The impact of peak-end demand models on promotion planning optimization with demand misspecification
Sales promotions provide an important tool in the retail industry and can have a significant impact on a retailer's revenue. Research in the area of promotion planning focuses on two main aspects - prediction and prescription. The prediction part aims at understanding consumers' price sensitivity in order to find how changes in price can affect the demand (current and future). As a result, the goal when investigating the prediction aspect is to provide a functional form of the demand given a set of features. The prescription aspect, on the other hand, concerns with finding the optimal pricing decision subject to business constraints. Depending on the structure of the demand function, the promotion planning optimization problem is either provably NP-hard or can be provably solved in polynomial time. In this research, we study the trade-off between prediction accuracy and optimization complexity.
We introduce a compact set of demand features, which includes the last seen price as well as the minimum price seen within a bounded number of past time periods. We refer to this model as the bounded-memory-peak-end model. Using principles from duality theory, we show that even if the true underlying demand exhibits a different demand structure than the bounded memory peak-end, the suggested bounded-memory-peak-end model can still predict the true demand with provably low prediction error.
Moreover, this demand model allows us to solve the promotion planning optimization problem in polynomial time. In the cases where the demand follows a different model, we still suggest to use the bounded-memory-peak-end and establish what would be the estimation error. We then show how the estimation error translates into a bounded optimality gap on the revenue arising from the optimization aspect of the problem.