Dynamic Pricing and Inventory Control for Substitutable Products Based on Market Conditions

Problem definition: We study optimal integrated inventory and pricing decisions for substitutable products over a finite planning horizon with full backlogging and nonstationary costs and demands. The objective is to maximize the total expected discounted profit. Methodology/results: We present a unified demand model that encompasses many commonly used models in the literature. We show that the dynamic optimization problem is jointly concave in inventory and market-share vectors. This enables us to characterize the optimal integrated policy and develop exact algorithms to compute it. In each period, the optimal policy first pinpoints products that are overstocked and thus require no replenishment. It then specifies the optimal base-stock levels for the understocked products and the optimal market shares (and prices) for all products, contingent on the overstock levels. We also establish conditions under which the optimal base-stock levels decrease in the overstock levels, hence significantly simplifying computation. Additionally, we devise several computationally efficient heuristic policies aligned with the optimal policy structure and conduct numerical studies to gain insights. Managerial implications: Our study reveals the importance of accounting for overstocking risks for substitutable products in dynamic markets. Implementing an overstock-adjusted inventory and pricing strategy is particularly crucial during declining demand or when costs and demand fluctuate. The heuristic policies inspired by our optimal policy provide efficient and interpretable methods for quantifying critical trade-offs between inventory and pricing among substitutable products. Funding: X. Shen acknowledges financial support from the National Science Foundation of China [Grants 72222015, 72171215, and 72571260]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0227 .