Necessary optimality conditions for enterprises production programs

An idealized industrial group, consisting of two enterprises with vertical cooperation, is considered in this paper. We assume that the both enterprises, having necessary production capacities, act on the product markets once as the partners and once as the independent actors. The main problem of this kind of cooperation is to find the optimal conditions for the production programs for the both enterprises. The possible way of the mathematical problem formulation, as well as its relation to the optimal control problem, is the essence of this paper. The theoretical backgrounds for the solution of the optimal cooperation production program are developed using the Dubovitski-Milyutin method.