Robust Dual Sourcing Inventory Management: Optimality of Capped Dual Index Policies and Smoothing

We provide closed-form solutions to a robust optimization model for inventory management with two supply sources or modes with general lead times. The fast source is more expensive than the slow source. While the optimal stochastic policy for non-consecutive lead times has been unknown for over 50 years, we prove that the optimal robust policy is a dual index, dual base-stock policy that constrains or ``caps'' the slow order. Optimality is established in a rolling horizon model that can accommodate non-stationary demand. As the lead time difference grows, the capped dual index policy increasingly smoothes slow orders and, for stationary demand, converges to the tailored base surge policy, which places a constant slow order and has been shown to be asymptotically optimal. In an extensive simulation study, the capped dual index policy performs as well as, and can even outperform, the best heuristics presented in the stochastic inventory literature.