Bi-objective Non-strict Single Allocation Hub Location Problem: Mathematical Programming Model and a Solution Heuristic

Hub location problem (HLP) is one of the most important problems in the areas of logistics and telecommunication network design. In this paper we address the bi-objective non-strict single allocation hub location problem (BONSSAHLP). The non-strict property of this problem which allows establishment of direct links between pairs of non-hub nodes makes it somehow different from the conventional hub location problem in which the linkage between any pair on non-hub nodes must be through one or two hub nodes. The first objective in BONSSAHLP is to minimize the total system-wide cost (including cost of locating hub facilities, cost of establishing linking arcs, and cost of transporting commodities) and the second objective is to minimize the maximum commodity routing distance between pairs of nodes in the network. A novel mathematical programming formulation is developed for the problem and since the problem belongs to the class of NP-hard problems (because it is a generalization of the conventional hub location problem which belongs to the class of NP-hard problems); an efficient heuristic based on tabu search (TS) is proposed to solve it. Numerical results indicate the efficiency of the proposed heuristic both in terms of solution quality and CPU time.