Processing Games with Restricted Capacities

M. Meertens, P.E.M. Borm, J.H. Reijnierse, M. Quant

Research output: Working paperDiscussion paperOther research output

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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.There are no restrictions whatsoever on the processing schedule.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.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.An explicit core element is constructed.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages19
Volume2004-83
Publication statusPublished - 2004

Publication series

NameCentER Discussion Paper
Volume2004-83

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Processing
Costs

Keywords

  • games
  • capacity
  • scheduling
  • cooperation
  • allocation

Cite this

Meertens, M., Borm, P. E. M., Reijnierse, J. H., & Quant, M. (2004). Processing Games with Restricted Capacities. (CentER Discussion Paper; Vol. 2004-83). Tilburg: Operations research.
Meertens, M. ; Borm, P.E.M. ; Reijnierse, J.H. ; Quant, M. / Processing Games with Restricted Capacities. Tilburg : Operations research, 2004. (CentER Discussion Paper).
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Meertens, M, Borm, PEM, Reijnierse, JH & Quant, M 2004 'Processing Games with Restricted Capacities' CentER Discussion Paper, vol. 2004-83, Operations research, Tilburg.

Processing Games with Restricted Capacities. / Meertens, M.; Borm, P.E.M.; Reijnierse, J.H.; Quant, M.

Tilburg : Operations research, 2004. (CentER Discussion Paper; Vol. 2004-83).

Research output: Working paperDiscussion paperOther research output

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AB - 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.There are no restrictions whatsoever on the processing schedule.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.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.An explicit core element is constructed.

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Meertens M, Borm PEM, Reijnierse JH, Quant M. Processing Games with Restricted Capacities. Tilburg: Operations research. 2004. (CentER Discussion Paper).