We investigate where cities are located in a spatial economy and why they tend to get "locked-in" at particular sites. Building on Fujita and Krugman (1995) we show that geography and/or transportation technology must exhibit some "non-smoothness" for cities to possibly become "locked-in" in...

When dealing with location problems we are usually given a set of existing facilities and we are looking for the location of one or several new facilities. In the classical approaches weights are assigned to existing facilities expressing the importance of the new facilities for the existing...

Let a connected undirected graph G  =  (V, E) be given. In the classical p-median problem we want to find a set X containing p points in G such that the sum of weighted distances from X to all vertices in V is minimized. We consider the semi-obnoxious case where every vertex has either a...

Let T = (V, E) be a tree. A core of T is a path P, for which the sum of the weighted distances from all vertices to this path is minimized. In this paper, we consider the semi-obnoxious case in which the vertices have positive or negative weights. We prove that, when the sum of the weights of...

In this paper we look at two interesting extensions to the classical 2-Facility Weber Problem in ℝ d : At first problems are investigated where we do not allow the optimal locations to be in a specific region. Efficient algorithms for this Global Optimization problem are presented as well as...

Let a connected undirected graph G  =  (V, E) be given. In the classical p-median problem we want to find a set X containing p points in G such that the sum of weighted distances from X to all vertices in V is minimized. We consider the semi-obnoxious case where every vertex has either a...

Let T = (V, E) be a tree. A core of T is a path P, for which the sum of the weighted distances from all vertices to this path is minimized. In this paper, we consider the semi-obnoxious case in which the vertices have positive or negative weights. We prove that, when the sum of the weights of...

In this paper we look at two interesting extensions to the classical 2-Facility Weber Problem in ℝ<Superscript> d </Superscript>: At first problems are investigated where we do not allow the optimal locations to be in a specific region. Efficient algorithms for this Global Optimization problem are presented as well as...</superscript>