Modeling and solving the uncapacitated r-allocation p-hub median problem under congestion

The hub location problems deal with determining the optimal location of hub facilities and allocating the demand nodes to these hubs in such a way that the traffic between any origin-destination pair is routed effectively. This paper proposes the uncapacitated r-allocation p-hub median problem under congestion. The problem is formulated as a second-order cone programming and an efficient simulated annealing heuristic algorithm is proposed to solve the large instances of the problem. Extensive computational experiments are conducted based on three well-known data sets to demonstrate the efficiency of the proposed algorithm and also to study the effect of different input parameters on the optimal solutions. Some managerial insights are derived based on the obtained numerical results.