Integrated Airline Scheduling
4.3 Sequential Approach .1 Overview.1Overview
4.3.3 Solution Process
Flight Addition. In this step, new round-trip flights are created and included in the schedule. The number of new flights is chosen according to a percentage pnew∈[0,1]of the number of flights in the current schedule. The markets in which new flights are added are chosen randomly according to the size of the remaining demand in this market (high demand markets receive a higher selection probabil- ity). The parameter twnew=2·tw controls the length of the time window for the fleet assignment step (see page 103). The larger time window increases the flexi- bility which is necessary to fit the new flights into the schedule. The probability of assigning the attribute optional for the new flights is 1−popt.
114 4 Integrated Airline Scheduling
Flight Choice. The fleet assignment is infeasible if too many flights exist that have to be assigned to all aircraft or aircraft of one fleet type. The Flight Choice step changes the attribute optional of the flights indicating whether the fleet assignment model might remove the flight from the schedule. This step corresponds to the Flight Choice step presented on page 112.
Increase Connectivity. One goal of the maintenance routing is to construct one ro- tation per fleet. Thus, it is necessary that all flights can be ordered in a sequence that can be flown by one aircraft. In addition, the fleet assignment problem might be dif- ficult to solve or even infeasible if there are a lot of flights spread over many different airports. In this case, meeting the flow balance could be difficult to achieve for each fleet type. The Increase Connectivity step assists in both the following cases, main- tenance routing and fleet assignment. This algorithm changes, removes and inserts flights that increase the connectivity within the airline’s flight network. The number of flights being subject to modification is controlled as percentage pcnx∈[0,1]of the total number of flights. The selection of flights to be changed follows the amount of traffic at the airports: the more traffic at one airport according to the actual flights, the higher the chance that this airport will get additional (departing and arriving) flights, and vice versa. Any imbalances at the airports additionally increase the probability of modifying related flights to reduce the imbalance. In addition, the Flight Choice step is conducted, also simplifying the fleet assignment and the maintenance routing, because there are fewer flights that need to be assigned to a fleet or rotation.
Insert Maintenance Flights. The maintenance routing problem can only be solved if there are enough flights to a maintenance station at the end of each day. If there is no flight to a maintenance station, the three-day maintenance routing is infeasible and even the advanced mechanisms presented in Sect. 4.3.2.2 cannot produce a valid routing. If there are no sufficient flights to or from the maintenance stations for each fleet type, a flight departing from a maintenance station is created and included into the schedule for each affected fleet type. The maintenance station and the arrival airport are chosen randomly, the departure time is as early as possible. To prevent flow imbalances, the Balance Schedule mechanism needs to follow each insertion of a new maintenance flight. The new flight is necessary to comply with the main- tenance constraints but might have a poor profit share. To prevent the removal of this flight by the fleet assignment or assignment of another fleet to minimize costs, this flight receives the attribute maintenance (see page 103) indicating that the flight is fixed and may not be changed or removed by the fleet assignment algorithm.
However, the optimization steps might change this flight because these steps always consider the three-day-maintenance routing constraint when applying changes to the schedule. For example, a new maintenance flight with a poor profit share might be modified regarding its destination airport or departure time. In addition, the depart- ing maintenance station might be exchanged with another maintenance station for this flight.
Use Optimized Schedule. The sequential approach represents an iterative proce- dure: after the optimization steps presented in Sect. 4.3.2.3 the complete process starts again with the flight scheduling and fleet assignment step. Then, the fleet as- signment might be infeasible due to the new additional flights that were inserted with the last optimization step Flight Addition. The Use Optimized Schedule then assigns the attribute optional (see page 103) to some new flights and removes this attribute from old flights (that was set by the Flight Choice step), relaxing the fleet assignment problem. More than one attempt might be necessary until the fleet as- signment problem can be solved, in each attempt the number of affected flights is increased. If this percentage reaches 100%, the Flight Choice and Flight Addition steps are revoked and the schedule produced by the Airport Optimization represent- ing the last feasible solution step is processed by the fleet assignment.
4.3.3.2 Schedule Initialization
By combining the solution steps and the supportive functions to the overall plan- ning procedure, an airline schedule can be optimized following the sequential and iterative planning paradigm. However, the presented mechanisms need an initial schedule to start with. Because the maintenance routing algorithm and the optimiz- ing steps Slack Reduction and Flight Addition iteratively insert new flights into the schedule, an initialization method only needs to construct a very basic schedule which will then be improved and extended using the procedures mentioned. For this approach, this basic initial schedule is created by constructing one flight for each air- craft available. These flights are created in those markets with the highest remaining market size (passenger demand after subtracting passengers currently traveling on the competitors’ flights and own flights already included in the schedule). Departure times are the peak times of the demand distribution over the day (see Fig. 4.12). To be solvable by the first fleet assignment step, the Balance Aircraft Flow function is applied. Then, after the fleet assignment, the maintenance routing is likely to insert additional flights because the number of LOFs should be smaller than the number of aircraft and the LOFs might not be connected. After maintenance routing, the Slack Reduction method will insert additional flights, because there is a lot of idle ground time available since there is only one flight per aircraft in the schedule.
To summarize, schedule initialization does not consist of one single function cre- ating an extensive and acceptable first schedule; instead, it provides a very basic schedule that then is iteratively extended with new flights and improved using the solution steps and supportive functions.
4.3.3.3 Integration
The main challenge in constructing a complete airline scheduling procedure based on the described methods is to link the single steps so that each can solve its sub- problem based on the given output of the preceding step and produce a feasible solution. In addition, since the procedure should be able to construct schedules for
116 4 Integrated Airline Scheduling any given setting, there should be no restrictions on the given input data. After an initial schedule is created, the fleet assignment, maintenance routing, and schedule optimization are conducted; then, these three steps are performed iteratively until the optimizing steps cannot improve the schedule any more or until there was no increase in profit after imaxiterations.
Fig. 4.22 Sequential airline scheduling approach flowchart (part 1)
In the following figures, an overview of the complete sequential approach is pre- sented as a flowchart. Because of its complexity, the total procedure is split up into two figures 4.22 and 4.23. Transitions between both figures are denoted as circles with appropriate letters. The main solution and optimization steps can be identified by the boxes with thick frames.
Fig. 4.23 Sequential airline scheduling approach flowchart (part 2)
118 4 Integrated Airline Scheduling