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 a algorithm which an efficient implementation of the Weiszfeld technique is developed and is shown to converge to a global optimal solution. This anlysis 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 de points and computational experience are also provided. [ABSTRACT FROM AUTHOR]