With the development of economy, more and more people travel by plane. Many airports have added satellite halls to relieve the pressure of insufficient boarding gates in airport terminals. However, the addition of satellite halls will have a certain impact on connecting flights of transit passengers and increase the difficulty of reasonable allocation of flight and gate in airports. Based on the requirements and data of question F of the 2018 postgraduate mathematical contest in modeling, this paper studies the flight-gate allocation of additional satellite halls at airports. Firstly, match the seven types of flights with the ten types of gates. Secondly, considering the number of gates used and the least number of flights not allocated to the gate, and adding the two factors of the overall tension of passengers and the minimum number of passengers who failed to transfer, the multi-objective 0–1 programming model was established. Determine the weight vector $w=(0.112,0.097,0.496,0.395)$ of objective function by entropy value method based on personal preference, then the multi-objective 0–1 programming model is transformed into single-objective 0–1 programming model. Finally, a graph coloring algorithm based on parameter adjustment is used to solve the transformed model. The concept of time slice was used to determine the set of time conflicts of flight slots, and the vertex sequences were colored by applying the principle of “first come first serve”. Applying the model and algorithm proposed in this paper, it can be obtained that the average value of the overall tension degree of passengers minimized in question F is 35.179%, the number of flights successfully allocated to the gate maximized is 262, and the number of gates used is minimized to be 60. The corresponding flight-gate difficulty allocation weight is $\alpha =0.32$ and $\beta =0.40$ , and the proportion of flights successfully assigned to the gate is 86.469%. The number of passengers who failed to transfer was 642, with a failure rate of 23.337%.

中文翻译：

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机场登机口分配问题着色方法研究

随着经济的发展，越来越多的人乘飞机旅行。许多机场增加了卫星大厅，以缓解机场航站楼登机口不足的压力。但是，增加卫星大厅将对过境旅客的中转航班产生一定影响，并增加机场合理分配航班和登机口的难度。基于2018年研究生数学竞赛建模问题F的要求和数据，本文研究了机场其他卫星厅的飞行口分配。首先，将七种航班与十种登机口相匹配。其次，考虑使用的登机口数量和未分配给登机口的最少航班数量，加上旅客总体紧张程度和未能转移的最少人数这两个因素，建立了多目标的0-1规划模型。通过基于个人偏好的熵值法确定目标函数的权重向量$ w =（0.112,0.097,0.496,0.395）$，然后将多目标0-1编程模型转换为单目标0-1编程模型。最后，使用基于参数调整的图着色算法来求解变换后的模型。时间片的概念被用来确定飞行时隙的时间冲突的集合，并且通过应用“先到先得”的原则对顶点序列进行着色。应用本文提出的模型和算法，可以得出，将问题F最小化的总体旅客总体紧张程度的平均值为35.179％，成功分配给登机口的最大航班数量为262，使用的登机口数量最小为60。登机口难度分配权重为$ \ alpha = 0.32 $和$ \ beta = 0.40 $，成功分配给登机口的航班比例为86.469％。未中转的乘客人数为642，失败率为23.337％。