On the (r|Xp)-medianoid problem on a network with vertex and edge demands

This article considers the (r|Xp)-medianoid problem on a network N = (V, E) with vertex and edge demands. There are already p facilities located on the network and customers patronize the closest facility. The aim is to locate r additional facilities on the network where their captured demands will be maximized. Relationships with the (r|Xp)-medianoid problem with vertex demands are established. Complexity and algorithmic results are presented.