An Analysis of “Buy X, Get One Free” Reward Programs

Yan Liu (), Yacheng Sun () and Dan Zhang ()
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Yan Liu: Department of Logistics and Maritime Studies, Faculty of Business, Hong Kong Polytechnic University, Hong Kong 80309
Yacheng Sun: School of Economics and Management, Tsinghua University, Beijing 100086, China
Dan Zhang: Leeds School of Business, University of Colorado at Boulder, Boulder, Colorado 999077

Operations Research, 2021, vol. 69, issue 6, 1823-1841

Abstract: We study the effects of redemption hurdles on reward program members’ decision making and firm profitability. We focus on the popular “Buy X , Get One Free” (BXGO) programs, which set a redemption threshold ( X ) and possibly, an expiration term for the reward. In our model, forward-looking consumers interact with a monopolistic firm and strategically make purchase and redemption decisions over an infinite time horizon. Our analysis leads to the following results. First, a consumer’s purchase utility and purchase probability increase as her reward point inventory approaches the redemption threshold or expiration. These patterns are consistent with the “point pressure” phenomenon documented in the empirical literature. Second, a redemption threshold alone cannot improve the firm’s profit, unless it is coupled with a finite expiration term or a positive transaction utility that consumers may derive from reward redemption. Third, setting the optimal redemption threshold requires the program to strike a balance between the effective price paid by consumers and their purchase probabilities. These results have rich managerial implications for effectively designing reward programs.

Keywords: customer reward program; redemption threshold; finite expiration term; purchase acceleration; forward-looking consumer; dynamic programming; transaction utility (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:69:y:2021:i:6:p:1823-1841

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