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The Approximability of Assortment Optimization Under Ranking Preferences

18 Pages Posted: 3 Jun 2015 Last revised: 25 Oct 2016

Ali Aouad

Massachusetts Institute of Technology (MIT) - Operations Research Center

Vivek F. Farias

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

Retsef Levi

MIT Sloan School of Management - Operations Research Center

Danny Segev

University of Haifa - Department of Statistics

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. From a technical perspective, we show how to relate this model 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.

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

Massachusetts Institute of Technology (MIT) - Operations Research Center ( email )

77 Massachusetts Avenue
Bldg. E 40-149
Cambridge, MA 02139
United States

Vivek 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)

University of Haifa - Department of Statistics ( email )

Haifa 31905
Israel

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