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

28 Pages Posted: 9 May 2019 Last revised: 26 Aug 2022

See all articles by Xin Chen

Xin Chen

Georgia Institute of Technology Atlanta, USA

Alexander Stolyar

University of Illinois at Urbana-Champaign

Linwei Xin

University of Chicago - Booth School of Business

Date Written: August 25, 2022

Abstract

We consider a classical 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 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 due to 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, non-trivially extending the previous results in Federgruen and Yang (2014) that analyze a similar model but without capacity constraints.

Keywords: joint pricing and inventory control, lead time, asymptotic optimality, constant-order policy, random yield, vanishing discount factor approach

Suggested Citation

Chen, Xin and Stolyar, Alexander and Xin, Linwei, Asymptotic Optimality of Constant-Order Policies in Joint Pricing and Inventory Control Models (August 25, 2022). Available at SSRN: https://ssrn.com/abstract=3375203 or http://dx.doi.org/10.2139/ssrn.3375203

Xin Chen

Georgia Institute of Technology Atlanta, USA ( email )

Alexander Stolyar

University of Illinois at Urbana-Champaign

ISE Department and Coordinated Science Lab
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Linwei Xin (Contact Author)

University of Chicago - Booth School of Business ( email )

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