  In this paper, a non-linear p-robust hub location problem is extended to a
risky environment where augmented chance constraint with a min-max regret form
is employed to consider network risk as one of the objectives. The model
considers risk factors such as security, air pollution and congestion to design
the robust hub network. A Monte-Carlo simulation based algorithm, namely, a
sample average approximation scheme is applied to select a set of efficient
scenarios. The problem is then solved using a novel relax-and-decomposition
heuristic based on the coupling of an accelerated Benders decomposition with a
Lagrangian relaxation method. To improve the decomposition mechanism, a
multi-Pareto cut version is applied in the proposed algorithm. In our numerical
tests a modification of the well-known CAB data set is used with different
levels of parameters uncertainty. The results demonstrate the capability of the
proposed model to design a robust network. We also verify the accuracy of the
sample average approximation method. Finally, the results of the proposed
algorithm for different instances were compared to other solution approaches
which confirm the efficiency of the proposed solution method.
