Extension of the Weiszfeld procedure to a single facility minisum location model with mixed ℓ <Subscript> p </Subscript> norms

This paper presents a general mixed-norm minisum problem for locating a single facility in continuous space. It is assumed that several transportation modes exist between the new facility and a given set of fixed points (the customers), each mode being represented by a different ℓ <Subscript> p </Subscript> norm. A simple extension of Weiszfeld’s well known iterative procedure is proposed to solve the model. Convergence properties and optimality criteria are derived, and computational results are given. Copyright Springer-Verlag 2009