Facility location problem with capacity constraints: Algorithmic and mechanism design perspectives

Haris Aziz, Hau Chan, Barton E. Lee, Bo Li, Toby Walsh

Research output: Chapter in book / Conference proceedingConference article published in proceeding or bookAcademic researchpeer-review

4 Citations (Scopus)


We consider the facility location problem in the one-dimensional setting where each facility can serve a limited number of agents from the algorithmic and mechanism design perspectives. From the algorithmic perspective, we prove that the corresponding optimization problem, where the goal is to locate facilities to minimize either the total cost to all agents or the maximum cost of any agent is NP-hard. However, we show that the problem is fixed-parameter tractable, and the optimal solution can be computed in polynomial time whenever the number of facilities is bounded, or when all facilities have identical capacities. We then consider the problem from a mechanism design perspective where the agents are strategic and need not reveal their true locations. We show that several natural mechanisms studied in the uncapacitated setting either lose strategyproofness or a bound on the solution quality for the total or maximum cost objective. We then propose new mechanisms that are strategyproof and achieve approximation guarantees that almost match the lower bounds.

Original languageEnglish
Title of host publicationAAAI 2020 - 34th AAAI Conference on Artificial Intelligence
PublisherAAAI press
Number of pages8
ISBN (Electronic)9781577358350
Publication statusPublished - 2020
Externally publishedYes
Event34th AAAI Conference on Artificial Intelligence, AAAI 2020 - New York, United States
Duration: 7 Feb 202012 Feb 2020

Publication series

NameAAAI 2020 - 34th AAAI Conference on Artificial Intelligence


Conference34th AAAI Conference on Artificial Intelligence, AAAI 2020
Country/TerritoryUnited States
CityNew York

ASJC Scopus subject areas

  • Artificial Intelligence

Cite this