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.
Author: | Armin Fügenschuh, Roel van Veldhuizen, Ingmar Vierhaus |
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Document Type: | ZIB-Report |
Tag: | Non-Cooperative Two-Person Games; Mixed-Integer Nonlinear Optimization |
MSC-Classification: | 91-XX GAME THEORY, ECONOMICS, SOCIAL AND BEHAVIORAL SCIENCES |
Date of first Publication: | 2013/04/23 |
Series (Serial Number): | ZIB-Report (13-25) |
ISSN: | 1438-0064 |
Published in: | Appeared in: Proceedings of the 11th Global Conference on Sustainable Manufacturing (GCSM2013), G. Seliger (Hrsg.), Universitätsverlag der TU Berlin, Seite 588 -- 593 |
URL: | http://opus4.kobv.de/opus4-tuberlin/frontdoor/index/index/docId/4026 |
Licence (German): | Creative Commons - Namensnennung-Nicht kommerziell-Keine Bearbeitung |