Promotion Optimization for Multiple Items in Supermarkets

42 Pages Posted: 31 Oct 2017 Last revised: 5 Mar 2020

See all articles by Maxime Cohen

Maxime Cohen

Desautels Faculty of Management, McGill University

Jeremy Kalas

Massachusetts Institute of Technology (MIT)

Georgia Perakis

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

Date Written: October 29, 2017

Abstract

Promotions are a critical decision for supermarket managers who must decide the price promotions for a large number of items. Retailers often use promotions to boost the sales of the different items by leveraging the cross-item effects. We formulate the promotion optimization problem for multiple items as a non-linear integer program (IP). Our formulation includes several business rules as constraints. Our demand models can be estimated from data and capture the post-promotion dip effect as well as cross-item effects (substitution and complementarity). Since demand functions are typically nonlinear, the exact formulation is intractable. To address this issue, we propose a general class of IP approximations. For demand models with additive cross-item effects, we prove that it is sufficient to account for unilateral and pairwise contributions and derive parametric bounds on the performance of the approximation. We also show that the unconstrained problem can be solved efficiently via a linear program when items are substitutable and the price set has two values. For more general cases, we develop efficient rounding schemes to obtain an integer solution. We conclude by testing our method on realistic instances and convey the potential practical impact for retailers.

Keywords: Promotion Optimization, Dynamic Pricing, Retail Analytics, Integer Programming

Suggested Citation

Cohen, Maxime and Kalas, Jeremy and Perakis, Georgia, Promotion Optimization 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)

Desautels Faculty of Management, McGill University ( email )

1001 Sherbrooke St. W
Montreal, Quebec H3A 1G5
Canada

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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