An Analysis of "Buy X, Get One Free" Reward Programs. Operations Research.
Liu, Yan; Sun, Yacheng; Zhang, Dan. An Analysis of "Buy X, Get One Free" Reward Programs. Operations Research. Nov/Dec2021, Vol. 69 Issue 6, p1823-1841.
Redemption hurdles, such as finite expiration terms and redemption thresholds, are common for customer reward programs. In "An Analysis of 'Buy X, Get One Free' Reward Programs," Yan Liu, Yacheng Sun, and Dan Zhang study the economic rationale behind redemption hurdles and how they should be optimally set. They show analytically that redemption hurdles can be used as a price-discriminating vehicle that increases firm profitability. Redemption hurdles can facilitate the firm's price discrimination on consumers whose valuations may vary over time. Redemption threshold alone cannot ensure profitability, unless it is coupled with a finite expiration term or a positive transaction utility from the rewarded free product. Optimal design of redemption hurdles is not straightforward, and the interdependence between the two types of redemption hurdles and the price is nontrivial. Optimally set redemption hurdles may not only increase firm profitability but also, increase the welfare of consumers who purchase frequently. 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.