Applying Lagrangian relaxation-based algorithms for airline coordinated flight scheduling problems

20 and 21 employed network flow techniques to construct coordinated scheduling models for passenger- and cargo-transportation, respectively. These models are formulated as mixed integer multiple commodity network flow problems with side constraints (NFPWS) that are characterized as NP-hard. Problem sizes are expected to be huge making the model more difficult to solve than traditional passenger/cargo flight scheduling problems. Therefore, a family of Lagrangian based algorithm is developed to solve the coordinated fleet routing and flight scheduling problems. Numerical tests are performed to evaluate the proposed algorithm using real operating data from two Taiwan airlines. The test results indicate that these solution algorithms are a significant improvement over those obtained with CPLEX. Moreover, the Lagrangian based algorithms are better than the mixed-stop heuristic, consequently they could be useful for allied airlines to solve coordinated fleet routing and flight scheduling problems.