Facility location problems in the presence of two-circular forbidden regions with Euclidean distance norm

The paper presents the methodology to obtain the optimum location of a new facility in relation to the existing locations in the presence of two circular forbidden regions. The algorithms to compute the shortest constrained Euclidean distance in the presence of single and two-circular forbidden regions are presented. In case of constrained situations, the proposed method chooses the least path directly without computing all possible paths and thus minimizes the computation time. The programming system is interactive so that the user can opt for the optimization criteria as (i) mini-sum criteria, (ii) mini-max criteria and/or (iii) bicriteria with or without the presence of forbidden regions.