Simultaneous Schedule Design & Routing with Maintenance Constraints for Single Fleet Airlines

We propose to find simultaneously the flight schedule design and the aircraft routing, considering at the same time maintenance requirements. This approach leads to a closer global optimal solution than the typical sequential one, and it is practical for the case of airlines with a single fleet, such as many emerging young low-cost airlines. The formulation of this optimization problem is a Longest Path Problem with maintenance requirements as side constraints. It is based on a network diagram where a flight schedule is defined as the set of legs included in all routes to be flown. Then an algorithm to solve this integrated problem is proposed. It is a greedy heuristic that starting from a given large number of potential flight legs, it identifies at each cycle the route that provides the maximum profit. The model was tested using 7 instances extracted from real-world timetables of three Latin American airlines. It was found that the model can be solved using standard type of computers in less than a minute for single fleet airlines with less than 10 aircrafts. Results were compared to the ones obtained from a scheduling model that does not include maintenance constraints. This approach allowed comparing the results with lower bounds of the cost per flight times. It was found that for most of the instances, the proposed approach generates the same values.