Base-Stock Policies For Lost-Sales Problems With Stochastic Lead Times

We consider a system that faces stochastic demand, reviews the system periodically and places replenishment orders to raise the inventory position to exactly S at the beginning of every period. The lead time associated with each of these orders is random. However the lead time process is such that these orders are ful lled in a rst-in rst-out sequence. Demand that can not be met with inventory available on-hand in the system is lost permanantly. A cost function which is the discounted sum of purchase costs, holding costs and lost sales costs in the future is de ned and shown to be convex in the parameter S. This result justi es the use of common search procedures for determining the optimal base stock parameter S.