Euclidean Distance Location-Allocation Problems with Uniform Demands over Convex Polygons

In this paper we consider location-allocation problems in which the region to be served is a convex polygon having a uniform demand distribution. Both single and multifacility formulations are considered. For the single facility problem, an algorithm which uses an efficient implementation of the Weiszfeld technique is developed and is shown to converge to a global optimal solution. This analysis is extended to the nonconvex multifacility case. However, although global optimality of the fixed point that the algorithm converges to is not guaranteed, a method suggested for finding a good starting solution increases the likelihood of finding an optimal solution. Extensions of the above problems to include discrete demand points and computational experience are also provided.