(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 finite-horizon 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 base-stock 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.