Greedy-like algorithms for dynamic assortment planning under multinomial logit preferences

Ali Aouad, Retsef Levi, Danny Segev

Research output: Contribution to journalArticlepeer-review


We study the joint assortment planning and inventory management problem, where stock-out events elicit dynamic substitution effects, described by the multinomial logit (MNL) choice model. Special cases of this setting have been extensively studied in recent literature, notably the static assortment planning problem. Nevertheless, to our knowledge, the general formulation is not known to admit efficient algorithms with analytical performance guarantees before this work, and most of its computational aspects are still wide open. In this paper, we devise what is, to our knowledge, the first provably good approximation algorithm for dynamic assortment planning under the MNL model. We derive a constant-factor guarantee for a broad class of demand distributions that satisfy the increasing failure rate property. Our algorithm relies on a combination of greedy procedures, where stocking decisions are restricted to specific classes of products and the objective function takes modified forms. We demonstrate that our approach substantially outperforms state-of-the-art heuristic methods in terms of performance and speed, leading to an average revenue gain of 4% to 12% in computational experiments. In the course of establishing our main result, we develop new algorithmic ideas that may be of independent interest. These include weaker notions of submodularity and monotonicity, shown sufficient to obtain constant-factor worst-case guarantees, despite using noisy estimates of the objective function.

Original languageEnglish
Pages (from-to)1321-1345
Number of pages25
JournalOperations Research
Issue number5
StatePublished - Sep 2018

Bibliographical note

Publisher Copyright:
© 2018 INFORMS.


  • Approximation algorithms
  • Dynamic substitution
  • Inventory management
  • Multinomial logit choice model
  • Submodularity

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research


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