The approximability of assortment optimization under ranking preferences

Ali Aouad, Vivek Farias, Retsef Levi, Danny Segev

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1661-1669
Number of pages9
JournalOperations Research
Issue number6
StatePublished - Nov 2018

Bibliographical note

Publisher Copyright:
© 2018 INFORMS.


  • Approximation algorithms
  • Assortment optimization
  • Choice models
  • Hardness of approximation
  • Independent set

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research


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