The Mini-Max Multi-Facility Location Problem in the Presence of a Probabilistic Line Barrier

This study considers a Mini-Max multi-facility location problem in the presence of a line barrier that occurs randomly on a given horizontal route on the plane. The problem is to find the optimal location of n new facilities among m existing facilities with the objective of minimizing the maximum weighed expected rectilinear barrier distances between the locations of new facilities and new and existing facilities. Some properties of the problem, such as visibility and expected distance function, are expressed and a sample problem is solved by LINGO 9.0 software