Technical Note: Assortment Optimization with Small Consideration Sets

30 Pages Posted: 4 Aug 2017

See all articles by Jacob Feldman

Jacob Feldman

Washington University in St. Louis - John M. Olin Business School

Alice Paul

Cornell University - School of Operations Research and Industrial Engineering; Olin College of Engineering; Brown University, Data Science Initiative

Huseyin Topaloglu

Cornell University - School of Operations Research and Industrial Engineering

Date Written: July 26, 2017

Abstract

We study a customer choice model that captures purchasing behavior when there is a limit on the number of times that a customer will substitute among the offered products. Under this model, we assume each customer is characterized by a ranked preference list of products and, upon arrival, will purchase the highest ranking offered product. Since we restrict ourselves to settings in which customers consider a limited number of products, we assume that these rankings contain at most k products. We call this model the k-product nonparametric choice model. We focus on the assortment optimization problem under this choice model. In this problem, the retailer wants to find the revenue maximizing set of products to offer when the buying process of each customer is governed by the k-product nonparametric choice model. First, we show that the assortment problem is strongly NP-hard even for k = 2. Motivated by this result, we develop a linear programming-based randomized rounding algorithm that gives the best known approximation guarantee. We tighten the approximation guarantee further when each preference list contains at most two products and consider the case where there is a limit on the number of products that can be offered to the customers.

Keywords: Customer Choice Models, Assortment Optimization, Approximation Algorithms

Suggested Citation

Feldman, Jacob and Paul, Alice and Paul, Alice and Topaloglu, Huseyin, Technical Note: Assortment Optimization with Small Consideration Sets (July 26, 2017). Available at SSRN: https://ssrn.com/abstract=3013357 or http://dx.doi.org/10.2139/ssrn.3013357

Jacob Feldman (Contact Author)

Washington University in St. Louis - John M. Olin Business School ( email )

One Brookings Drive
Campus Box 1133
St. Louis, MO 63130-4899
United States

Alice Paul

Cornell University - School of Operations Research and Industrial Engineering ( email )

Ithaca, NY
United States

Olin College of Engineering ( email )

Olin Way
Needham, MA 02492-1200
United States

Brown University, Data Science Initiative ( email )

Box 1860
Providence, RI 02912
United States

Huseyin Topaloglu

Cornell University - School of Operations Research and Industrial Engineering ( email )

Ithaca, NY
United States

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