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Title: An analysis of “Buy X, Get One Free” reward programs
Authors: Liu, Y 
Sun, Y
Zhang, D
Issue Date: Nov-2021
Source: Operations research, Nov.-Dec. 2021 , v. 69, no. 6, p. 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
Publisher: Institute for Operations Research and the Management Sciences
Journal: Operations research 
ISSN: 0030-364x
EISSN: 1526-5463
DOI: 10.1287/opre.2021.2128
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