Mathematical Model for Bi-objective Maximal Hub Covering Problem with Periodic Variations of Parameters

The problem of maximal hub covering as a challenging problem in operation research. Transportation programming seeks to find an optimal location of a set of hubs to reach maximum flow in a network. Since the main structure's parameters of the problem such as origin-destination flows, costs and travel time, change periodically in the real world applications, new issues arise in handling it. In this paper, to deal with the periodic variations of parameters, a bi-objective mathematical model is proposed for the single allocation multi-period maximal hub covering problem. The e-constraint approach has been applied to achieve non-dominated solutions. Given that the single-objective problem found in the e-constraint method is computationally intractable. Benders decomposition algorithm by adding valid inequalities is developed to accelerate the solution process. Finally, the proposed method is carried out by CAB data set, and the results confirm the efficiency of it regarding optimality and running time.