Robust crew pairing for managing extra flights

This paper discusses a modeling approach to robust crew pairing when a set of extra flights is likely to be added to the regular flight schedule. The set of these possible extra flights is known at the planning stage. We demonstrate that these extra flights may be incorporated into the schedule if necessary by modifying the planned crew pairings appropriately and without delaying or canceling existing flights. To this end, we either identify a pair of crews whose schedules may be (partially) swapped while adding an extra flight into the schedule or show that an extra flight may be inserted into the schedule of a crew without affecting others. We note that deadheading may be necessary in either case. For these two types of solutions, we define the appropriate feasibility rules with respect to the common airline regulations. We then propose two robust mathematical programming models that consider incorporating such solutions into the set of selected pairings while keeping the increase in the crew cost at an acceptable level. The baseline solution for comparison is found by a conventional crew pairing model in the literature which ignores robustness at the planning stage and relies on recovery procedures at the time of operation. We also propose the variations of the two models, where the double counting of the possible solutions across extra flights is prevented. Finally, we conduct computational experiments on a set of data generated from the actual data of an airline company. We solve the crew pairing problem both with the proposed robust models and the conventional model. Our results demonstrate the benefits of the proposed modeling approach and indicate that the proposed robust models provide natural options to recovery without disrupting the existing flights at a relatively small incremental cost, which is visible at the planning stage.