Ordering Policies in an environment of Stochastic Yields and Substitutable Demands

In this paper, we model production problems where yields are stochastic, demands are substitutable, and several items are jointly produced. We formulate this problem as a profit maximizing convex program, and study two approximation procedures. The first method solves finite horizon stochastic programs on a rolling horizon basis. We develop a decomposition algorithm for solving the finite horizon problems. The finite horizon problems are linear programs. Our algorithm utilizes the network-like structure of the coefficient matrix of the linear programs. The second method is a heuristic procedure that is based on the structure of the optimal policy for two-period problems. The heuristic parallels the decision rules used by managers in practice. The computational results suggest that the performance of this heuristic is comparable to that of the rolling horizon approach.