Models and column generation approach for the resource-constrained minimum cost path problem with relays

We present a pattern-chain formulation and develop a column generation based exact approach for the RMCPR. We design a Lagrangian relaxation based method to efficiently price out columns to enter the basis. We present computational results on three sets of 560 randomly generated instances with different properties. Computational results demonstrate that our proposed algorithm is an efficient exact method for solving the RMCPR.