Extension of the Weiszfeld Procedure to a Single Facility Minisum Location Model with Mixed 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 norm. A simple extension of Weiszfeld’s well-known iterative procedure is proposed to solve the model. Convergence properties and opti- mality criteria are derived, and computational results are given.