To Whom, When, and How Much to Discount? A Constrained Optimization of Customized Temporal Discounts

Customized temporal discounts are price cuts or coupons that are tailored by size, timing, and household to maximize profits to a retailer or manufacturer. The authors show how such discounts allow companies to optimize to whom, when, and how much to discount. Such a scheme allows firms to send just enough discounts just prior to the individual's purchase of a rival brand. To do so, the authors model household purchase timing and brand choice in response to discounts and use Bayesian estimation to obtain individual household parameters. They illustrate the model on a Japanese data set having price cuts, a US data set having coupons, and another US data set having discounts. They formulate the optimization task of customized temporal coupons as a constrained multiple-knapsack problem under a given budget. They use simulations of the empirical contexts to obtain optimal solutions and to assess improvement in profits relative to existing practice and alternate models in the literature. The proposed model yields increase in profits of 18-40 percent relative to a standard model that optimizes the value but not timing of discounts.