Locating a distance-dependent facility on an undirected network with continuous link weights

This paper considers two problems of locating a facility on an undirected network with a restriction imposed on maximal distance (λ⩾0) from the facility to weighted points that are discretely distributed over all the associated nodes but continuously distributed on all the associated links. One problem is to find a location point of a desirable facility that could serve linearly-decreasing demand generated from weighted points within a λ-boundary along paths from the location point. The other problem is to find a location point of an undesirable facility that could inflict linearly-decreasing damage on weighted points within a λ-boundary along paths from the location point. In the problem analysis, some optimal solution properties are found. Using these properties, the solution mechanisms for both problems are derived and tested with several numerical examples.