J.-H. Kim, H.-S. Ahn and R. Righter, “Optimal Production Policies with Multistage Stochastic Leadtimes,” Probability in the Engineering and Informational Sciences, vol. 23, pp. 515-543, 2009.
Abstract: We study the value of multistage 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 that is not immediately filled at its due date will be backordered. The producer must decide whether or not to produce 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 significantly 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 identifies the conditions under which MADI is most beneficial and shows that the heuristic performs almost as well as the optimal policy when MADI is most beneficial.