element of such a game by means of a generalized Bird allocation. We apply the approach to both existing and new classes of cost allocation problems related to operational research problems: sequencing situations without initial ordering, maintenance problems, minimum cost spanning tree situations, permutation situations without initial allocation, public congestion network situations, traveling salesman problems, shared taxi problems and traveling repairman problems.

Suggested Citation

  • John Kleppe & Peter Borm & Ruud Hendrickx & Hans Reijnierse, 2018. "On Analyzing Cost Allocation Problems: Cooperation Building Structures and Order Problem Representations," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(04), pages 1-28, December.
    • Handle: RePEc:wsi:igtrxx:v:20:y:2018:i:04:n:s021919891850007x
    DOI: 10.1142/S021919891850007X
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    Keywords

    Cost allocation problem; cooperation building structure; order problem representation; transferable utility game; generalized Bird allocation;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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