Yan Liu, Yacheng Sun, and Dan Zhang. 2021. An Analysis of "Buy X, Get One Free" Reward Programs. Operations Research, 69(6): 1823-1841.
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.
A Harvard Business Review article summarizing the findings of this paper and Sun and Zhang (2019) can be found here.