, Volume 14, Issue 1, pp 57–75 | Cite as

Assortment optimization under a multinomial logit model with position bias and social influence

  • Andrés Abeliuk
  • Gerardo Berbeglia
  • Manuel Cebrian
  • Pascal Van HentenryckEmail author
Research paper


Motivated by applications in retail, online advertising, and cultural markets, this paper studies the problem of finding an optimal assortment and positioning of products subject to a capacity constraint in a setting where consumers preferences can be modeled as a discrete choice under a multinomial logit model that captures the intrinsic product appeal, position biases, and social influence. For the static problem, we prove that the optimal assortment and positioning can be found in polynomial time. This is despite the fact that adding a product to the assortment may increase the probability of selecting the no-choice option, a phenomenon not observed in almost all models studied in the literature. We then consider the dynamics of such a market, where consumers are influenced by the aggregate past purchases. In this dynamic setting, we provide a small example to show that the natural and often used policy known as popularity ranking, that ranks products in decreasing order of the number of purchases, can reduce the expected profit as times goes by. We then prove that a greedy policy that applies the static optimal assortment and positioning at each period, always benefits from the popularity signal and outperforms any policy where consumers cannot observe the number of past purchases (in expectation).


Assortment optimization Marketing Social influence 

Mathematics Subject Classification




We thank the reviewers for their constructive remarks and suggestions. NICTA is funded by the Australian Government through the Department of Communications and the Australian Research Council through the ICT Centre of Excellence Program.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Andrés Abeliuk
    • 1
  • Gerardo Berbeglia
    • 2
  • Manuel Cebrian
    • 1
  • Pascal Van Hentenryck
    • 3
    Email author
  1. 1.The University of Melbourne and National ICT AustraliaMelbourneAustralia
  2. 2.Melbourne Business SchoolThe University of Melbourne and National ICT AustraliaMelbourneAustralia
  3. 3.Department of Industrial and Operations EngineeringThe University of MichiganAnn ArborUSA

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