Lower and upper bounds for linear production games

Endre Bjørndal and Kurt Jörnsten

European Journal of Operational Research, 2009, vol. 196, issue 2, 476-486

Abstract: We study the problem of allocating the total profit of a production enterprise among the resource owners, using the game-theoretic framework introduced by Owen [Owen, G., 1975. On the core of linear production games. Mathematical Programming 9, 358-370]. We provide lower (upper) bounds on the values of the game by aggregating over columns (rows) of the LP-problem. By choosing aggregation weights corresponding to optimal solutions of the primal (dual) LP-problem, we can create new games whose core form a superset (subset) of the original core. An estimate of the resulting error, in terms of an [epsilon]-core, is obtained by solving a mixed integer programming problem, and we also suggest an iterative procedure for improving the bounds. Using a set of numerical examples, we investigate how the performance of the aggregation approach depends on the structure of the problem data.

Keywords: Linear; programming; Cooperative; game; theory; Production (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:196:y:2009:i:2:p:476-486

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