Chapter 5
the airline and the assignment of the resources. Hence, an optimal schedule repre- sents the most efficient and effective deployment of an airline’s resources while best satisfying potential passenger demand. It is the central element within an airline’s corporate planning system, because it affects almost every operational decision and has the largest impact on profitability.
As a consequence, the construction of an airline schedule is one of the most impor- tant but also most complex planning tasks of each airline. Many factors such as de- mands in various markets, competition, and available resources have to be taken into account. Unfortunately, a single optimization model for the complete airline schedul- ing problem is intractable when using exact optimization techniques. Instead, this problem is solved in a sequential approach. The overall problem is decomposed into subproblems of less complexity; these subproblems are solved in a sequence, and the solution of one problem serves as input for the next problem. Some subproblems are grouped together to form airline scheduling phases. One possible decomposition of the overall problem and aggregation of the subproblem to scheduling phases is pro- posed on page 10. Many different solution approaches were developed for individual planning steps. An extensive presentation of these models and the underlying prob- lems including their objectives and constraints are given in Sect. 2. Since in general a decomposition of a problem cuts interdependencies between decision variables, and a solution sequence limits flexibility of later planning steps, only suboptimal or even infeasible solutions of the problem can be achieved. To reduce these disadvan- tages for the airline scheduling problem, airlines usually implement iterations in the planning process where solutions or details of later planning steps are processed to earlier steps. However, since it is impossible that a sequential solution approach can achieve better or equal solutions than a simultaneous approach, research focuses on the integration of different subproblems into a single optimization model. Models that aim at integrating selected subproblems are presented in Sect. 2.5.
The objective of this study is to fill a large gap between the status quo in airline scheduling and the optimal scheduling using a fully integrated optimization model that includes all subproblems and represents airline operations on a sufficient level of detail. For this purpose, two airline scheduling approaches were developed that integrate the flight schedule generation and aircraft scheduling phase into a single scheduling approach. Their only requirement is to receive a quality measure for each schedule processed. As schedule evaluation applications used by airlines and their required parameters and data are not available for this study, a custom evaluation procedure was developed that estimates the operating profit for any given airline schedule (Sect. 4.2). One of the two approaches for airline schedule optimization (presented in Sect. 4.3) follows the traditional planning paradigm of iteratively and sequentially solving subproblems of the overall airline scheduling problem. For the individual solution steps, existing models from literature were used, which are then integrated in a complete planning procedure. The other airline scheduling approach (presented in Sect. 4.4) is based on self-adaptive metaheuristic optimization in which complete airline schedules are processed at once. Because in each schedule the sub- problems and interdependencies are included implicitly, the optimization results in a truly simultaneous airline scheduling approach.
5.3 Future Work 175 A comparison in which both approaches are applied to the same scenarios con- firmed the postulated higher performance of a simultaneous optimization since the simultaneous approach outperformed the sequential approach with regard to the operating profit of the obtained schedules and the required computational effort (Sect. 4.5.1). The capability of the simultaneous approach is further demonstrated by verifying its results for systematically modified planning scenarios (Sect. 4.5.2).
5.2 Conclusion
The simultaneous planning approach of this study optimizes a large portion of the overall airline scheduling problem in an integrated procedure while minimizing sim- plifying assumptions in comparison to existing solution models. It can be used for decision support for flexible airline scheduling, because it only requires given exter- nal data and the supply data from an airline. Furthermore, the objective of scheduling is not limited to maximizing operating profit but can include any quantifiable goal.
Thus, many of the challenges or requirements formulated in state-of-the-art air- line operations research literature are fulfilled. The main objective – further inte- grating subproblems towards the ideal model of a fully integrated overall scheduling approach – is achieved. Until now, an integrated model including the subproblems network design, frequency assignment, flight scheduling, fleet assignment, and air- craft routing has not been developed. All schedule elements that are assumed to be given in other approaches (like the network structure, number of hubs, etc.) are a result of optimization. Thus, this model represents the most integrative airline scheduling approach at this time. Experiments on the simultaneous and sequential approach were conducted that verify the postulated better performance of a simul- taneous optimization for the test scenarios used in this study.
Compared to existing models, the planning approach of this study represents air- line operations on a high level of detail without simplifying assumptions. For exam- ple, existing models assume uniformly distributed passenger demand, a monopoly situation, a single fleet, a given and static hub-and-spoke network structure etc.
In contrast, the simultaneous planning approach presented here optimizes airline schedules for any given planning scenario. This allows a very flexible scheduling, since only given external data and the supply data of the airline have to be provided;
a modification of the solution approach is not necessary. In addition, the ability to easily change the objective function or to include restrictions or managerial con- straints as penalty costs further increases the flexibility of the approach. Changes in the input can be easily evaluated according to the given objective and operational impacts. Furthermore, an airline can apply what-if scenarios to review future direc- tions and to test different courses of action. Thus, the planning approach enables a powerful decision support for airline scheduling.
5.3 Future Work
As described in the corresponding sections, many further enhancements to improve scope and solution quality are possible. The simultaneous solution approach pro- vides large flexibility and allows easy modifications of the optimization objective or
general conditions. Sect. 4.6.4 presents how some basic elements of crew scheduling can be included in the planning approach of this study. However, since crew costs represent one of the highest expenses of an airline, additional effort is necessary to incorporate the complete crew planning into this scheduling approach. If success- fully accomplished, the resulting model should be close to the ideal model airline operations research demands, since all subproblems currently tackled independently could then be solved in one step.
Another challenge receiving much attention by researchers today is to increase the robustness of airline schedules. Traditional solution models are based on determin- istic data, although many influencing factors are of stochastic nature. Thus, often the schedule is not executed as planned. For example, adverse weather or maintenance issues cause irregular operations in the scheduled activities. To minimize the effect of these disruptions, stochastic elements can be included in the schedule evaluation.
Then for example, a schedule is not only evaluated according to the operating profit but also to the probability and the extent of possible delays caused by disruptions.
Although such an assessment of a schedule might represent a complex task itself, it could be easily included as fitness function for the presented metaheuristic search.
Although the level of detail in which airline operations are represented is much higher in this study than in previous contributions, there is still much room for fur- ther enhancements regarding practical considerations. For example, the schedule evaluation procedure does not yet distinguish between business and leisure travelers and different seating configurations of the aircraft. Furthermore, curfew restrictions only take required runway lengths and a single period of night-flying restrictions per airport into consideration. In reality, these influences consist of many different elements that should be modeled in the airline scheduling approaches. Another lim- iting factor is airport slots. In Europe, the major airports usually have fewer slots available than airlines demand. Taking into account the expected future growth in airline traffic, slots will even more reduce the degree of freedom in airline schedul- ing. As a consequence, the scheduling procedures presented in this study should be further extended to include slot restrictions.
Until now, this study represents a theoretic framework; its applicability in real- world airline scheduling still has to be assessed. Hence, the planning scenarios and all input used in this study should be replaced by existing data from an airline. This also should enable the use of planning scenarios from regions other than Europe, to which this study was limited because of the availability of data. If possible and applicable, using the same scenario and prerequisites for optimization which real airline schedules were based on, the presented approach can be further evaluated and compared to the corresponding real-world schedules. Additional enhancements based on such practical experience would then advance the presented approach for integrated airline scheduling to an important and valuable optimization technique for both theory and practice.