Capacity and Pricing Management with Demand Learning

48 Pages Posted: 19 Apr 2023 Last revised: 1 Dec 2023

See all articles by Jian Chen

Jian Chen

Tsinghua University - School of Economics and Management

Zechao Li

Tsinghua University - Tsinghua University School of Economics and Management

Anyan Qi

University of Texas at Dallas - Naveen Jindal School of Management

Yining Wang

University of Texas at Dallas

Date Written: November 26, 2023

Abstract

In an environment where demand is unknown to the firm, it is important to investigate how capacity adjustment and dynamic pricing can be integrated so that the firm can learn about the demand on the fly while making capacity and pricing decisions. In this paper, we design learning algorithms for the joint capacity and pricing management problem. To evaluate the performance of our algorithms, we consider a large-demand asymptotic regime where the demand and capacity are scaled up with the selling horizon T. We first establish an $\Omega(T^{3/5})$ lower bound on the regret under any admissible policy. We then propose a novel double-trisection algorithm that utilizes pricing decisions to collect demand information and tune capacity rate levels safely, attaining a $\tilde O(T^{3/5})$ regret upper bound that matches the lower bound. We also modify our algorithm to address the issue when the number of capacity adjustment opportunities K is limited and find that only a few opportunities to adjust capacity levels, i.e., $K\gtrsim \ln\ln T$, are sufficient to achieve the optimal regret rate. We finally conduct numerical experiments on a testing bed inspired by public operational and financial data.

Keywords: regret minimization, capacity investment, dynamic pricing, nonparametric learning

JEL Classification: D42

Suggested Citation

Chen, Jian and Li, Zechao and Qi, Anyan and Wang, Yining, Capacity and Pricing Management with Demand Learning (November 26, 2023). Available at SSRN: https://ssrn.com/abstract=4414361 or http://dx.doi.org/10.2139/ssrn.4414361

Jian Chen

Tsinghua University - School of Economics and Management ( email )

Beijing, 100084
China

Zechao Li

Tsinghua University - Tsinghua University School of Economics and Management

Beijing
China

Anyan Qi (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

P.O. Box 830688
Richardson, TX 75083-0688
United States

Yining Wang

University of Texas at Dallas ( email )

2601 North Floyd Road
Richardson, TX 75083
United States

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