Optimizing Promotions for Multiple Items in Supermarkets

Abstract

Promotion planning is an important problem for supermarket retailers who need to decide the price promotions for thousands of items. One of the key reasons retailers use promotions is to increase sales and profits by exploiting relations among the different items. We formulate the promotion optimization problem for multiple items as a nonlinear Integer Program (IP). Our formulation captures several business requirements, as well as important economic factors such as the post-promotion dip effect (due to the stockpiling behavior of consumers) and cross-item effects (substitution and complementarity). Our demand models are estimated from data and are typically nonlinear, hence rendering the exact formulation intractable. In this chapter, we discuss a class of IP approximations that can be applied to any demand function. We then show that for demand models with additive cross-item effects, it is enough to account for unilateral and pairwise deviations, leading to an efficient method. In addition, when the products are substitutable and the price ladder is of size two, we show that the unconstrained problem can be solved efficiently by a linear program. This result is unexpected as the feasible region of the formulation is not totally unimodular. Next, we derive a parametric worst-case guarantee on the accuracy of the approximation relative to the optimal solution. Finally, we test our model on realistic real-world instances and show its performance and practicality. The model and tool presented in this chapter allow retailers to solve large realistic instances and to improve their promotion decisions.