Capacity and Pricing Management with Demand Learning

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