(r|p)-centroid problems on networks with vertex and edge demand

This paper analyzes (r|p)-centroid$(r|p)\mathrm{-}\mathrm{centroid}$ problems on networks with vertex and edge demand under a binary choice rule. Bilevel programming models are presented for the discrete problem class. Furthermore, NP-hardness proofs for the discrete and continuous (1|p)-centroid$(1|p)\mathrm{-}\mathrm{centroid}$ problem on general networks with edge demand only are provided. Nevertheless, an efficient algorithm to determine a discrete (1|p)-centroid$(1|p)\mathrm{-}\mathrm{centroid}$ of a tree network with vertex and edge demand can be derived.