Optimal Control Theory applied to a cooperative game between a manufacturer and a retailer
In this work, we consider a process of production, storage and sales of a perishable consumer good as a cooperative game between a manufacturer and a retailer. Both parties want to choose such a strategy (optimal production plan, optimal reselling plan, etc.) that will maximize their cumulative profits. The problem is reduced to the maximizing of the corresponding functionals of profit and solved with the use of the Optimal Control Theory. Computer programs are written in MAPLE in order to demonstrate and confirm our analytical results.