A geometrical solution for quadratic bicriteria location models

This paper deals with a single-facility, unweighted, quadratic bicriteria location problem defined in the continuous space. First we describe an analytical method for constructing the set of Pareto-optimal locations for this problem based on the farthest-point Voronoi diagram. Then we present an analytical method for finding the solution to the scalarized location problems based on the Pareto-optimal locations. The analytical results enable planners to carry out some sensitivity analyses. Since both methods are based entirely on geometrical analysis, they can be understood intuitively.