Fleet type assignment and robust airline scheduling with chance constraints under environmental emission considerations

Fleet Type Assignment and Robust Airline Scheduling is to assign optimally aircraft to paths and develop a flight schedule resilient to disruptions. In this study, a Mixed Integer Nonlinear Programming formulation was developed using controllable cruise time and idle time insertion to ensure passengers’ connection service level with the objective of minimizing the costs of fuel consumption, CO2 emissions, idle time and spilled passengers. The crucial contribution of the model is to take fuel efficiency of aircraft into considerations to compensate for the idle time insertion as well as the cost of spilled passengers due to the insufficient seat capacity. The nonlinearity in the fuel consumption function associated with controllable cruise time was handled by second order conic reformulations. In addition, the uncertainty coming from a random variable of non-cruise time arises in chance constraints to guarantee passengers’ connection service level, which was also tackled by transforming them into conic inequalities. We compared the performance of the schedule generated by the proposed model to the published schedule for a major U.S. airline. On the average, there exists a 20% total cost saving compared to the published schedule. To solve the large scale problems in a reasonable time, we also developed a two-stage algorithm, which decomposes the problem into planning stages such as fleet type assignment and robust schedule generation, and then solves them sequentially.