Reliable hub network design: Formulation and solution techniques

In this paper, we investigate the issue of unreliability in hub location planning. A mixed integer nonlinear programming model is formulated for optimally locating p uncapacitated hubs, each of which can fail with a site-specific probability. The objective is to determine the location of hubs and the assignment of demand nodes to hubs in order to minimize expected demand weighted travel cost plus a penalty if all hubs fail. A linear version of the model is developed employing a specialized flow network called a probability lattice to evaluate compound probability terms. A Tabu search algorithm is proposed to find optimal to near optimal solutions for large problem instances. A parallel computing strategy is integrated into the Tabu search process to improve performance. Experimental results carried out on several benchmark instances show the efficiency of our linearized model and heuristic algorithm. Compared to a standard hub median model that disregards the potential for hub failures, our model produces solutions that serve larger numbers of customers and at lower cost per customer.