Branch and bound method for the weber problem with rectangular facilities on lines in the presence of forbidden gaps

Abstract

The problem of location of connected rectangular facilities on parallel lines in the presence of forbidden gaps is studied. The rectangular metric is used. The centers of the placed facilities are connected with the centers of the gaps. The facilities are impossible to place in forbidden gaps. It is necessary to place the facilities on the lines so that the total cost of connections between the facilities and between facilities and gaps was minimized. The problem is an adequate model of many practical situations. It is known that the original continuous problem for one–line variant is reduced to discrete subproblems. In this paper, the review of the properties and the algorithms for solving of the problem on one line are described. The branch and bound method for solving the problem is proposed. Results of computational experiments on comparison of the branch and bound method and a heuristic proposed in [27] are reported. In the experiments, a integer programming model and IBM ILOG CPLEX package are used.