An application of stochastic programming on robust airline scheduling

Abstract

The aim of this study is to create flight schedules which are less susceptible to unexpected flight delays. To this end, we examine the block time of the flight in two parts, cruise time and non-cruise time. The cruise time is accepted as controllable within some limit and it is taken as a decision variable in our model. The non-cruise time is open to variations. In order to consider the variability of non-cruise times in the planning stage, we propose a nonlinear mixed integer two stage stochastic programming model which takes the non-cruise time scenarios as input. The published departure times of flights are determined in the first stage and the actual schedule is decided on the second stage depending on the non-cruise times. The objective is to minimize the airline’s operating and passenger dissatisfaction cost. Fuel and CO2 emission costs are nonlinear and this nonlinearity is handled by second order conic inequalities. Two heuristics are proposed to solve the problem when the size of networks and number of scenarios increase. A computational study is conducted using the data of a major U.S. carrier. We compare the solutions of our stochastic model with the ones found by using expected values of non-cruise times and the company’s published schedule.