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

arXiv: https://arxiv.org/abs/1911.09813 · HTML: https://mlsanity.com/paper/1911.09813/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Nov 2019.

## Built on by (most cited first, 8 of 8)

- [Strategyproof and Proportionally Fair Facility Location](https://mlsanity.com/paper/2111.01566/) (2021)
- [Mechanism Design With Predictions for Obnoxious Facility Location](https://mlsanity.com/paper/2212.09521/) (2022)
- [Strategic Facility Location with Clients that Minimize Total Waiting Time](https://mlsanity.com/paper/2211.14016/) (2022)
- [Nash Welfare and Facility Location](https://mlsanity.com/paper/2310.04102/) (2023)
- [Facility Location Games Beyond Single-Peakedness: the Entrance Fee Model](https://mlsanity.com/paper/2204.11282/) (2022)
- [Facility Location Games with Scaling Effects](https://mlsanity.com/paper/2402.18908/) (2024)
- [MAC Advice for Facility Location Mechanism Design](https://mlsanity.com/paper/2403.12181/) (2024)
- [Mechanism Design for Facility Location using Predictions](https://mlsanity.com/paper/2508.03818/) (2025)

## Abstract (arXiv)

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.