A nonlinear programming model for a multi-facility location problem with a probabilistic line barrier

In this paper, a Mixed-integer non linear programming (MINLP) model for a multi-facility location problem in the presence of a probabilistic line barrier is presented in which the starting point of the line barrier uniformly distributed. It is supposed that the distances metric is rectilinear. The objective function minimizes the summation of the weighted expected rectilinear barrier distances between the n new facilities and the m existing facilities and also between the new facilities. To show the applicability of the model, a numerical example is provided. It is worth noting that the global optimal solution is found.