A Network-Based Model for the Integrated Weekly Aircraft Maintenance Routing and Fleet Assignment Problem

Most studies in airline operations planning research are focused on the optimization problems that deal with a daily flight schedule, which is considered to be the same for every day in the week. While the weekly schedule is more realistic and practical, it increases the complexity of the optimization problems drastically. In this paper, we present a novel weekly rotation-tour network representation for the weekly aircraft maintenance routing problem WAMRP. Based on this representation, we propose a new network-based mixed-integer linear programming LP formulation for the WAMRP; namely, weekly rotation-tour network model WRTNM. The main advantage of this formulation is that the size of WRTNM only increases linearly with the size of the weekly schedule, and it provides a very tight LP relaxation. In addition, because of the tight LP relaxation, we develop a diving heuristic to solve WRTNM efficiently and effectively. To assess the performance of WRTNM, we tested the WRTNM using eight real-life test cases. The computational results show that the proposed model is very compact and scalable, and is able to find the optimal solutions to the schedule with 5,700 flights and 330 aircraft, approximately the size of the world's largest airlines fleet, within five minutes. We also propose an integrated model to solve the WAMRP with the weekly fleet assignment problem simultaneously. We tested the integrated model on nine self-constructed test cases. The computational results show that the integrated model generates near-optimal solutions to the schedules with 1,700 flights, 8 fleets with 110 aircraft, and approximately a medium-sized airline, in a reasonable time.