The Fleet Assignment Problem (FAP) of aircraft scheduling in airlines is studied, and the optimization model of FAP is proposed. The objective function of this model is revenue maximization, and it considers comprehensively the difference of scheduled flights and aircraft models in flight areas and mean passenger flows. In order to solve the model, a selfadapting genetic algorithm is supposed to solve the model, which uses natural number coding, adjusts dynamically crossover and mutation operator probability, and adopts intelligent heuristic adjusting to quicken optimization pace. The simulation with production data of an airline shows that the model and algorithms suggested in this paper are feasible and have a good application value.
Fleet Assignment Problem (FAP) is to assign an aircraft model for each scheduled flight according to the capability of passengers, running cost, and planned revenue of each fleet. This is an important work of aircraft scheduling and planning in airlines. The results of FAP affect not only the cost and revenue of airlines, but also the continuing works, such as linking problem between flights, aircraft’s maintenance route, crew assigning, and flight gate assigning. The aircraft scheduling is a controlling work of production scheduling in airlines. Because of the importance and complexity of the aircraft scheduling work in the air transport, the indepth research and application have been carried out in aviation developed countries of Europe and America [
In this paper, according to Chinese factual situation, FAP in airlines is studied in order to establish a foundation for aircraft planning and scheduling automation. Based on the research result, an optimization model of FAP is proposed, which takes the total revenue maximum as objective and can assign an appropriate aircraft type to each flight. For solving the complicated optimization model, an improved genetic algorithm is suggested, which can find out optimal solution quickly. After deep studying, the model and algorithm can be applied in production scheduling of other countries’ airlines.
In production scheduling of airlines, Fleet Assignment Planning is to assign the most appropriate aircraft type to each flight. The flying performance of different aircraft model is different, for example, voyage range, flying altitude ceiling, maximum takeoff weight, and climbing ability. So, a particular route is not suitable for all models of the aircraft to perform. In addition, different models have different seating layout, and their operating costs are not the same. For instance, the seats number of the B737300 aircraft is about 144, and its direct operating costs are between 30 and 50 thousands of RMB per hour. But the A340200 aircraft can seat up to about 380 people, and its direct operating cost is more than 100,000 of RMB per hour. The basis for the development of the work is the airworthiness limitations of flight route on aircraft models, each model's cabin distribution, operational cost analysis of the models in the different routes, as well as forecasts of passenger and freight traffic on each flight. The goal is to optimize the allocation of models to flight, in order to minimize the operating costs to complete the flight running tasks.
Considering the feature of Chinese flight route net and flight plan, under constraints of determined flight schedules, not considering the flight stopovers, only considering aircraft A check, and enough airport capacity, the FAP model which considers the models match, model flying area, as well as the traffic match conditions is proposed as follows:
The objective function (
It is difficult to solve the FAP optimization model with mathematical programming methods, because FAP is an NPhard problem. The genetic algorithm (GA) is an adaptive search algorithm which is based on the natural evolution and selection mechanism. And it has been successfully applied to a variety of optimization problems. In this paper, an improved hybrid heuristic genetic algorithm is constructed to solve the model, considering the limitations of the general genetic algorithm. The algorithm uses natural number coding method and dynamically adjusts the crossover and mutation probability.
The usual method for solving constrained optimization problems is to convert it to unconstrained optimization problem, which incorporated the constrained constraints into the evaluation function using the method of weighting coefficients. Thus, although constrained optimization problems can be solved, infeasible solutions may exist in aviation production scheduling production. In order to guarantee that individuals of each generation are feasible solutions, the algorithm will filter the infeasible solution in each generation solutions for every individual and then adjust the infeasible solutions with intelligent heuristic adjustment method. The heuristic rules of the intelligent heuristic adjustment method are based on expert knowledge and relevant constraints. When the individual does not meet the constraint needed to be adjusted, the algorithm adjusts it according to the individual situation and determines the direction and size of adjustment with the expert knowledge rules. Its goal is to ensure that the adjusted individual is feasible solution and is adjusted along the optimized search direction.
In order to avoid genetic algorithm falling into a local optimum value and having rapid convergence, genetic operator probability adjustment method in the algorithm is used to dynamically adjust the crossover and mutation probability after [
Inputting the data required by model solving: read the corresponding data information to be calculated.
Algorithm parameters initialization: determine the algorithm population numbers and the end of the maximum cycle algebra, the initial values of crossover probabilities
Heuristic correction of the current generation of chromosomes: check the infeasible solutions in chromosomes, and then correct infeasible solutions using the intelligent heuristic rules until they become the feasible solutions.
Calculate the adaptation function value of the current generation of chromosome, and record the best individual as the optimal solution. Then, judge whether to satisfy the end criterion; if the answer is yes, jump to (8), or else, jump to (5).
Adaptive dynamics: adjust the current chromosome probability, and calculate the probability of crossover and mutation
Current chromosome genetic manipulation: Cross is completed with probability
Generation of chromosomes will be selected as the current generation of chromosome; return to (3).
Output current optimal solution as the solution of the algorithm.
In order to validate the model and algorithm supposed in this paper, the data of a mediumsized airline, including 4 aircraft models, 50 flights, is selected to study. Raw data are shown in Tables
The information of aircraft models.
Aircraft 
Model  Maximum passenger 
Code of 

