We present a game-theoretic model for the line planning problem in public transportation, in which each line acts as player. Each player aims to minimize its own delay, which is dependent on the traffic load along its edges. We show that there exists a line plan at equilibrium, which minimizes...

In this paper the following facility location problem in a mixed planar-network space is considered: We assume that traveling along a given network is faster than traveling within the plane according to the Euclidean distance. A pair of points (A <Subscript> i </Subscript>,A <Subscript> j </Subscript>) is called covered if the time to...</subscript></subscript>

In this paper we consider the problem of locating an axis-parallel rectangle in the plane such that the sum of distances between the rectangle and a finite point set is minimized, where the distance is measured by the Manhattan norm ℓ <Subscript>1</Subscript>. In this way we solve an extension of the Weber problem...</subscript>

We introduce the path player game, a noncooperative network game with a continuum of mutually dependent set of strategies. This game models network flows from the point of view of competing network operators. The players are represented by paths in the network. They have to decide how much flow...

We introduce the path player game, a noncooperative network game with a continuum of mutually dependent set of strategies. This game models network flows from the point of view of competing network operators. The players are represented by paths in the network. They have to decide how much flow...

A global optimization procedure is proposed to find a line in the Euclidean three-dimensional space which minimizes the sum of distances to a given finite set of three-dimensional data points. Although we are using similar techniques as for location problems in two dimensions, it is shown that...

In this paper we consider the location of stops along the edges of an already existing public transportation network. This can be the introduction of bus stops along some given bus routes, or of railway stations along the tracks in a railway network.The positive effect of new stops is given by...