The Optimality of Profit Sharing in Loyalty Reward Programs

Abstract

This paper concerned with finding the optimal allocation of profit arrangement under profit-sharing plans in loyalty rewards programs (LRP). Previous studies did not consider the customer’s purchase experience as a factor in their decision to buy and customers are not taken into account in profit-sharing plans. We show how optimal profit sharing can be computed when the objective function of profit maximizing is specified for the loyalty reward program by using stochastic dynamic programming. We consider a firm selling goods or services through two periods and we treat customers’ valuation as a random variable by considering their post-purchase satisfaction level on loyalty program. We solve the optimization problem analytically and the obtained solution provides some useful information on the effects of customers’ satisfaction with the loyalty program.