Dynamic Pricing and Inventory Control of Substitutable Products in a Nonstationary Environment

Abstract

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. 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 a numerical study to gain insights. Our policy and algorithms empower businesses to formulate prescriptive analytics for multi-product dynamic pricing and inventory decisions in a nonstationary setting. We demonstrate how to strategically determine pricing and replenishment decisions for substitutable products according to their inventory status. This approach can substantially elevate profits, especially when confronting high overstock levels in a volatile environment.

Keywords: Inventory, Dynamic Pricing, Substitution, Consumer Choice, Market Share, Optimal Policy, Nonstationary