Optimal location of a single facility with circular demand areas

The single facility minimum location problem in Euclidean space has usually been studied with a certain number of discrete demand points. Some authors have also described the possibility of demand areas. In the present work, a new approach is offered to the optimal location of a single facility, which should serve a number of circular demand areas, each with uniform demand density, along with some discrete demand points. The effect of a circular demand area on the service facility at each stage of the Weiszfeld-like iterative procedure is evaluated for the three possible cases of the incumbent service point being outside, inside, or on the circumference of such a circle. Some limiting cases are considered, such as that of the demand area being very far from the service point to be optimally located. The amended Weiszfeld iterative procedure is described, and some numerical experience of solving such problems is reported.