A stochastic model on the profitability of loyalty programs

Effectiveness of customers’ loyalty programs has been the focal point of some recent studies. While empirical research shows mixed findings, analytical studies on the efficacy of loyalty programs are in their early stages. In this paper, we develop an analytical model on the profitability of loyalty programs in which customers’ valuations along with their satisfaction levels are incorporated as stochastic variables. The model consists of a revenue-maximizing firm selling a product through two periods. A loyalty reward is offered to two-period buyers in the form of an absolute-value discount on the price in the second period. The satisfaction level is represented by the difference between a customer’s original and post-purchase valuation. The formulation yields a stochastic programming problem with a nonlinear non-convex objective function. The problem is solved in terms of the model parameters. The results reveal that depending on the mean and variance of the satisfaction levels, the firm may be better off not to offer a loyalty reward. Specifically, if the mean of satisfaction levels turns out to be positive with a coefficient of variation less than a certain threshold, not adopting the loyalty program is optimal.

► In this paper, an analytical model is developed on the profitability of loyalty programs.
► Customers’ valuation and their satisfaction level are incorporated in the model as norally distributed random variables.
► The resulting stochastic programming model is solved and optimal solution is found in terms of the model parameter.
► The solution reveals some certain conditions under which not adopting the loyalty program is optimal.