Optimal Price Promotions Over Time

The paper addresses the problem of determining a retailer's optimal price promotions of two brands in a product category. A dynamic model is constructed, taking into account interbrand substitution effects as well as a promotion's effects on postpromotion demands. For the case of a forward looking retailer, the magnitudes of optimal discounts as well as durations of promotions are identified by using dynamic programming in two partial settings. For the case of a myopic retailer, optimal discounts and their durations can be determined simultaneously in forward time.