Scheduling airline reserve crew using a probabilistic crew absence and recovery model

Airlines require reserve crew to replace delayed or absent crew, with the aim of preventing consequent flight cancellations. A reserve crew schedule specifies the duty periods for which different reserve crew will be on standby to replace any absent crew. For both legal and health-and-safety reasons the reserve crew's duty period is limited, so it is vital that these reserve crew are available at the right times, when they are most likely to be needed and will be most effective. Scheduling a reserve crew unnecessarily, or earlier than needed, wastes reserve crew capacity. Scheduling a reserve crew too late means either an unrecoverable cancellation or a delay waiting for the reserve crew to be available. Determining when to schedule these crew can be a complex problem , since one crew member could potentially cover a vacancy on any one of a number of different flights, and flights interact with each other, so a delay or cancellation for one flight can affect a number of later flights. This work develops an enhanced mathematical model for assessing the impact of any given reserve crew schedule, in terms of reduced total expected cancellations and any resultant reserve induced delays, whilst taking all of the available information into account, including the schedule structure and interactions between flights, the uncertainties involved, and the potential for multiple crew absences on a single flight. The interactions between flights have traditionally made it very hard to predict the effects of cancellations or delays, and hence to predict when best to allocate reserve crew and lengthy simulation runs have traditionally been used to make these predictions. This work is motivated by the airline industry's need for improved mathematical models to replace the time-consuming simulation-based approaches. The improved predictive probabilistic model which is introduced here is shown to produce results that match a simulation model to a high degree of accuracy, in a much shorter time, making it an effective and accurate surrogate for simulation. The modelling of the problem also provides insights into the complexity of the problem that a purely simulation based approach would miss. The increased speed enables potential deployment within a real time decision support context, comparing alternative recovery decisions as disruptions occur. To illustrate this, the model is used in this paper as a fitness function in meta-heuristics algorithms to generate disruption minimising reserve crew schedules for a real airline schedule. These are shown to be of a high quality, demonstrating the effectiveness and reliability of the proposed approach