In this paper, an adjustable robust optimization with a polyhedral uncertainty set is used to deal with uncertain transportation cost in an uncapacitated multiple allocation balanced hub location problem. Adjustable robust optimization is modeled as two-stage or multi-stage problems in which decisions are determined in two or multi-separated stages. In two-stage robust optimization, first, the location of hubs is determined in the absence of uncertain parameters; then, the second-stage decision determined flows path in the presence of uncertainty. Two new mathematical models are proposed for this problem with mixed-integer linear and non-linear structures. Benders decomposition algorithm with stronger cut (Pareto-optimal cut) is used to solve proposed models. Adjustable robust models and accelerated Benders decomposition algorithms are analyzed using well-known AP data set with different levels of uncertainty. Also, a size reduction method is introduced to solve medium and large instances with good solution quality and shorter computation time. The numerical experiment shows the superiority of the Pareto-optimal cut Benders decomposition algorithm comparing with a classic one. Also, the mixed-integer non-linear model has better results in CPU time and the gap in comparison with the linear integer one. Flow balancing affects hub configuration with a decreasing number of hub facilities. Also by increasing the uncertainty budget, more hubs are established and with increasing discount factor, number of hub facilities are decreased.
