Obnoxious facility location: the case of weighted demand points

TL;DR

This paper introduces three new optimal solution methods for the weighted obnoxious facility location problem, efficiently solving large instances by leveraging geometric and global optimization techniques.

Contribution

It proposes two variants of the 'Big Triangle Small Triangle' method and an intersection-based approach, outperforming existing methods in solving large-scale problems.

Findings

Optimal solutions for 1,000 demand points in seconds

New geometric and global optimization methods demonstrated effectiveness

Comparison shows improved performance over SNOPT multi-start approach

Abstract

The problem considered in this paper is the weighted obnoxious facility location in the convex hull of demand points. The objective function is to maximize the smallest weighted distance between a facility and a set of demand points. Three new optimal solution approaches are proposed. Two variants of the "Big Triangle Small Triangle" global optimization method, and a procedure based on intersection points between Apollonius circles. We also compared the results with a multi-start approach using the non-linear multi-purpose software SNOPT. Problems with 1,000 demand points are optimally solved in a fraction of a second of computer time.