Optimal production decision for two substitutable products with capacity constraint of manufacturer

A single period production decision model with one manufacturer who produces two substitutable products was considered in this paper. Facing random products demand, how to decide the production quantities for these two products to maximize the manufacturerpsilas profit when demand realized is of managerial interest. To the best of our knowledge, there is no good results on this problem because of the notorious difficulty of substitution problem. This paper explores the problem under the cases where the manufacturer with capacity constraint and the manufacturer without capacity constraint. The concavity of the manufacturerpsilas expected profit function was proved, and the effect of productspsila substitution to the manufacturerpsilas decisions was also investigated. Some properties of the optimal production quantities were given, which is helpful to search for the optimal production quantities.