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 the postpromotion demand for the brands. For the case of a myopic retailer who makes her marketing decisions on a period-by-period basis, optimal discounts and their durations can be determined simultaneously in forward time.

On the other hand, if the retailer is forward looking, the depths of optimal discounts as well as the timing and duration of promotions cannot be identified by such a procedure. As an approximation, we first determine optimal discounts, given that durations already are fixed. Next, we solve the problem of finding the optimal timing and durations of the promotions, given that discounts are fixed. This resembles the use in practice of a promotional menu that specifies regular prices as well as the discounts to be applied if a promotion is decided. If a discount is made, the retailer then decides the duration.

There is no general concensus in empirical marketing literature on what is net impact of a promotion on consumer response over time. The paper focuses on three main effects: (1) The immediate and positive impact of a price deal on the sales of a promoted brand during the promotional period. (2) Brand substitution within the category makes some consumers switch from a nonpromoted brand to a lower priced promoted brand. (3) Consumers stockpile a promoted brand during a deal period, which affects postpromotional demand of the brands in the category. This effect can last for a shorter or longer interval of time.

The main contribution of the paper is the characterization of optimal discounts, and the timing and duration of promotions, of a myopic and a forward looking retailer. We also provide a series of results that identify the dependence of discounts and durations upon key parameters of the model.