The Approximability of Assortment Optimization Under Ranking Preferences

20 Pages Posted: 3 Jun 2015 Last revised: 2 Feb 2018

See all articles by Ali Aouad

Ali Aouad

London Business School

Vivek F. Farias

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

Retsef Levi

MIT Sloan School of Management - Operations Research Center

Danny Segev

Tel Aviv University - School of Mathematical Sciences

Date Written: June 1, 2015

Abstract

The main contribution of this paper is to provide best-possible approximability bounds for assortment planning under a general choice model, where customer choices are modeled through an arbitrary distribution over ranked lists of their preferred products, subsuming most random utility choice models of interest. From a technical perspective, we show how to relate this optimization problem to the computational task of detecting large independent sets in graphs, allowing us to argue that general ranking preferences are extremely hard to approximate with respect to various problem parameters. These findings are complemented by a number of approximation algorithms that attain essentially best-possible factors, proving that our hardness results are tight up to lower-order terms. Surprisingly, our results imply that a simple and widely studied policy, known as revenue-ordered assortments, achieves the best possible performance guarantee with respect to the price parameters.

Keywords: Assortment optimization, choice models, hardness of approximation, independent set, approximation algorithms

Suggested Citation

Aouad, Ali and Farias, Vivek F. and Levi, Retsef and Segev, Danny, The Approximability of Assortment Optimization Under Ranking Preferences (June 1, 2015). Available at SSRN: https://ssrn.com/abstract=2612947 or http://dx.doi.org/10.2139/ssrn.2612947

Ali Aouad

London Business School ( email )

Sussex Place
Regent's Park
London, London NW1 4SA
United Kingdom

Vivek F. Farias

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

100 Main Street
E62-416
Cambridge, MA 02142
United States

Retsef Levi

MIT Sloan School of Management - Operations Research Center ( email )

100 Main Street
E62-416
Cambridge, MA 02142
United States

Danny Segev (Contact Author)

Tel Aviv University - School of Mathematical Sciences ( email )

Tel Aviv 69978
Israel

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