Column generation approaches to a robust airline crew pairing model for managing extra flights

The airline crew pairing problem (CPP) is one of the classical problems in airline operations research due to its crucial impact on the cost structure of an airline. Moreover, the complex crew regulations and the large scale of the resulting mathematical programming models have rendered it an academically interesting problem over decades. The CPP is a tactical problem, typically solved over a monthly planning horizon, with the objective of creating a set of crew pairings so that every ight in the schedule is covered, where a crew pairing refers to a sequence of ights operated by a single crew starting and ending at the same crew base. This paper discusses how an airline may hedge against a certain type of operational disruption by incorporating robustness into the pairings generated at the planning level. In particular, we address how a set of extra fights may be added into the fight schedule at the time of operation by modifying the pairings at hand and without delaying or canceling the existing fights in the schedule. We assume that the set of potential extra fights and their associated departure time windows areknown at the planning stage. We note that this study was partially motivated during our interactions with the smaller local airlines in Turkey which sometimes have to add extra fights to their schedule at short notice, e.g., charter fights. These airlines can typically estimate the potential time windows of the extra fights based on their past experiences, but prefer to ignore this information during planning since these flights may not need to be actually operated. Typically, these extra flights are then handled by recovery procedures at the time of operation which may lead to substantial deviations from the planned crew pairings and costs. The reader is referred to [3] for an in-depth discussion of the conceptual framework of this problem which we refer to as the Robust Crew Pairing for Managing Extra Flights (RCPEF). In [3], the authors introduce how an extra flight may be accommodated by modifying the existing pairings and introduce a set of integer programming models that provide natural recovery options without disrupting the existing flights. These recovery options are available at the planning stage and render operational recovery procedures that pertain to crew pairing unnecessar