The Optimal Solution Set of the Multi-source Weber Problem

Abstract

This paper considers the classical multi-source Weber problem (MWP), which is to find M new facilities with respect to N customers to minimize the sum of transportation costs between these facilities and the customers. We propose a modified algorithm in the spirit of Cooper’s work for solving the MWP including a location phase and an allocation phase. The task of location phase is to find the optimal solution sets of many single-source Weber problems (SWPs), which are reduced by the heuristic of the nearest center reclassification for the customers in the previous allocation phase. Some examples are stated to clarify the proposed algorithms. Moreover, we present an algorithm with O(dlog d) time for finding the optimal solution set of SWP in the collinear case; where d is the number of customers. © 2018, The Author(s).