Optimal Dual Sourcing Strategy with Capacity Constraint and Fixed Bilateral Adjustment Costs

This paper studies a finite horizon, single product, periodic review inventory system with two supply nodes. Supply nodes are differentiated by their fixed and variable costs, delivery lead times, as well as constraints on the order sizes. The buyer faces interesting tradeoffs: Procuring from one of the supplier, referred to “onshore supplier”, involves a high variable cost but a shorter delivery delay, while procuring from the other supplier, “offshore supplier”, involves a low variable cost but a longer delivery delay. Each order from both suppliers incurs a fixed cost as well as a constraint on the maximum order size. Excess inventories could be salvaged at the end of each period with a fixed cost or be carried over to the next period. We show that the cost-to-go function satisfies a certain convexity, called (CK1,K2)convexity introduced in this paper. We also show that the (CK1,K2)-convexity is preserved in certain types of optimizations and derive structural results for solutions of these optimizations involving (CK1,K2)-convex functions. Based on these structural results, we partially characterize the optimal sourcing and salvaging decisions.