The center location-dependent relocation problem with a probabilistic line barrier

This paper presents a new mixed-integer nonlinear programming (MINLP) for a multi-period rectilinear distance center location-dependent relocation problem in the presence of a probabilistic line-shaped barrier that uniformly occurs on a given horizontal route. In this problem, the demand and location of the existing facilities have a dynamic nature and the relocation is dependent to the location of new facilities in previous period. The objective function of the presented model is to minimize the maximum expected weighted barrier distance between the new facility and the existing facilities during the planning horizon. The optimum solution of small-sized test problems is obtained by the optimization software. For large-size test problems which the optimization software is unable to find the optimum solution in the runtime limitation, two meta-heuristics based on the genetic algorithm (GA) and imperialist competitive algorithm (ICA) are applied. To validate the meta-heuristics, a lower bound problem based on the forbidden region instead of the line barrier is generated. Related results of numerical experiments are illustrated and are then compared.