Correspondence: Moutaz Khouja, Business Information Systems and Operations Management Department, The Belk College of Business Administration, The University of North Carolina — Charlotte, Charlotte, NC 28223, USA. Tel: +1 704 687 3242; Fax: +1 704 687 6330; E-mail: mjkhouja@email.uncc.edu

¹Moutaz Khouja received a BS in Mechanical Engineering, an MBA from the University of Toledo and a PhD in Operations Management from Kent State University. Currently, he is a Professor of Operations Management in the Belk College of Business Administration at the University of North Carolina at Charlotte. His research interests are in the areas of inventory management, production planning and control, pricing and forecasting. His publications have appeared in many leading journals including Computers and Operations Research, Decision Sciences, IIE Transactions, European Journal of Operational Research, International Journal of Production Research, International Journal of Production Economics, Journal of the Operational Research Society, and Omega.

²Stephanie S. Robbins received a PhD in Management from Louisiana State University. She is currently a Professor of MIS/OM at The University of North Carolina at Charlotte. Dr Robbins does research in the areas of management information systems, marketing management and strategy development for non-profit organisations. Her publications have appeared in journals such as International Journal of Electronic Commerce, European Journal of Operations Research, International Journal of Production Economics, Information and Management, The Journal of Computer Information Systems, Behavioral Science and the Journal of the Academy of Marketing Science. She has also presented numerous papers at international, national and regional professional meetings.

³Hari K. Rajagopalan earned his PhD in Information Technology from the University of North Carolina at Charlotte in 2006. Apart from his PhD, he also has an MBA in Finance and an MS in Computer Science. His research interests include locating emergency response systems, pricing of digital products and obsolescence in the high-technology industry. His research has published in the European Journal of Operational Research, Computers and Operations Research and other journals. He is also an active participant at INFORMS, Decision Sciences, and European Working Group in Transportation Meeting and Mini EURO Conferences. He is currently the Assistant Professor in Management at Francis Marion University.

Received 10 July 2007; Revised 10 July 2007.

Abstract

Delayed incentives in the form of cash mail-in rebates have become very popular. We develop and solve a model for jointly determining optimal price and rebate value for a heterogeneous consumer market. Consumers are divided into three segments: rebate independent, fully rebate dependent, and partially rebate dependent. Partially rebate-dependent consumers' redemption probability depends on the value of the rebate relative to a reference value. Data show that the probability of redemption increases linearly in rebate value for small rebate values and at a decreasing rate as the rebate value becomes large. The model shows that two consumer attributes are critical in determining the effectiveness of rebates. The first is the reference value. The larger the reference value, the larger the optimal rebate value and the higher the profit. The second is the distribution of consumers among the three segments. Profit decreases as the proportion of consumers in the probabilistic redeemers segment decreases. There is, however, a threshold value where profit increases as the proportion of consumers in the partially rebate-dependent segment decreases. This occurs because as the rebate-independent and fully rebate-dependent consumers are priced out of the market, a seller can increase both price and rebate value substantially without having to be burdened by the heavy cost of rebates for the fully rebate-dependent segment. If the reference value for the partially rebate-dependent segment is high, such a strategy may prove profitable.