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

Abstract

Problem definition: How to dynamically replenish inventory from two supply sources or shipping modes with general lead times. The fast source is more expensive than the slow source. Academic/practical relevance: Dual sourcing provides supply chain flexibility to mitigate demand and supply risk. Despite its relevance in practice, characterizing the optimal dual sourcing policy is extremely challenging, and the optimal stochastic policy for nonconsecutive lead times has been unknown for over 50 years. Methodology: We present and solve a robust rolling horizon model for periodically reviewed dual sourcing inventory systems that minimizes the total cost of purchasing, inventory holding, and backlogging. Results: We prove that the optimal robust policy is a dual-index, dual-base-stock policy that constrains or “caps” the slow order and provide closed-form expressions for the three control parameters. The optimality result is established for general lead times and can accommodate nonstationary demand. Our numerical study shows that, as the lead time difference grows, the capped dual index policy increasingly smooths 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. Managerial implications: Our capped dual index policy is easy to understand, explain, and implement in practice. 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.