Distributionally Robust Multilocation Newsvendor at Scale: A Scenario-Based Linear Programming Approach

Problem definition: How should retailers and sellers distribute inventory across a large network of (potentially hundreds of) distribution centers? Motivated by the emerging challenges of inventory allocation in a volatile market, we study the distributionally robust multilocation newsvendor problem with a scenario-based approach. Methodology/results: We consider a scenario-wise ambiguity set that is adaptable to feature information. By exploiting the supermodularity property of the multilocation newsvendor problem, we obtain a scalable linear programming formulation. We characterize the optimal inventory decision for a symmetric two-location problem under single-scenario and two-scenario ambiguity sets. Our analysis shows how the optimal safety stock level varies according to the scenario information and network structure. We demonstrate the promising out-of-sample performance of our approach via a real-world case study using data from a logistics service provider. Managerial implications: By comparing the two-scenario solution to the one-scenario solution, we illustrate the value of scenario-wise ambiguity set in delineating useful distributional information for the newsvendor problem. The numerical results suggest our approach is robust against distributional demand shifts and provides a competitive solution against other data-driven methods.