GENERALIZED HULL PROPERTIES FOR LOCATION-PROBLEMS

This paper considers a general form of the single facility minisum loc ation model, also known as the Fermat-Weber problem, in which the cost components are increasing differentiable functions of a norm. In part icular, attention is restricted to a broad class of norms referred to as round norms, a formal definition of which is included. It is shown that all locally optimal locations of the new facility in the two-dime nsional problem (N-dimensional for the Euclidean norm) must be within the convex hull of the destinations. The results are extended to a gen eral form of the multifacility minisum location problem.