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. The problem for player A to find an optimal production plan without information on the strategy of player B can be formulated as a nonlinear mathematical optimization problem. In its naive formulation the model is too large, making its solution practically impossible. After a reformulation, it turns into a much smaller model, which is solved by spatial branch-and-cut methods and linear programming. It turns out that player A can have a production strategy which yields an income for A that player B cannot beat, no matter how he produces.
- Social Science Research Center Berlin (WZB)
- Zuse Institute Berlin
- DFG, Collaborative Research Center SFB-1026.
- Armin Fügenschuh, Roel van Veldhuizen, Ingmar Vierhaus, Production Planning for Non-Cooperating Companies with Nonlinear Optimization , Proceedings of the 11th Global Conference on Sustainable Manufacturing, Universitätsverlag der TU Berlin, pp. 588-593, 2013. (Also available as ZIB Technical Report ZR-13-25 , 2013.)