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

• Recent technological advances in media, data, and methods have created a unique opportunity for marketers to better control to whom, when, and how much to discount.
• To determine the optimal value and timing of the discount we model individual household purchase incidence and brand choice in response to the value and timing of a discount.
• To select the customers who receive the discount we formulate a constrained multiple-knapsack model which picks the most valuable customers for a given marketing budget.
• We illustrate the model using a Japanese dataset for customized temporal price-cut, a US dataset for customized temporal coupon and another US dataset for 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.

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