EXPRESS: Multi-Sourcing Procurement Management: A Closed-Form Mean-Variance Approach

In the post-pandemic era, multi-sourcing is rapidly becoming the preferred approach for companies to drive optimized cost, quality and turnaround times. However, multi-sourcing systems present a myriad of challenges in designing an effective planning model. In this paper, we propose a robust capacity planning model with multiple supply sources, and demonstrate how the capacity plan can be efficiently solved via a parsimonious mean-variance approach. We apply the max-min criterion to design a distributionally robust multi-source capacity plan. We use a new approach to deriving a set of optimality conditions on the robust capacity plan. These conditions enable us to derive the worst distribution, the optimal robust capacity vector, and the worst-case expected profit in closed form. The new approach bypasses numerous tedious intermediate procedures in the traditional distributionally robust optimization literature and allows us to derive the optimal solution based on exogenous cost parameters. This closed-form solution appears to be hitherto unknown and has important ramifications for the multi-sourcing capacity planning problem. Our findings reveal that, despite the complexity of multi-sourcing, the worst-case demand scenario can be reduced to just n + 1 distinct outcomes, structured by two key sequences derived from supplier characteristics. The optimal capacity plan has a clear structure–allocations align with the midpoints between these demand scenarios. Surprisingly, we also find that most of the robustness benefits of a full supplier portfolio can be achieved by engaging just the two best-matched sources. This provides a practical and cost-effective road map for robust capacity planning in multi-sourcing environments.