Maxime Cohen

 

Faculty Speaker Maxime Cohen [MIT Sloan School of Management]
Title The Impact of Linear Optimization on Promotion Planning
Date & Time Thursday, February 19, 2015 at 10:00am
Place UCLA Anderson School of Management 
Room D-307

 

Abstract
In many important settings, promotions are a key instrument for driving sales and profits. Examples include promotions in supermarkets among others. The Promotion Optimization Problem (POP) is a challenging problem as the retailer needs to decide which products to promote, what is the depth of price discounts and finally, when to schedule the promotions. We introduce and study an optimization formulation that captures several important business requirements as constraints. We propose two general classes of demand functions depending on whether past prices have a multiplicative or an additive effect on current demand. These functions capture the promotion fatigue effect emerging from the stock-piling behavior of consumers and can be easily estimated from data. The objective is nonlinear (neither convex nor concave) and the feasible region has linear constraints with integer variables. Since the exact formulation is \hard", we propose a linear approximation that allows us to solve the problem efficiently as a linear program (LP) by showing the integrality of the integer program (IP) formulation. We develop analytical results on the accuracy of the approximation relative to the optimal (but intractable) POP solution by showing guarantees relative to the optimal profits. In addition, we show computationally that the formulation solves fast in practice using actual data from a grocery retailer and that the accuracy is high. Together with our industry collaborators from Oracle Retail, our framework allows us to develop a tool which can help supermarket managers to better understand promotions by testing various strategies and business constraints. Finally, we calibrate our models using actual data and determine that they can improve profits by 3% just by optimizing the promotion schedule and up to 5% by slightly modifying some business requirements.

Maxime Cohen