The Impact of Linear Optimization on Promotion Planning

65 Pages Posted: 21 Jan 2014 Last revised: 18 Nov 2017

See all articles by Maxime Cohen

Maxime Cohen

McGill University

Ngai-Hang Zachary Leung

City University of Hong Kong

Kiran Panchamgam

Oracle Retail Science

Georgia Perakis

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

Anthony Smith

Oracle RGBU

Date Written: January 20, 2014

Abstract

Sales promotions are important in the fast-moving consumer goods (FMCG) industry due to the significant spending on promotions and the fact that a large proportion of FMCG products are sold on promotion. This paper considers the problem of planning sales promotions for a FMCG product in a grocery retail setting. The category manager has to solve the promotion optimization problem (POP) for each product, i.e., how to select a posted price for each period in a finite horizon so as to maximize the retailer's profit. Through our collaboration with Oracle Retail, we developed an optimization formulation for the POP that can be used by category managers in a grocery environment. Our formulation incorporates business rules that are relevant in practice. We propose general classes of demand functions (including multiplicative and additive) which incorporate the post-promotion dip effect, and can be estimated from sales data. In general, the POP formulation has a nonlinear objective and is NP-hard. We then propose a linear integer programming (IP) approximation of the POP. We show that the IP has an integral feasible region and hence, can be solved efficiently as a linear program (LP). We develop performance guarantees for the profit of the LP solution relative to the optimal profit. Using sales data from a grocery retailer, we first show that our demand models can be estimated with high accuracy and then, demonstrate that using the LP promotion schedule could potentially increase the profit by 3%, with a potential profit increase of 5% if some business constraints were to be relaxed.

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

Suggested Citation

Cohen, Maxime and Leung, Ngai-Hang and Panchamgam, Kiran and Perakis, Georgia and Smith, Anthony, The Impact of Linear Optimization on Promotion Planning (January 20, 2014). Available at SSRN: https://ssrn.com/abstract=2382251 or http://dx.doi.org/10.2139/ssrn.2382251

Maxime Cohen (Contact Author)

McGill University ( email )

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

Ngai-Hang Leung

City University of Hong Kong ( email )

83 Tat Chee Avenue
Kowloon
Hong Kong

Kiran Panchamgam

Oracle Retail Science ( email )

Burlington, MA Massachusetts 01803
United States

Georgia Perakis

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

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

Anthony Smith

Oracle RGBU ( email )

Burlington, MA 01803
United States

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