A novel matheuristic approach for a two-stage transportation problem with fixed costs associated to the routes

•We focus on the two-stage transportation problem with fixed costs associated to the routes.•We present a matheuristic approach for solving problem.•Our algorithm is obtained by incorporating a linear programming optimization problem within the framework of a genetic algorithm.•The computational results that we achieved, demonstrate that our solution approach is efficient in yielding high quality solutions. Transportation problems are nowadays strategic issues which aim at selecting the routes to be opened between different facilities in order to achieve an efficient distribution strategy. This paper presents a matheuristic approach for solving the two-stage transportation problem with fixed costs associated to the routes. Our heuristic algorithm is designed to fit the challenges of the investigated transportation problem and is obtained by incorporating a linear programming optimization problem within the framework of a genetic algorithm. In addition we integrated within our proposed genetic algorithm a powerful local search procedure capable of fine tuning the global search. We evaluated the performance of the proposed solution approach on two sets of benchmark instances available in the literature. The computational results that we achieved, demonstrate that the solution approach we propose is efficient in yielding solutions that are high in quality which occur during running times that are considered reasonable, besides its superiority in comparison with other existing competing methods from the literature.