Management Science Research Centre Seminar

The Desautels Faculty of Management
Management Science Research Centre

presents
Professor Sridhar Seshadri
University of Texas

Friday, December 4th, 2009
12:00 PM – 2:00 PM
Bronfman Bldg., Rm. 204

All are cordially invited to attend.

Abstract:

Fixed Versus Random Proportion Demand Models for Retail Assortment Planning

We consider the problem of determining the optimal assortment of products to offer in a given product category when customers have heterogeneous tastes.  We assume that customers arrive sequentially over one period and choose from the set of products remaining in inventory at the time of their visit. This is called dynamic substitution.  It is conventional to assume that the type of customer is a random variable that is determined upon arrival. This is called the random proportion demand model. This problem has been shown to be very hard to solve and no efficient method to obtain the optimal solution is known to our knowledge. However, if the number of customers of each type is a fixed proportion of demand we show that there is an efficient algorithm for solving for the optimal assortment. Additionally, we show that by assuming that there are a fixed proportion of customers of each type we obtain an upper bound to the expected profit.  Numerical results suggest that the bound is tight. This bound may be used to compare the performance of many heuristics that have been suggested by various authors to solve the assortment planning problem with dynamic substitution. We also provide a bound for the component wise absolute difference in expected sales between the fixed proportion approximation and the original model, which provides the lower bound to the expected profit.