We study the problem of locating a public facility on a real line or an interval, when agents’ costs are their (expected) distances from the location of the facility. Our goal is to minimize the maximum envy over all agents, which we will refer to as the minimax envy objective, while at the same time ensuring that agents will report their most preferred locations truthfully. First, for the prob...

We study a system of linear inequalities associated with some facility location problems. We show that this system defines a polytope with integer extreme points if and only if the graph does not contain a certain type of odd cycles. We also derive odd cycle inequalities and give a separation algorithm.

This paper presents a single facility location problem in the presence of a probabilistic line barrier. The aim of this problem is to minimize bi-objectives, namely the total expected barrier distance and the maximum expected barrier distance from each demand point to the new facility point. Based on our best knowledge, there is no such a mathematical model to present this problem in the litera...

We investigate a multi-commodity capacitated facility location problem involving sustainability concerns (e.g., restrained carbon emission). In addition, this incorporates complementarity demand function. show that incorporation can lead to superior decisions both analytically and computationally. The resultant formulation is 0–1 mixed-integer non-concave quadratic program with equilibrium cons...