Facility location with rectilinear tour distances

Abstract

<p>This problem concerns the location of a facility among n points where the points are serviced by "tours" take n from the facility. Tours include m points at a time and each group of m points ma y become active (may need a tour) with some known probability. Distances are assumed to be rectilinear. An exact solution procedure is provided for m < 3 and a bounded heuristic algorithm is suggested when some tours have 4 or more points. It is shown that in the latter case the objective function becomes multimodal.</p>