Integrated Airline Scheduling
4.3 Sequential Approach .1 Overview.1Overview
4.3.5 Summary and Conclusion
126 4 Integrated Airline Scheduling
Fig. 4.34 Profit contribution by individual solution steps (scenario A, run3)
50000 100000 150000 200000 250000 300000 350000 400000 450000 500000
Profit
Iteration
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Fig. 4.35 Profit contribution by individual solution steps between iteration 3 and 5 (scenario A, run3)
100000 150000 200000 250000 300000 350000 400000 450000 500000
Fleet Assignment Maintenance Routing Slack Reduction Airport Removal Airport Optimization Fleet Assignment Maintenance Routing Slack Reduction Airport Removal Airport Optimization Fleet Assignment Maintenance Routing Slack Reduction Airport Removal Airport Optimization
Profit
Iteration 3 Iteration 4 Iteration 5
the fleet assignment step (for example in iteration 5 in Fig. 4.35) can be explained by the objective function of this step, which is to minimize costs (operating and spill costs). Because revenues are not taken into account, minimizing operating costs can contradict maximizing profit. For example, if no flights at all are conducted, operat- ing costs are minimized without earning operating profit.
manual inputs and feedback loops are necessary to apply the models to airline scheduling; in the scheduling procedure presented here, these assisting decisions are made by some modifications to the existing (original) models and by supportive functions. Their objective is to better link the individual solution steps. If a feasible solution cannot be obtained by one model, its input is modified in order to increase the chance of finding a good solution.
Parameters that control the overall planning procedure were obtained by testing various settings with regard to the operating profit for five different planning sce- narios. The calibrated model was then applied to these scenarios for an analysis of the obtained solutions and the search process. The solutions of the different runs are stable with regard to the resulting operating profit, number of flights, number of pas- sengers etc. However, differences exist in the effort of the optimization runs. There are large variations in the number of fitness evaluations and in the number of solu- tion iterations. One factor contributing to this observation is the unstable optimiza- tion progress which is characterized by peaks and drops of the profit even between succeeding iterations. A closer look at the profit contribution of each solution step within an iteration unveils the fact that the application of the maintenance routing step is most likely responsible for the drops, which are then again compensated by the optimization steps. Since the fleet assignment preceding the maintenance rout- ing might produce schedules that consist of locked rotations or do not fulfill the maintenance requirements, the schedules have to be repaired, which is conducted regardless of the profit.
4.3.5.2 Conclusion
Because of the stepwise approach, supportive functions had to be included that assist each step to find a feasible solution and to integrate the individual solution steps into one iterative procedure, leading to a rather complex planning procedure.
The (simplified) flowchart in figures 4.22 and 4.23 gives an impression of this complexity. Consequently, different parameters had to be set to control the plan- ning procedure.19Their calibration was conducted ceteris paribus. Because inter- dependencies between the parameters are likely to exist, an extensive calibration process in which all possible parameter combinations are tested should be con- ducted in future work. In addition, some alternative options within each solution step could be tested to find out whether they would result in more profitable so- lutions (for example the LIFO-rule instead of the FIFO-rule in maintenance rout- ing or the number of flight arcs per flight in the fleet assignment model). Another option is to change the order in which the three individual optimization steps are conducted.
A major drawback of the presented approach is its sequential planning paradigm.
Each solution step has a different objective function which conflict to some extent.
For example, the objective of fleet assignment is to minimize costs (operating and
19Many more additional, but less important parameters could be selected in some of the planning approach’s functions. Since unlimited effort could be made to test all values for all parameters, they were set by common sense.
128 4 Integrated Airline Scheduling spill costs), not to maximize revenue. Thus, minimizing operating costs could be realized by conducting only a small number of flights.20In addition to conflicting objectives, constraints of one solution step can often not be fulfilled based on the given input from the preceding step. For example, the maintenance routing has to find a routing that is feasible with regard to maintenance restrictions. For this pur- pose, the flights and the fleet assignment might be changed, reducing the solution quality. Although in this study these modifications take market sizes into account, this effect is rather strong because sometimes it is difficult to find a feasible routing.
In such cases, many changes are applied to the schedule, often resulting in a much lower solution quality. This effect can be observed in figures 4.34 and 4.35, in which a decrease in solution quality follows the maintenance routing step.
In addition to some drawbacks resulting from the stepwise planning paradigm and the inadequate linkage between the steps, the individual solution steps inhibit some limitations. For example, the optimization steps are straightforward but not exclusive. They represent local search operators, which could be further improved by enlarging the neighborhood related to each modification or by changing the type of modification (for example, changing the fleet assignment). A second example is the maintenance routing step, representing a simplified model of the real mainte- nance problem that does not take all practical requirements into account. There is no capacity constraint for maintenance at the airports; in general, there could be a solution with every aircraft undergoing maintenance at the same airport on the same day, which would be unrealistic in practice. In addition, it is assumed that maintenance always takes place at night after at least three days, there is no consid- eration of the real flight hours conducted and the minimal time of duration required by maintenance. In practice, maintenance is performed after a maximum number of flight hours or landings and requires a specific amount of time, varying across different fleet types and airports.
On the other hand, the separation of the different solution steps allows a straight- forward improvement of the individual tasks. Necessary input and output data of each step is known (and – if necessary – modified by the supportive functions), and each individual procedure can be replaced by an improved version. These improve- ments can also include an extension of the scope and further integration, reducing the amount of supportive functions necessary. For example, if an improved fleet assignment model including maintenance consideration could be implemented, the destructive effects of the maintenance routing algorithm might be reduced possi- bly leading to a much more progressive optimization process.21Since many differ- ent procedures are included in the overall planning approach (solutions steps and supportive functions), there are many starting points for further improvements and enhancements.
20This applies to flights with the attribute optional, since all other flights have to be conducted
21Of course, an extended model must include at least the capability of the previous model. In this example, an improved fleet assignment model still has to decide on the flight scheduling.