Facility Location Problem with Capacity Constraints: Algorithmic and Mechanism Design Perspectives


  • Haris Aziz UNSW Sydney
  • Hau Chan University of Nebraska-Lincoln
  • Barton Lee UNSW Sydney
  • Bo Li University of Oxford
  • Toby Walsh UNSW Sydney




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 %on the returned solution 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.




How to Cite

Aziz, H., Chan, H., Lee, B., Li, B., & Walsh, T. (2020). Facility Location Problem with Capacity Constraints: Algorithmic and Mechanism Design Perspectives. Proceedings of the AAAI Conference on Artificial Intelligence, 34(02), 1806-1813. https://doi.org/10.1609/aaai.v34i02.5547



AAAI Technical Track: Game Theory and Economic Paradigms