An interactive solution approach for a bi-objective semi-desirable location problem

In this study, we consider a semi-desirable facility location problem in a continuous planar region considering the interaction between the facility and the existing demand points. A facility can be defined as semi-desirable if it has both undesirable and desirable effects to the people living in the vicinity. Our aim is to maximize the weighted distance of the facility from the closest demand point as well as to minimize the service cost of the facility. The distance between the facility and the demand points is measured with the rectilinear metric. For the solution of the problem, a three-phase interactive geometrical branch and bound algorithm is suggested to find the most preferred efficient solution. In the first two phases, we aim to eliminate the parts of the feasible region the inefficiency of which can be proved. The third phase has been suggested for an interactive search in the remaining regions with the involvement of a decision maker (DM). In the third phase, the DM is given the opportunity to use either an exact or an approximate procedure to carry out the search. The exact procedure is based on the reference point approach and guarantees to find an efficient point as the most preferred solution. On the other hand, in the approximate procedure, a hybrid methodology is used to increase the efficiency of the reference point approach. The approximate procedure can be used when the DM prefers to see locally efficient solutions so as to save computation time. We demonstrate the performance of the proposed method through example problems.