Full ordering Voronoi sets for bi-facility bicriterium (max, sum) location on networks (Q2704993)

The authors treat a specific problem in network location analysis, the bi-facility max-sum location problem. It consists of finding a pair of locations on a given network minimizing the maximum distance to a finite set of users on the one hand (center problem) and also minimizing the sum of the distances between each user node and their nearest location on the other hand (median problem). Based on an analysis of the used distance function they identify a kind of Voronoi sets where the order of the user nodes from the farthest one to the nearest one does not change. They show how to use these basics for a geometrical construction of the sets pairs of values of the objective functions for all the solutions. This set consists of the union of triangles where the bidimensional objective is a linear function. The dominance between the vertices and sides of these triangles can be used to identify all Pareto-optimal and Bayes-optimal solutions of this location problem.