Confined location of facilities on a graph

Location problems on a graph are usually classified according to the form that the set of located facilities takes, the specification of the demand location set and the objective function of distances between facilities and demand points. This paper supposes that a given number of located facilities is confined to the same number of edges. It considers eight types of optimality criteria: minimizing (or maximizing) the minimum (or maximum) distance from a demand to its nearest (farthest) facility.