(s, S) Policies for a Dynamic Inventory Model with Stochastic Lead Times

This study analyzes a stochastic lead time inventory model under the assumptions that (a) replenishment orders do not cross in time and (b) the lead time distribution for a given order is independent of the number and sizes of outstanding orders. The study extends the existing literature on the finitehorizon version of the model and yields an intuitively appealing dynamic program that is nearly identical to one that would apply in a transformed model with all lead times fixed at zero. Hence, many results that have been derived for fixed lead time models generalize easily. Conditions for the optimality of myopic basestock policies, and for the optimality of (s, S) policies are established for both finite and infinite planning horizons. The infinite-horizon model analysis is extended by adapting the fixed lead time results for the efficient computation of optimal and approximately optimal (s, S) policies.