Asymptotic Optimality of Constant-Order Policies in Joint Pricing and Inventory Models.

This article addresses a classic joint pricing and inventory control problem with lead times, focusing on the development and analysis of constant-order dynamic pricing policies. Unlike traditional base-stock list price policies, the proposed constant-order policies order a fixed inventory amount each period and adjust prices based on inventory levels, independent of lead time. The authors prove that the best constant-order dynamic pricing policy is asymptotically optimal as lead times grow large, a setting where optimal policies are typically computationally intractable due to the curse of dimensionality. Methodologically, the problem is mapped to a random yield inventory model with zero lead time and ordering capacities, and convergence from discounted to long-run average cost criteria is established using a vanishing discount factor approach. Numerical experiments demonstrate that while base-stock policies perform better for small lead times, constant-order policies become increasingly effective and computationally efficient as lead times increase, supporting the theoretical findings.