Locating an axis-parallel rectangle on a Manhattan plane

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 to extensive facility location. As a model, our problem is appropriate for position sensing of rectangular objects. Copyright Sociedad de Estadística e Investigación Operativa 2014