A SIMPLIFICATION AND GENERALIZATION OF THE EXCLUSION THEOREM: A TECHNICAL NOTE

Several researchers have proven that for the integrated production-location problem on the Weberian triangle, intermediate points on the edge of the triangle can never be optimal locations. Authors of previous proofs of this result have used cumbersome trigonometric arguments. We present a much simpler algebraic proof of the result, and present it in terms of the more general n -input model, where the feasible location space is a convex polygon rather than a triangle. In addition, the result generalizes immediately to other cases, such as (1) multifacility production-location problems, (2) stochastic versions of one-facility and multifacility production-location problems, and (3) comparable pure location problems (e.g., the Weber problem).