A Multi-Period 1-Center Location Problem in the Presence of a Probabilistic Line Barrier

This paper investigates a multi-period rectilinear distance 1-center location problem considering a line-shaped barrier, in which the starting point of the barrier follows the uniform distribution function. In addition, the existing points are sensitive to demands and locations. The purpose of the presented model is to minimize the maximum barrier distance from the new facility to the existing facilities during the finite planning horizon. Additionally, a lower bound problem is generated. The presented model is mixed-integer nonlinear programming (MINLP); however, an optimum solution is reached.