LAGRANGIAN HEURISTICS FOR THE 2-ECHELON, SINGLE-SOURCE, CAPACITATED FACILITY LOCATION PROBLEM

Facility location problems form an important class of integer programm ing problems, with application in the distribution and transportation industries, In this paper we are concerned with a particular type of f acility location problem in which there exist two echelons of faciliti es. Each facility in the second echelon has limited capacity and can b e supplied by only one facility (or depot) in the first echelon. Each customer is serviced by only one facility in the second echelon. The n umber and location of facilities in both echelons together with the al location of customers to the second-echelon facilities are to be deter mined simultaneously. We propose a mathematical model for this problem and consider six heuristics based on Lagrangian relaxation for its so lution. To solve the dual problem we make use of a subgradient optimiz ation procedure. We present numerical results for a large suite of tes t problems. These indicate that the lower-bounds obtained from some re laxations have a duality gap which frequently is one third of the one obtained from traditional linear programming relaxation. Furthermore, the overall solution time for the heuristics are less than the time to solve the LP relaxation. (C) 1997 Elsevier Science B.V.