SINGLE FACILITY LOCATION PROBLEM WITH REGION-DEPENDENT DISTANCE METRICS

A single facility location problem where the distance is measured diff erently in different regions on the plane is considered. For example, if some demand points are in a city with streets located as horizontal or vertical lines on the map and if other demand points are outside t he city where travel in a straight line is possible using, e.g. helico pters, we obtain a mixed distance problem and the current model become s applicable. We first formulate the problem as a mixed integer non-li near programming problem. Next, we prove the non-convexity of the cost function by showing that it is discontinuous along the line that divi des the two regions. Bounds on the value of the cost function are prov ided. We propose a heuristic, as a modified version of the Weiszfeld a lgorithm, to solve the problem and compare its performance with a glob al optimization method. A numerical example and sensitivity analyses a re discussed comparing the efficiency of the modified algorithm with t he results of the global optimization method.