A Facility Location Problem with Tchebychev Distance in the Presence of a Probabilistic Line Barrier

This paper considers the Tchebychev distance for a facility location problem with a probabilistic line barrier in the plane. In particular, we develop a mixed-integer nonlinear programming (MINLP) model for this problem that minimizes the total Tchebychev distance between a new facility and the existing facilities. A numerical example is solved to show the validity of the developed model. Because of difficulty in solving this problem while increasing the number of existing facilities, we propose and design an efficient meta-heuristic algorithm, namely differential evolution (DE), for the given problem. Finally, the associated results are compared with the exact solution and lower bound for the different-sized problems.