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

Abstract

We consider a traditional joint pricing and inventory control problem with lead times, which has been extensively studied in the literature but is notoriously difficult to solve due to the complex structure of the optimal policy. In this work, rather than analyzing the optimal policy, we propose a class of so-called constant-order dynamic pricing policies, which are quite different from base-stock heuristics, the primary focus in the existing literature. Under such a policy, a constant-order amount of new inventory is ordered every period and a pricing decision is made based on the on-hand inventory. The policy is independent of the lead time and does not suffer from the curse of dimensionality. We prove that the best constant-order dynamic pricing policy is asymptotically optimal as the lead time grows large, which is exactly the setting in which the problem becomes computationally intractable due to the curse of dimensionality. As a main methodological contribution, we implement the so-called vanishing discount factor approach and establish the convergence to a long-run average random yield inventory model with zero lead time and ordering capacities by its discounted counterpart as the discount factor goes to one, non-trivially extending the previous results in Federgruen and Yang (2014) that analyze a similar model but without capacity constraints.