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

Abstract

We consider a classic joint pricing and inventory control problem with lead times, which is extensively studied in the literature but is notoriously difficult to solve because of the complex structure of the optimal policy. In this work, rather than analyzing the optimal policy, we propose a class of constant-order dynamic pricing policies, which are fundamentally different from base-stock list price policies, the primary emphasis 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 inventory level. The policy is independent of the lead time. 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 because of the curse of dimensionality. As our main methodological contributions, we 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, nontrivially extending the previous results in Federgruen and Yang that analyze a similar model but without capacity constraints. Funding: Research of X. Chen and L. Xin was partly supported by the National Science Foundation [Grant CMMI-1635160].