Extensions to the planar p-median problem

In this paper we propose three models for locating multiple facilities anywhere in the plane. The facilities serve demand points and require raw materials from a list of available sources. Problem characteristic originally proposed in 1909 by Weber for manufacturing systems. Weber argued that optimal locations involve minimizing total transport cost which was comprised of the costs of transporting the raw materials and the delivery cost of the final product when plant production and location costs were invariant across the plane. Both the parameters of raw material sources and demand points affect the best locations for the facilities. In this paper, a special algorithm is designed to heuristically solve these three models. The algorithm exploits the special structure of the models. Problems with up to 2000 demand points and 20 facilities were tested. The results are compared with applying available non-linear solvers in a multi-start approach. The special algorithm performed better in most instances especially for a large number of facilities and a large number of demand points.