Probabilistic Airline Reserve Crew Scheduling Model

This paper introduces a probabilistic model for airline reserve crew scheduling. The model can be applied to any schedules which consist of a stream of departures from a single airport. We assume that reserve crew demand can be captured by an independent probability of crew absence for each departure. The aim of our model is to assign some fixed number of available reserve crew in such a way that the overall probability of crew unavailability in an uncertain operating environment is minimised. A comparison of different probabilistic objective functions, in terms of the most desirable simulation results, is carried out, complete with an interpretation of the results. A sample of heuristic solution methods are then tested and compared to the optimal solutions on a set of problem instances, based on the best objective function found. The current model can be applied in the early planning phase of reserve crew scheduling, when very little information is known about crew absence related disruptions. The main conclusions include the finding that the probabilistic objective function approach gives solutions whose objective values correlate strongly with the results that these solutions will get on average in repeated simulations. Minimisation of the sum of the probabilities of crew unavailability was observed to be the best surrogate objective function for reserve crew schedules that perform well in simulation. A list of extensions that could be made to the model is then provided, followed by conclusions that summarise the findings and important results obtained. 1998 ACM Subject Classification G.1.6 Optimization, G.3 Probability and Statistics