Extending the problem of capacitated single-allocation air hub location is considered in this research. One of the parts of the transportation decision-making process is capacity of the hubs, and the balancing requisites become imposed on the network. Also, inclement weather or emergency conditions are the controversial issues in programming air transportation networks. Here, hub facilities cannot temporarily provide a good service for their spoke nodes. Therefore, some other types of pre-determined underutilized facilities in the network are applied as virtual hubs to host some or all connections of original hubs to improve the incurred incapacitation, and to enhance network flexibility and demand current. In such a situation, it is sensible to expect some imprecise or obscure information. To account for this issue, a robust optimization approach is applied to present a more realistic problem. Here, this study develops a new robust mixed integer linear model to propose a dynamic virtual hub location problem with balancing requisites. Minimizing opening, maintenance, closing, and transportation costs in the network are the objectives of the study. Furthermore, a meta-heuristic algorithm called self-adaptive imperialist competitive algorithm (SAICA) is utilized for the hub location problem. Finally, this study carries out various computational experiments to investigate proposed model and solution approaches.
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