Dynamic Assortment with Limited Inventories and Set-Dependent Revenue Functions

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We consider an online assortment problem with [n] := {1,2,...,n} sellers, each holding exactly one item i ? [n] with initial inventory {c_i} \in {\mathbb{Z}_ + }, and a sequence of homogeneous buyers arriving over a finite time horizon t = 1,2,...,m. There is an online platform whose goal is to offer a subset St ? [n] of sellers to the arriving buyer at time t to maximize the expected revenue derived over the entire horizon while respecting the inventory constraints. Given an assortment St at time t, it is assumed that the buyer will select an item from St based on the well-known multinomial logit model, a well-justified choice model from the economic literature. In this model, the revenue obtained from selling an item i at a given time t critically depends on the assortment St offered at that time and is given by the Nash equilibrium of a Bertrand game among the sellers in St. This imposes a strong dependence/externality among the offered assortments, items revenues, and inventory levels. Despite that challenge, we devise a constant-competitive algorithm for the online assortment problem with homogeneous buyers and evaluate its performance via numerical results.

Original languageEnglish (US)
Title of host publication2020 59th IEEE Conference on Decision and Control, CDC 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781728174471
StatePublished - Dec 14 2020
Event59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, Korea, Republic of
Duration: Dec 14 2020Dec 18 2020

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Conference59th IEEE Conference on Decision and Control, CDC 2020
Country/TerritoryKorea, Republic of
CityVirtual, Jeju Island


  • Bertrand game
  • Nash equilibrium
  • Online assortment
  • multinomial logit model
  • revenue management

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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