Optimal Production Policies with Multistage Stochastic Demand Leadtimes

We study the value of multi-stage advance demand information (MADI) in a production system in which customers place an order in advance of their actual need, and each order goes through multiple stages before it becomes due. Any order which is not immediately …lled at its due date will be backordered. The producer must decide whether to produce or not based on real-time information regarding current and future orders. We formulate the problem as a Markov decision process and analyze the impact of the demand information on the production policy and the cost. We show that the optimal production policy is a state-dependent base-stock policy, and we show that it has certain monotonicity properties. We also introduce a simple heuristic policy that is signi…cantly easier to compute and that inherits the structural properties of the optimal policy. In addition, we show that its base-stock levels bound those of the socially optimal policy. Numerical study identi…es the conditions under which MADI is most bene…cial and shows that the heuristic performs almost as well as the optimal policy when MADI is most bene…cial.