TY - CHAP A1 - Fügenschuh, Armin A1 - van Veldhuizen, Roel A1 - Vierhaus, Ingmar T1 - Production Planning for Non-Cooperating Companies with Nonlinear Optimization T2 - 11th Global Conference on Sustainable Manufacturing : Proceedings N2 - 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. Y1 - 2013 SP - 536 EP - 541 PB - Universitätsverlag der TU Berlin CY - Berlin ER - TY - GEN A1 - Fügenschuh, Armin A1 - van Veldhuizen, Roel A1 - Vierhaus, Ingmar T1 - Production Planning for Non-Cooperating Companies with Nonlinear Optimization N2 - 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. T3 - ZIB-Report - 13-25 KW - Non-Cooperative Two-Person Games; Mixed-Integer Nonlinear Optimization Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-18163 UR - http://opus4.kobv.de/opus4-tuberlin/frontdoor/index/index/docId/4026 SN - 1438-0064 ER -