Relating the Approximability of the Fixed Cost and Space Constrained Assortment Problems

29 Pages Posted: 6 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

Date Written: August 3, 2017

Abstract

Customer choice models are a fundamental tool used by retailers to optimize inventory, pricing, and stocking decisions. One important optimization problem is the assortment problem in which the retailer wants to determine which products to offer to customers to maximize expected revenue. This paper relates two variants of this assortment problem: the space constrained assortment problem, in which the retailer has a limit on the total space of the offered assortment, and the fixed cost assortment problem, in which the retailer incurs a fixed cost for each offered product. In particular, we develop an approximation scheme for the space constrained problem for any random utility choice model that only relies on the ability to solve the corresponding fixed cost assortment problem. We then apply this technique to give the first constant factor approximation scheme for the space constrained assortment problem under a general choice model for vertically differentiated products. Last, we present computational results to show the efficacy of this approach.

Keywords: Customer Choice Models, Assortment Optimization, Approximation Algorithms

Suggested Citation

Feldman, Jacob and Paul, Alice and Paul, Alice, Relating the Approximability of the Fixed Cost and Space Constrained Assortment Problems (August 3, 2017). Available at SSRN: https://ssrn.com/abstract=3013319 or http://dx.doi.org/10.2139/ssrn.3013319

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

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
93
Abstract Views
448
rank
355,315
PlumX Metrics