Optimal Policies for a Dual-Sourcing Inventory Problem with Endogenous Stochastic Lead Times

We consider a single-product, two-source inventory system with Poisson demand and backlogging. Inventory can be replenished through a normal supply source, which consists of a two-stage tandem queue with exponential production time at each stage. We can also place an emergency order by skipping the first stage, for a fee. There is no fixed order cost. There are linear order, holding, and back-order costs. Through a new approach, we obtain optimal ordering policies for the discounted or long-run average cost and also characterize near-optimal heuristic policies. The approach consists of four steps. The first step is to establish an equivalent system, in the sense that it has the same optimal policy as the original system. The second step is to construct a tandem queueing system, where costs are charged in accord with the equivalent system’s cost structure. The third step derives an optimal control of the service rate at each server so as to minimize the tandem queue’s system-wide cost. The fourth and final step is to translate the queue’s optimal policy to an optimal policy for the equivalent system and hence the original system.