Reverse minisum single facility location problem with variable weights

In the classical minisum facility location problem, the goal is to find the placement of a new facility that minimizes the sum of weighted distances to a given set of client points. In contrast, the reverse minisum single facility location problem assumes a fixed facility location and focuses on adjusting the weights of the client points. The objective is to improve the weighted distances between the facility and clients, subject to a budget constraint on weight modifications. This paper introduces an O(n\log n) algorithm for the reverse problem with variable weights, applicable to both network and continuous location models. Experimental results on diverse instances demonstrate the algorithm's effectiveness.

Keywords:

Reverse facility location , Variable weights , Continuous facility location , Minisum