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Lower and upper bounds for linear production games

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  • Bjørndal, Endre
  • Jörnsten, Kurt

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.

Suggested Citation

  • Bjørndal, Endre & Jörnsten, Kurt, 2009. "Lower and upper bounds for linear production games," European Journal of Operational Research, Elsevier, vol. 196(2), pages 476-486, July.
    • Handle: RePEc:eee:ejores:v:196:y:2009:i:2:p:476-486
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    References listed on IDEAS

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    1. Curiel, I. & Derks, J. & Tijs, S.H., 1989. "On balanced games and games with committee control," Other publications TiSEM 43993ad7-6225-435d-bfa4-b, Tilburg University, School of Economics and Management.
    2. Paul H. Zipkin, 1980. "Bounds on the Effect of Aggregating Variables in Linear Programs," Operations Research, INFORMS, vol. 28(2), pages 403-418, April.
    3. Fred Glover, 1975. "Improved Linear Integer Programming Formulations of Nonlinear Integer Problems," Management Science, INFORMS, vol. 22(4), pages 455-460, December.
    4. Warren P. Adams & Hanif D. Sherali, 1990. "Linearization Strategies for a Class of Zero-One Mixed Integer Programming Problems," Operations Research, INFORMS, vol. 38(2), pages 217-226, April.
    5. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
    6. van Gellekom, J. R. G. & Potters, J. A. M. & Reijnierse, J. H. & Engel, M. C. & Tijs, S. H., 2000. "Characterization of the Owen Set of Linear Production Processes," Games and Economic Behavior, Elsevier, vol. 32(1), pages 139-156, July.
    7. Paul H. Zipkin, 1980. "Bounds for Row-Aggregation in Linear Programming," Operations Research, INFORMS, vol. 28(4), pages 903-916, August.
    8. Tijs, S.H. & van Gellekom, J.R.G. & Potters, J.A.M. & Reijnierse, J.H. & Engel, M.C., 2000. "Characterization of the Owen set of linear production processes," Other publications TiSEM bdf0c618-e9f1-496a-b977-0, Tilburg University, School of Economics and Management.
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    1. Phuoc Hoang Le & Tri-Dung Nguyen & Tolga Bektaş, 2020. "Efficient computation of the Shapley value for large-scale linear production games," Annals of Operations Research, Springer, vol. 287(2), pages 761-781, April.

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