Airline Schedules Planning Process

The airline schedules planning process is a very complex process which consists of subsequent stages and involves a large number airline resources. The process is usually decomposed into four subproblems: schedule design, fleet assignment, aircraft routing, and crew scheduling. By assuming that flight schedules can be operated as planned, the optimization model for each subproblem is traditionally solved deterministically. But, in day-to-day operations, the schedules are often disrupted and it causes flight delays. These delays often incur significant additional cost, such as excess fuel cost, overtime pay for crews, and re-accommodating passengers cost.

To reduce the operating costs, airlines should minimize the number of flight delays. If

We first to need to analyze historical delay data to see which flights and at which airports that have bigger chances to be delayed. Furthermore, we can model primary delay distributions at the airports which covered by the schedule. For each flight delay in an airport, we record two important characteristics: its delay duration and the departure time of the flight. These characteristics which we collect for an airport, by implementing Kernel Density Estimation approach, yield bivariate distributions for total departure delay and primary delay of the flights depart from the airport. By applying this approach to the other airports which covered by the schedule, we then have bivariate distributions for total departure delay and primary delay of the flights in the schedule. By these bivariate distributions, delay events in an airport can be captured by only one distribution. If we need to focus on delay events in a certain departure time, we can extract the conditional distribution on that time that can be obtained easily from the bivariate distribution. This approach is more general than what we have been done by many researches in which flight delay events are modeled by univariate distribution depend only on delay durations or delay-time. For example, Lan \cite{Lan} modeled arrival delay using a log-normal distribution, Schaefer et al \cite{Schaefer} modeled flight delay and ground

Lan et al. \cite{Lan} constructed a re-timing model to obtain robust aircraft routes which minimized the expectation of total propagated delays, where the model might construct new aircraft routing due to re-timing. The other model was also developed in \cite{Lan} to select departure time of flights that minimized the expected number of disrupted passengers, while maintained the current fleeting, aircraft routes, and passenger itineraries. The re-timing models have been considered to improve the robustness of the integrated schedules. Lee \cite{Lee} introduced a multi-objective model to revise departure time of flights without change the fleet assignment, aircraft routings, and crew pairings. The same approach is used by \cite{Burke} for simultaneous re-timing flights and aircraft re-routing, subject to fixed fleet assignment. The paper by AhmadBeygi et al \cite{AhmadBeygi} and Chiraphadhanakul and Bernhart \cite{Chiraphadhanakul} are the papers that are the most closely related to our research. Both focus on re-distributed slacks by re-timing flights. In \cite{AhmadBeygi}, they derived deterministic mix-integer programming models to re-time departure time of flights. The models are constructed to reduce delay propagations due to aircrafts and cockpit