1  B737800  170  1 
2  A320  180  2 
3  B757  239  2 
4  A340  295  3 
The information of flights.
Sequence number  Flight number  Day in week  Departure  Time of departure  Destination  Arrival time  Model code  Mean passengers  Code of flying area  The result of FAP model and algorithm 

1  nx001  1  PEK  16:10  MFM  19:35  1  150  1  4 
2  nx001  2  PEK  16:10  MFM  19:35  1  150  1  2 
3  nx001  3  PEK  16:10  MFM  19:35  1  150  1  2 
4  nx001  4  PEK  16:10  MFM  19:35  1  150  1  1 
5  nx001  5  PEK  16:10  MFM  19:35  1  150  2  3 











44  nx197  3  CTU  17:20  MFM  19:30  3  150  1  3 
45  nx197  5  CTU  17:20  MFM  19:30  3  200  1  2 
46  nx197  7  CTU  17:20  MFM  19:30  3  200  1  3 
47  nx198  3  MFM  14:00  CTU  16:30  3  150  3  2 
48  nx198  1  MFM  14:00  CTU  16:30  3  150  3  1 
49  nx198  5  MFM  14:00  CTU  16:30  3  200  3  2 
50  nx198  7  MFM  14:00  CTU  16:30  3  200  3  1 
The income and cost statistical data of models perform flights (money unit: ten thousands RMB).
Flight sequence  Model code  

1  2  3  4  
Cost  
Revenue  Fixed cost  Variable cost  Revenue  Fixed cost  Variable cost  Revenue  Fixed cost  Variable cost  Revenue  Fixed cost  Variable cost  
1  15  2  1.5  15  2.1  1.8  15  3  2.5  15  4  3 
2  15  2  1.5  15  2.1  1.8  15  3  2.5  15  4  3 
3  15  2  1.5  15  2.1  1.8  15  3  2.5  15  4  3 
4  15  2  1.5  15  2.1  1.8  15  3  2.5  15  4  3 
5  15  2  1.5  15  2.1  1.8  15  3  2.5  15  4  3 













44  13.5  2.2  1.8  13.5  2.5  2  13.5  3  2.6  13.5  4.5  3.2 
45  18  2.2  1.8  18  2.5  2  18  3  2.6  18  4.5  3.2 
46  18  2.2  1.8  18  2.5  2  18  3  2.6  18  4.5  3.2 
47  13.5  2.2  1.8  13.5  2.5  2  13.5  3  2.6  13.5  4.5  3.2 
48  13.5  2.2  1.8  13.5  2.5  2  13.5  3  2.6  13.5  4.5  3.2 
49  18  2.2  1.8  18  2.5  2  18  3  2.6  18  4.5  3.2 
50  18  2.2  1.8  18  2.5  2  18  3  2.6  18  4.5  3.2 
The parameters are selected as follows: the number of population genetic algorithm is 20; the IGA initial crossover probabilities are
Adaptation value curve of two type algorithms (IGA and GA).
According to the algorithm results, the model and algorithm can quickly select execution models for flights and meet the requirements of flight operation. At the same time, it is the good result. According to the chart and tables of the operation results, the improved hybrid genetic algorithm established in this paper is better than the basic genetic algorithm. The result of the operation is better, and the algorithm can quickly jump out of local optimal value. As can be seen from Figure
Many domestic airlines adopt the manner of manpower or halfmanpower to work out FAP plan now. Considering flights listed in tables, it usually takes several hours for dispatcher to weave a feasible fleet assigning plan. And the dispatcher does not have ability to consider too many flights. But with the model and algorithm proposed in this paper, it only takes no more than 1 minute to work out a fleet assigning plan, and this plan is more excellent than former. This can improve the work efficiency and save manpower resource. With the increase of the number of model types and aircraft, the number of flights increasing, that FAP plan worked out by manpower or halfmanpower will become more and more difficult. However, the model and algorithm can work out the FAP plan quickly and greatly improve the level of automation.
In this paper, FAP in airline production scheduling is studied, and the optimization model of FAP is suggested, which considers the requirements of flight operation and takes the consolidated income maximization as the goal considering all flights. At the same time, an adaptive genetic algorithm is constructed to solve the model, which can find out the suitable solution rapidly. The researching on practical production data shows that the model and algorithm are practical and the effect of FAP planning is nice. And if this technique is applied in production scheduling and planning of airlines, the automation level of airlines will be improved, and the running cost will be reduced.
This work is supported by the Unite Foundation of National Natural Sciences Foundation of China and Civil Aviation Administration of China (no. U1233107).