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. Due to dependencies between flights the timing of a duty period of a reserve crew member influences the probabilities of flight cancellations and also the probabilities that other reserve crew are required to replace absent. These interactions make the exercise of scheduling reserve crew duties a combinatorial optimisation problem. This work develops an enhanced mathematical model for assessing the impact of any given reserve crew schedule, in terms of expected cancellations and reserve induced delays. The proposed model produces results that match a simulation model, in a much shorter time. The model is then used as a fitness function in metaheuristic algorithms and the results are analysed in detail.