The effect of stochastic supply times on optimal policies in inventory control

This paper solves a special case of the EOQ model with stochastic lead times. It considers only the family of policies that comply with the following two stipulations: (1) orders do not cross each other, and (2) the system experiences both positive inventory and backlogs between any two consecutive orders, namely, it regenerates itself each cycle. The first assumption is almost imperative to preserve mathematical tenability and is widespread. The second one, however, is specific to this paper and enables it to obtain simple, closed form results which clearly pinpoint the role of randomness through the straight-forward dependence of the optimal solution on the variances of the lead times.