Integrated commercial and operations planning model for schedule design, aircraft rotation and crew scheduling in airlines

The commercial and operations planning in airlines has traditionally been a hierarchical process starting with flight schedule design, followed by fleet assignment, aircraft rotation planning and finally the crew scheduling. The hierarchical planning approach has a drawback that the optimal solution for a planning phase higher in hierarchy may either be infeasible for the subsequent phase or may lead to a sub-optimal overall solution. In this paper, we solve a profit-maximizing integrated planning model for clean-sheet “rotated” schedule design with flight re-time option and crew scheduling for a low-cost carrier (LCC) in an emerging market. While the aircraft rotation problem has been traditionally modeled in the literature as a daily routing of individual aircraft for maintenance requirement, in this work we address the requirement of planned aircraft rotations as part of schedule design for LCCs. The planned aircraft routing is important in our case to create as many via-flights as possible due to the underserved nature of the emerging market. We solve this large-scale integer-programming problem using two approaches – Benders Decomposition and Lagrangian Relaxation. For Lagrangian Relaxation, we exploit the special structure of our problem and intuitive understanding behind the Lagrangian duals to develop a multiplier adjustment approach to find an improved lower bound of integrated model solution. The crew-pairing sub-problem is solved using column generation through multi-label shortest path algorithm followed by branch-and-price for integer solution. We test our solution methodology on a flight universe of 378 unique flights for different problem sizes by varying the number of aircraft available for operations. Our computational results show that within a reasonable run time of few hours both the approaches, Benders Decomposition and Lagrangian Relaxation, are successful in finding lower bounds of the integrated model solution, which are higher than the solution of traditional hierarchical approach by 0.5%–2.5%. We find Lagrangian Relaxation methodology to usually attain an improved solution faster than the Benders Decomposition approach, particularly for large-scale problems.