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Production Planning for Non-Cooperating Companies with Nonlinear Optimization

  • We consider a production planning problem where two competing companies are selling their items on a common market. Moreover, the raw material used in the production is a limited non-renewable resource. The revenue per item sold depends on the total amount of items produced by both players. If they collaborate they could apply a production strategy that leads to the highest combined revenue. Usually the formation of such syndicates is prohibited by law; hence we assume that one company does not know how much the other company will produce. We formulate the problem for company A to find an optimal production plan without information on the strategy of company B as a nonlinear mathematical optimization problem. In its naive formulation the model is too large, making its solution practically impossible. After a reformulation we find a much smaller model, which we solve by spatial branch-and-cut methods and linear programming. We discuss the practical implications of our solutions.

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Author:Armin Fügenschuh, Roel van Veldhuizen, Ingmar Vierhaus
Document Type:In Proceedings
Parent Title (English):11th Global Conference on Sustainable Manufacturing : Proceedings
First Page:536
Last Page:541
Publisher:Universitätsverlag der TU Berlin
Place of publication:Berlin
Year of first publication:2013
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