Lower and upper bounds for linear production games |
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Authors: | Endre Bjø rndal,Kurt Jö rnsten |
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Affiliation: | Department of Finance and Management Science, Norwegian School of Economics and Business Administration, Helleveien 30, 5045 Bergen, Norway |
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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 ?-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. |
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Keywords: | Linear programming Cooperative game theory Production |
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