ISO-cost contours to facility location problems in the presence of circular and polygonal forbidden regions

The paper presents a methodology to obtain a library of alternate sub-optimal level planar locations to a proposed facility among a set of existing facilities and in the presence of circular and polygonal forbidden regions. To the problems involving polygonal forbidden regions, Sloping Line Search (SLS) Technique developed by the authors for determining the shortest unconstrained Euclidean distance between any two planar locations, in the presence of a single / two convex / non-convex polygonal forbidden region, is used together with bi-section method. Further, for applications involving circular forbidden regions an improved logic that enables direct selection of the shortest feasible path, among alternate paths, is developed and implemented. Applications of the revised method effectively minimized the limitations experienced and reported in earlier works leading to obtaining solutions to situations involving non-convex polygonal forbidden regions also.