Simple Monotonic Readjustment Policies with Applications to Markdown Pricing and Pricing in the Presence of Strategic Customers

We consider a canonical revenue management problem wherein a monopolist seller seeks to maximize expected total revenues from selling a fixed inventory of a product to customers who arrive sequentially over time, and the seller is restricted to implement a pricing policy that is monotonic (either nonincreasing or nondecreasing) over time. Gallego and Van Ryzin [Gallego G, Van Ryzin G (1994) Optimal dynamic pricing of inventories with stochastic demand over finite horizons. Management Sci. 40(8):999–1020] show that the simplest monotonic price policy, the fixed price policy, is asymptotically optimal in the high-volume regime in which both the seller’s initial inventory and the length of the selling horizon are proportionally scaled. Specifically, the revenue loss of the fixed price policy is $O(k^{1/2})$, where k is the system’s scaling parameter. Following the publication of Gallego and Van Ryzin [Gallego G, Van Ryzin G (1994) Optimal dynamic pricing of inventories with stochastic demand over finite horizons. Management Sci. 40(8):999–1020], several papers have attempted to improve the performance of the fixed price policy. Among them, Jasin [Jasin S (2014) Reoptimization and self-adjusting price control for network revenue management. Oper. Res. 62(5):1168–1178] develops a simple modification of the fixed price policy (that allows prices to move either up or down) with a guaranteed revenue loss of order $O(\ln k)$. In this paper, we propose a novel family of monotonic readjustment policy, which restricts the prices to only move in one direction (i.e., either up or down). We show that, if the seller updates the price for only a single time, then the revenue loss of our policy is $O(k^{1/3}{(\ln k)}^{2\alpha })$ for some $\alpha >1/2$. If, however, the seller updates the prices with a frequency $O(\ln k/\ln \ln k)$, then the revenue loss of our policy is $O({(\ln k)}^{7\alpha })$ for some $\alpha >1/2$. These results show the power of dynamic pricing even in the presence of monotonic price restriction. We discuss two applications of our policy: markdown pricing and pricing in the presence of strategic customers.

Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2020.0774.