Descent-ascent technique for solving the multi-source Weber problem

Abstract

The multi-source Weber problem requires locating m new facilities in continuous space in order to minimize a sum of transportation costs to n fixed points or customers with known demands. Several heuristic methods have been developed to solve this problem. Typically, these algorithms move in descent directions from a specified starting solution until a local minimum is reached. In this paper, we consider the original heuristic proposed by Cooper (1963, 1964, 1972), which has no inherent neighbourhood structure. We show how a neighbourhood structure can be defined and a descent-ascent procedure employed to enhance the Cooper algorithm Computational results are reported.