Estimating the minimal revenue tolls in large-scale roadway networks using the dynamic penalty function method

•The dynamic penalty function method is used to estimate a toll vector that guarantees the SO flows in the network.•Numerical results show that this toll vector is a good estimation for the MinRev optimal solution.•The proposed method is fast and memory effect for large-scale implementations.•We used the method for sensitivity analysis on MinRev tolled links.•More practical solutions were explored for two large networks using sensitivity analysis.