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Models of the Spiral-Down Effect in Revenue Management

Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota 55455
Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208
School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0205
billcoop{at}me.umn.edu
tito{at}northwestern.edu
anton{at}isye.gatech.edu

The spiral-down effect occurs when incorrect assumptions about customer behavior cause high-fare ticket sales, protection levels, and revenues to systematically decrease over time. If an airline decides how many seats to protect for sale at a high fare based on past high-fare sales, while neglecting to account for the fact that availability of low-fare tickets will reduce high-fare sales, then high-fare sales will decrease, resulting in lower future estimates of high-fare demand. This subsequently yields lower protection levels for high-fare tickets, greater availability of low-fare tickets, and even lower high-fare ticket sales. The pattern continues, resulting in a so-called spiral down. We develop a mathematical framework to analyze the process by which airlines forecast demand and optimize booking controls over a sequence of flights. Within the framework, we give conditions under which spiral down occurs.

Subject classifications: pricing: revenue management; forecasting: estimation and control; probability: applications.
History: Received January 2004; revision received December 2004; accepted August 2005.

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