Formulation and solution of a two-stage capacitated facility location problem with multilevel capacities

In this paper, the multi-product facility location problem in a two-stage supply chain is investigated. In this problem, the locations of depots (distribution centres) need to be determined along with their corresponding capacities. Moreover, the product flows from the plants to depots and onto customers must also be optimised. Here, plants have a production limit whereas potential depots have several possible capacity levels to choose from, which are defined as multilevel capacities. Plants must serve customer demands via depots. Two integer linear programming (ILP) models are introduced to solve the problem in order to minimise the fixed costs of opening depots and transportation costs. In the first model, the depot capacity is based on the maximum number of each product that can be stored whereas in the second one, the capacity is determined by the size (volume) of the depot. For large problems, the models are very difficult to solve using an exact method. Therefore, a matheuristic approach based on an aggregation approach and an exact method (ILP) is proposed in order to solve such problems. The methods are assessed using randomly generated data sets and existing data sets taken from the literature. The solutions obtained from the computational study confirm the effectiveness of the proposed matheuristic approach which outperforms the exact method. In addition, a case study arising from the wind energy sector in the UK is presented

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. (C) 2000 Elsevier Science B.V. All rights reserved

New facets for the two-stage uncapacitated facility location polytope

Location, Two-stage, Set packing, Facet, Combinatorial optimization,