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

This article investigates the optimal integrated inventory and pricing decisions for substitutable products over a finite planning horizon with full backlogging and nonstationary costs and demands, aiming to maximize total expected discounted profit. It introduces a unified demand model encompassing common models such as linear and multinomial logit (MNL) models, and demonstrates that by transforming prices into market shares, the dynamic optimization problem becomes jointly concave in inventory and market-share vectors. The study characterizes the optimal policy structure, highlighting the critical role of overstocked products—those with inventory exceeding base-stock levels—and develops exact algorithms (branching and pooling) to compute optimal decisions, with sufficient conditions identified for computational simplification. To address computational challenges in multiperiod settings, two heuristic policies are proposed: a myopic policy optimal under certain demand conditions, and an asymptotic policy based on piecewise-linear upper bounds of the value function, which better accounts for future overstocking risks. Numerical experiments reveal that the asymptotic policy significantly outperforms the myopic policy in dynamic markets with declining or fluctuating demand, underscoring the managerial importance of overstock-adjusted inventory and pricing strategies for substitutable products.