A solution method for the shared resource-constrained multi-shortest path problem

We tackle the problem of finding, for each network within a collection, shortest path between two given nodes, while not exceeding limits set shared resources. present an integer programming (IP) formulation this and propose parallelizable matheuristic consisting three phases: (1) generation feasible solutions, (2) combination (3) solution improvement. show that paths found with our procedure correspond to some type scheduling problems such as Air Traffic Flow Management (ATFM) problem. Our computational results include finding optimal solutions small medium-size ATFM instances by applying Gurobi IP formulation. use those assess quality output produced proposed matheuristic. For largest instances, which actual flight plans in ATFM, exact methods fail we means Lagrangian bounds. Computational suggest is effective approach family discuss here.