Distributionally robust joint inventory and pricing control across products

Abstract

We study a single-period, two-item joint inventory and pricing control problem under demand uncertainty, where only the means and variances of product demands are known. The model incorporates cross-price effects, meaning that the demand for each product is influenced by the prices of both products. To address this, we develop a distributionally robust optimization framework that determines ordering and pricing decisions to maximize the worst-case expected profit over all demand distributions consistent with the known moments. Under certain conditions, we derive closed-form optimal solutions. Theoretical analysis reveals that the economic relationships between products may differ from the perspectives of retailers and customers. We also extend the model to capture additional practical considerations such as customer behavior and supply unreliability. To evaluate the proposed approach, we conduct numerical experiments that demonstrate the closeness of our closed-form solutions to the optimal policies under the true distribution in cases with mild variances, as well as to the results derived from deterministic demand and the Sample Average Approximation method. Furthermore, we analyze the impact of distributional misspecification and find that our DRO-based solutions are more robust. Sensitivity analysis further shows that while variance has a moderate impact on expected profit, increasing variance leads to a greater discrepancy between the worst-case and true expected profit.