Optimal Timing of Switches between Product Sales for Sports and Entertainment Tickets Matthew J. Drake Schools of Business Duquesne University Pittsburgh, PA 15282-0180 drake987@duq.edu Serhan Duran • Paul M. Griffin • Julie L. Swann H. Milton Stewart School of Industrial and Systems Engineering Georgia Institute of Technology Atlanta, GA 30332-0205 sduran@isye.gatech.edu • pgriffin@isye.gatech.edu • jswann@isye.gatech.edu Under second review at Naval Research Logistics June 2007 Like airlines and hotels, sports teams and entertainment venues can benefit from revenue man- agement efforts for their ticket sales. Teams and entertainment venues usually offer bundles of tickets early in their selling horizon and put single-event tickets on sale at a later date. All of these organizations must determine the best time to offer individual tickets because both types of ticket sales consume the same fixed inventory. We model the seller’s optimal a priori timing decision for switching product offerings from selling bundles to individual tickets in order to maximize revenue when bundle and single-ticket customers each arrive according to independent, non-homogeneous Markovian death processes with a linear death rate that can vary over time. We characterize the circumstances in which it is optimal for the seller to practice mixed bundling and when the seller should only sell bundles or individual tickets. We establish comparative statics for the optimal timing decision for the special case of constant customer arrival rates as model parameters such as bundle size, marginal revenues, and customer arrival rates vary. We extend our results to find the optimal time for offering products with different demand characteristics, and we apply the model to a data set obtained from the sports industry. 1 Introduction Revenue management has its origins in the transportation industry, and extensive research in the field has been accomplished in the past two decades. Much of this research has addressed optimal and heuristic pricing or inventory policies for selling a fixed number of airline tickets for a specific flight in order to maximize the expected revenue. Extensions have been developed for products with similar demand characteristics such as hotel reservations and car rentals. A decidedly smaller library of research exists concerning revenue management for non-travel industries. In particular, the market for sports and entertainment event tickets has not received a great deal of attention. 1