Optimizing Promotions for Multiple Items in Supermarkets

36 Pages Posted: 31 Oct 2017 Last revised: 19 Nov 2017

See all articles by Maxime Cohen

Maxime Cohen

New York University (NYU) - Leonard N. Stern School of Business

Jeremy Kalas

Massachusetts Institute of Technology (MIT)

Georgia Perakis

Massachusetts Institute of Technology (MIT) - Sloan School of Management

Date Written: October 29, 2017

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 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

Suggested Citation

Cohen, Maxime and Kalas, Jeremy and Perakis, Georgia, Optimizing Promotions for Multiple Items in Supermarkets (October 29, 2017). Available at SSRN: https://ssrn.com/abstract=3061451 or http://dx.doi.org/10.2139/ssrn.3061451

Maxime Cohen (Contact Author)

New York University (NYU) - Leonard N. Stern School of Business ( email )

44 West 4th Street
Suite 9-160
New York, NY NY 10012
United States

Jeremy Kalas

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Georgia Perakis

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

100 Main Street
E62-565
Cambridge, MA 02142
United States

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