FLIGHT: Facility Location Integrating Generalized, Holistic Theory of Welfare

TL;DR

This paper introduces FLIGHT, a unified framework for the Facility Location Problem that encompasses various welfare functions, providing theoretical insights, approximation bounds, and concentration results under distributional assumptions.

Contribution

The paper presents a novel, comprehensive framework for FLP that integrates multiple welfare notions and offers new structural, approximation, and concentration analyses.

Findings

Structural properties of FLP solutions are established.

Approximation bounds show welfare notion irrelevance with many agents.

Concentration bounds are derived under distributional assumptions.

Abstract

The Facility Location Problem (FLP) is a well-studied optimization problem with applications in many real-world scenarios. Past literature has explored the solutions from different perspectives to tackle FLPs. These include investigating FLPs under objective functions such as utilitarian, egalitarian, Nash welfare, etc. Also, there is no treatment for asymmetric welfare functions around the facility. We propose a unified framework, FLIGHT, to accommodate a broad class of welfare notions. The framework undergoes rigorous theoretical analysis, and we prove some structural properties of the solution to FLP. Additionally, we provide approximation bounds, which provide insight into an interesting fact: as the number of agents arbitrarily increases, the choice of welfare notion is irrelevant. Furthermore, the paper also includes results around concentration bounds under certain distributional assumptions over the preferred locations of agents.