Optimizing Promotions for Multiple Items in Supermarkets
36 Pages Posted: 31 Oct 2017 Last revised: 19 Nov 2017
Date Written: October 29, 2017
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 that retailers use promotions is to increase the sales/profits of their different items by exploiting the relations among those items. We formulate the promotion optimization problem for multiple items as a non-linear 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 usually nonlinear, hence rendering the exact formulation intractable. In this paper, we propose 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. Interestingly, this technique can be applied to more general nonlinear binary IP problems beyond the context of retail promotions. In addition, when the items 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 paper allow retailers to solve large realistic instances, and improve their promotion decisions.
Keywords: Promotion Optimization, Dynamic Pricing, Integer Programming, Retail Operations
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