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Production Planning for Non-Cooperating Companies with Nonlinear Optimization

Please always quote using this URN: urn:nbn:de:0297-zib-18163
  • 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:ZIB-Report
Tag:Non-Cooperative Two-Person Games; Mixed-Integer Nonlinear Optimization
Date of first Publication:2013/04/23
Series (Serial Number):ZIB-Report (13-25)
Published in:Appeared in: Proceedings of the 11th Global Conference on Sustainable Manufacturing (GCSM2013), G. Seliger (Hrsg.), Universitätsverlag der TU Berlin, Seite 588 -- 593
Licence (German):License LogoCreative Commons - Namensnennung-Nicht kommerziell-Keine Bearbeitung
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