Airlines need to expand their flight network with developing new routes and introducing more flights to increase their market share. In this work, we propose a two-stage stochastic mixed integer nonlinear program (MINLP), which expands an existing flight schedule by operating new flights either with existing fleet resources or a leased aircraft while considering the impact of departure time decisions on the probability distribution of random demand. Moreover, our study helps an airline to link a strategic decision of leasing an aircraft to the tactical aircraft assignment decisions by considering the fuel efficiency and the seat capacity of the aircraft alternatives in response to new passenger demand. However, the large number of scenarios, nonlinear fuel burn function and nonlinearities due to the decision dependent probabilities become main challenges of solving the problem. To deal with the computational requirements of a two-stage stochastic MINLP with decision dependent probabilities, we propose strong conic quadratic and McCormick inequalities, and an exact scenario group wise decomposition algorithm with a new bounding method. In our computational results, we clearly demonstrate the effectiveness of proposed decomposition algorithm and the strength of the reformulations.

This is a joint work with Prof. M. Selim Akturk and Assoc. Prof. Ozlem Cavus Iyigun.