A By-Product Production System with an Alternative

This paper considers the optimal control of a production system which is composed of two distinct production processes, types A and B, that produce two different products, 1 and 2, having distinct random demands. Production type A produces both products in amounts determined by a fixed set of production coefficients. Type B can only be used to make product 2. Costs consist of linear production costs and convex holding and shortage costs. Each period, the optimal production level of each type must be determined. The criterion is the minimum expected discounted total cost. Results show that the decision space of each period is partitioned into four regions by three monotone functions and a point. Extensions include capacitated production, nonstationary costs, lost sales, fixed lead times aid the general m process-n product system.