Two algorithms for the multi-Weber problem

This paper develops two methods for finding building-blocks for solving Rosing's multi-Weber problem as a set-covering problem in zero–one programming. The building blocks are those subsets of the universe of points to be partitioned that do not contain any non-members within their own convex hulls. For a particular universe of 100 cities, there are almost six billion such subsets, and the paper sets out computational methods that make this enumeration feasible. Some of these methods have wider applications, but the central methods are closely tailored to this problem. Means are also suggested for reducing the number of subsets to be enumerated, without ruling out possibly optimal solutions for the complete problem.