Dynamic Pricing Without Knowing the Demand Function: Risk Bounds and Near-Optimal Algorithms

Operations Research, Vol. 57, No. 6, pp. 1407-1420, November-December 2009

Columbia Business School Research Paper

14 Pages Posted: 19 Oct 2011

See all articles by Omar Besbes

Omar Besbes

Columbia Business School - Decision Risk and Operations

Assaf Zeevi

Columbia Business School - Decision Risk and Operations

Date Written: 2009

Abstract

We consider a single product revenue management problem where, given an initial inventory, the objective is to dynamically adjust prices over a finite sales horizon to maximize expected revenues. Realized demand is observed over time, but the underlying functional relationship between price and mean demand rate that governs these observations (otherwise known as the demand function or demand curve), is not known. We consider two instances of this problem: i.) a setting where the demand function is assumed to belong to a known parametric family with unknown parameter values; and ii.) a setting where the demand function is assumed to belong to a broad class of functions that need not admit any parametric representation. In each case we develop policies that learn the demand function "on the fly," and optimize prices based on that. The performance of these algorithms is measured in terms of the regret: the revenue loss relative to the maximal revenues that can be extracted when the demand function is known prior to the start of the selling season. We derive lower bounds on the regret that hold for any admissible pricing policy, and then show that our proposed algorithms achieve a regret that is "close" to this lower bound. The magnitude of the regret can be interpreted as the economic value of prior knowledge on the demand function; manifested as the revenue loss due to model uncertainty.

Suggested Citation

Besbes, Omar and Zeevi, Assaf, Dynamic Pricing Without Knowing the Demand Function: Risk Bounds and Near-Optimal Algorithms (2009). Operations Research, Vol. 57, No. 6, pp. 1407-1420, November-December 2009; Columbia Business School Research Paper. Available at SSRN: https://ssrn.com/abstract=1946390

Omar Besbes (Contact Author)

Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

Assaf Zeevi

Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States
212-854-9678 (Phone)
212-316-9180 (Fax)

HOME PAGE: http://www.gsb.columbia.edu/faculty/azeevi/

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