Dual Sourcing Made Easy: Distributionally Robust Optimization of Inventory Systems Under Independent Demand

We generalize Scarf’s classical min-max newsvendor model from a single-period setting to a multiperiod inventory system with independent demand across periods. This extension leverages mean–variance analysis to capture the dynamic effects of lead times, yielding closed-form expressions for the optimal base-stock level. As a concrete application, we study a single-product, dual-sourcing system with constant lead times and backlogging. We show that the optimal tailored base–surge policy admits a tractable closed-form approximation, with the base stock explicitly calibrated to account for lead-time effects. This provides a simple, distribution-free rule for trading off inventory cost against service level in a dual-sourcing system. Empirical validation using data from a multinational food manufacturer demonstrates the model’s practical advantages. Applying our method to historical demand and sourcing data improves service levels and reduces stockouts compared with traditional approaches, while maintaining cost-effectiveness. The model’s capacity to adapt base-stock levels to different lead times and demand conditions proved especially valuable in mitigating the impact of supply chain volatility. These findings confirm the theoretical performance of our approach and highlight its potential as a scalable, cost-effective tool for firms facing lead-time demand uncertainty.

Funding: This work was supported in part by the National Natural Science Foundation of China [Grants 72401173, 92567302, 62432003, 72192830, 72192832, 72531005] and the Liaoning Revitalizing Talent Program [Grant XLYC2202045].

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2024.1481.