Inventory Management With an Exogenous Supply Process

We study single- and multi-stage inventory systems with stochastic leadtimes. We study a class of stochastic leadtime processes, which we refer to as exogenous leadtimes. This class of leadtime processes includes as special cases all leadtime models from existing literature (such as Kaplan's leadtimes with no order crossing, see Kaplan [1970], or i.i.d. leadtimes with order crossing, among others) but is a substantially broader class. For a system with an exogenous leadtime process, we provide a method to determine base stock levels and to compute the cost of a given base stock policy. The method relies on relating the cost of a base stock policy to the cost of a threshold policy in a related single-unit, single-customer problem. This single-unit method is exact for single stage systems and for multi-stage systems under certain conditions. If the conditions are not satisfied, the method obtains near optimal base stock levels and accurate approximations of cost for multi-stage systems.