A bicriteria approach for the semi-desirable facility location problem

Semi-desirable facilities have both desirable and undesirable effects on the demand points in their vicinity, which necessitates them to be located both close to and far away from those points. In this study, a bi-objective semi-desirable facility location problem with both desirable and undesirable effects is considered. The first objective minimizes the total transportation cost between the facility and the demand points and tends to locate the facility closer to these points. Assuming that the transportations are made on road maps, the rectilinear distance metric is used to compute the first criterion. The second objective function minimizes the maximum undesirable effect of the facility on the demand points, and it thus tends to locate the facility farther from the demand points. The undesirable effect of the facility on a demand point is represented with a function based on the distance between them. The undesirable effect stays constant within a close proximity of the facility, beyond this proximity it decreases linearly and becomes zero. Assuming that the undesirable effects spread radially from the facility, the Euclidean distance metric is used to compute the second criterion. We first develop a mixed integer nonlinear programming model for the problem. As a second approach, the Big Square Small Square (BSSS) algorithm that searches for a solution by dividing the solution area into sub-regions is adapted to the problem. A mathematical model with low computational requirements is developed to effectively evaluate whether there is an efficient solution in the sub-regions or not. The approach is demonstrated on two large problem instances, in which efficient solutions are obtained quickly by reducing the solution area.