Hub network design involves the location of hub sites in a network through which flows from origins to destinations must be routed at least cost. Many practical applications of hub location exist for transportation, telecommunications, and other logistics systems. In this talk, I will focus on a critical issue in hub location planning that has, thus far, received little attention in the literature: hub reliability. The few existing studies dealing with hub reliability unrealistically assume that either dedicated backups can be located which never fail or that at most one unreliable hub will fail at any given time.
A more general approach for designing reliable hub networks would be to account for multiple, random hub failures. To this end, formulation and solution techniques are proposed for the uncapacitated, single allocation p-hub median location problem with independent hub failure probabilities. A mixed integer nonlinear programming model is formulated for locating unreliable hubs and assigning demand nodes to hubs in order to minimize the expected demand weighted cost of customer flows plus a penalty in the event all hubs fail. One of the key accomplishments is the development of a linear model which embeds a specialized flow network structure referred to as a probability lattice. A probability lattice extends the concept of probability chains recently introduced in the OR literature for evaluating high-order probability terms. A probability lattice involves interlinking multiple probability chains together to form a backbone probability chain and series of spur probability chains.
A Tabu search algorithm which makes use of a parallel computing strategy is also proposed to find optimal to near optimal solutions for large problem instances. Experimental results carried out on several benchmark instances show the efficiency of the linearized model and heuristic algorithm. Compared to a standard hub median model that disregards the potential for hub failures, the proposed model produces solutions that serve larger numbers of customers and at lower cost per customer.
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