An exact method for the two‐echelon, single‐source, capacitated facility location problem

Facility location problems form an important class of integer programming problems, with applications in the telecommunication, distribution and transportation industries. In this paper we are concerned with a particular type of facility location problem in which there exist two echelons of facilities. Each facility in the second echelon has limited capacity and can be supplied by only one facility in the first echelon. Each customer is serviced by only one facility in the second echelon. The number and location of facilities in both echelons together with the allocation of customers to the second‐echelon facilities are to be determined simultaneously. We propose a Lagrangian relaxation‐based branch and bound algorithm for its solution. We present numerical results for a large suite of test problems of realistic and practical size. These indicate that the method is efficient. It provides smaller branch and bound trees and requires less CPU time as compared to LP‐based branch and bound obtained from a 0–1 integer package.