A multi-period facility location-relocation problem in the presence of a probabilistic line barrier

This paper presents a mixed-integer nonlinear programming model (MINLP) for a multi-period facility location-relocation problem in the presence of a line-shaped barrier, which the starting point of the barrier follows the uniform distribution function. Rectilinear metric for the distance between points is supposed. The objective function of the proposed model minimizes the cost of traveled expected barrier distance and the cost of relocation, if occur, during the finite planning horizon. In addition, to show the capability of the proposed model, a numerical example is investigated and the associated results are compared with the results of problem without barrier.