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Processing games with restricted capacities

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Author Info

  • Reijnierse, Hans
  • Borm, Peter
  • Quant, Marieke
  • Meertens, Marc

Abstract

This paper analyzes processing problems and related cooperative games. In a processing problem there is a finite set of jobs, each requiring a specific amount of effort to be completed, whose costs depend linearly on their completion times. The main feature of the model is a capacity restriction, i.e., there is a maximum amount of effort per time unit available for handling jobs. There are no other restrictions whatsoever on the processing schedule. Assigning to each job a player and letting each player have an individual capacity for handling jobs, each coalition of cooperating players in fact faces a processing problem with the coalitional capacity being the sum of the individual capacities of the members. The corresponding processing game summarizes the minimal joint costs for every coalition. It turns out that processing games are totally balanced. The proof of this statement is constructive and provides a core element in polynomial time.

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Bibliographic Info

Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 202 (2010)
Issue (Month): 3 (May)
Pages: 773-780

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Handle: RePEc:eee:ejores:v:202:y:2010:i:3:p:773-780

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Related research

Keywords: Scheduling Individual capacity Cooperation Core allocation;

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References

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  1. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 9(2), pages 139-199, December.
  2. Curiel, I. & Pederzoli, G. & Tijs, S.H., 1989. "Sequencing games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154243, Tilburg University.
  3. Legut, J. & Potters, J.A.M. & Tijs, S.H., 1994. "Economies with land: A game theoretical approach," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154193, Tilburg University.
  4. Legut J. & Potters J. A. M. & Tijs S. H., 1994. "Economies with Land--A Game Theoretical Approach," Games and Economic Behavior, Elsevier, vol. 6(3), pages 416-430, May.
  5. Curiel, Imma & Pederzoli, Giorgio & Tijs, Stef, 1989. "Sequencing games," European Journal of Operational Research, Elsevier, vol. 40(3), pages 344-351, June.
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Cited by:
  1. Quant, M. & Meertens, M. & Reijnierse, J.H., 2004. "Processing Games with Shared Interest," Discussion Paper 2004-126, Tilburg University, Center for Economic Research.

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