In this paper, an adjustable robust optimization with a polyhedral un-certainty 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.

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