Multi-Stage Optimization Method for Dispatch of Ground-Service Vehicles at the Airports During Peak Flight Period
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摘要: 在航班运行高峰时段内，地面服务需求更加集中，机场可调度的地勤车辆数量有限，可能引发航班延误，导致机场多方面损失。针对该问题，研究了地勤车辆多阶段优化调度方法，重点考虑摆渡车和加油车2种地勤保障车路由与时间窗口限制，以航班准点率及延误时间为评价指标进行优化调度。构建了具有4类节点和5类弧的容量-费用网络G1，通过设置合适弧容量及费用参数，确定最小费用流规划模型；采用拉格朗日松弛启发式算法对模型求解，通过不断寻优，设置对偶间隙初值、容许误差，最大迭代次数，输出预测结果；深入分析高峰时段的航班运行状态，构建基于时空网络的整数线性规划模型，优化第一阶段未服务航班的总延误时间；结合最小化最大值定理，构建单航班服务延误模型，将单个航班延误造成的损失降到最低。最后，基于实际航班数据，结合机坪平面布局开展仿真实验和验证，结果表明：利用优化调度得到加油车和摆渡车准时服务的最大航班数分别为30，131架?次，待服务航班的最小总延误时间分别为223，542 min，航班总延误下降21.56%，显著缩短航班延误时间，提升了机场场面的整体运行效率。Abstract: During the peak hours of flights, the demand for ground service is more concentrated. Plus, the limited number of available handing vehicles for dispatching at the airport, flights delay occurs, which have caused losses to the airport in many aspects. Aiming at this issue, a multi-stage optimization method for dispatch of ground-services vehicles is proposed, with a focus on considering the routing and time window constraints of shuttle buses and refueling vehicles. The flight punctuality rate and delay time are used as evaluation indexes to dispatch-optimization. A capacity-cost network G1 with four types of nodes and five types of arcs is developed. By setting appropriate arc capacity and cost parameters, the planning model of the minimum cost flow is determined, and Lagrangian relaxation heuristic algorithm is used to solve the problem. Through continuous optimization, the initial value of the dual gap, the allowable error, and the maximum number of iterations are set, and the prediction results are output. The flight operation status during peak hour is deeply analyzed, and an integer linear programming model is proposed based on a time-space network, in which the total delay of unserved flights is optimized in the first stage. Combined with the minimum-maximum theorem, a delay model for a single flight is developed to minimize the loss. Finally, based on the real flight data, simulation experiments and the method validation are carried out combing with the apron layout. The results shown that: ① the maximum number of flights served on-time by refueling and shuttle vehicles are 30 and 131, respectively; ② the minimum total delay of flights to be served are 223 and 542 min, respectively; ③ the total flight delay decreased by 21.56%, significantly shortening the flight delay and improving the overall operational efficiency at the airport.
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图 6 模型Ⅰ求解加油车、摆渡车调度迭代过程
Figure 6. Model Ⅰ solves the iterative process of fuel truck and ferry scheduling
图 7 多种优化算法求解最小费用流模型的效果对比
Figure 7. Comparison of the effectiveness of various optimizationalgorithms for solving minimum cost flow models
表 1 机场地面保障车辆功能及服务需求
Table 1. Airport ground support vehicle function and service requirements
名称 功能 服务需求 加油车 主要保障出港航班的燃油需求 小型机场采用罐式加油车，单车容量一般不低于20 000 L；大型机场配备管线及适量罐式，各机场最低配备数量应不少于2辆。 摆渡车 远机位进出港旅客的接送 B类及以下飞机配备1辆，C类飞机1~2辆，D类飞机2~3辆，E、F类飞机2~4辆。 
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表 2 航班原始信息（部分）
Table 2. Original flight information (partial)
航班号 起飞时刻 落地时刻 停机位 机型 性质 B1 11：35 13：26 127 A321 离港 B2 10：09 11：12 158 B738 离港 B3 12：52 15：35 712 B738 到港 B4 07：55 10：34 714 A320 到港 B5 14：03 16：20 135 B738 离港 B6 13：00 14：04 139 B738 到港 B7 14：45 15：44 136 A333 离港 B8 20：25 21：15 161 B737 离港 B9 20：37 21：39 524R B738 离港 B10 21：43 00：07 723 B737 到港 B11 08：37 09：37 105 B737 离港 B12 19：33 21：04 724 A320 离港 B13 14：52 16：36 324 A320 到港 B14 18：12 20：23 533 B737 离港 B15 20：32 22：16 111 B737 离港
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表 3 不同停机坪之间以及停机坪与车场之间的车辆行驶时间
Table 3. Vehicle travel distance between different aprons and between aprons and car parks
单位: min 地点 停机坪C3 停机坪C5 停机坪C7 停机坪E5 停机坪E3 车场P1 停机坪C3 0 8 2 4 4 2 停机坪C5 8 0 8 6 11 9 停机坪C7 2 8 0 2 4 2 停机坪E5 4 6 2 0 6 3 停机坪E3 4 11 4 6 0 5 车场P1 2 9 2 3 5 0
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表 4 机场摆渡车调度方案
Table 4. Airport ferry scheduling program
车辆编号 优先服务航班序列 次服务航班序列 总服务时间/min 车辆编号 优先服务航班序列 次服务航班序列 总服务时间/min 1 1 → 14 → 27 → 33 → 56 74 210 16 7 → 21 → 35 → 48 62 → 71 234 2 1 → 14 → 27 → 33 → 56 75 201 17 7 → 20 → 36 → 48 63 → 74 242 3 2 → 14 → 27 → 34 → 57 None 174 18 8 → 20 → 36 → 49 63 211 4 2 → 16 → 30 → 34 → 57 None 184 19 8 → 22 → 39 → 49 64 206 5 2 → 16 → 30 → 43 → 55 72 209 20 9 → 22 → 39 → 50 64 228 6 3 → 18 → 28 → 43 → 55 72 202 21 9 → 25 → 37 → 50 65 217 7 3 → 18 → 28 → 44 → 58 None 174 22 10 → 25 → 37 → 51 65 → 75 259 8 4 → 15 → 29 → 44 → 58 None 174 23 10 → 26 → 38 → 51 66 196 9 4 → 15 → 29 → 45 → 59 None 181 24 11 → 26 → 38 → 52 67 212 10 5 → 17 → 29 → 45 → 59 None 174 25 11 → 23 → 42 → 52 68 204 11 5 → 17 → 31 → 46 → 70 60 223 26 11 → 23 → 42 → 52 68 204 12 5 → 19 → 31 → 46 → 70 60 224 27 12 → 24 → 41 → 53 66 210 13 6 → 19 → 32 → 46 → 71 61 216 28 12 → 24 → 41 → 53 67 204 14 6 → 21 → 32 → 47 61 → 73 246 29 13 → 17 → 54 69 150 15 7 → 21 → 35 → 47 62 → 73 247 30 13 → 17 → 54 69 150
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表 5 机场加油车调度方案
Table 5. Airport fuel truck dispatching program
车辆编号 优先服务航班序列 次服务航班序列 总服务时间/min 车辆编号 优先服务航班序列 次服务航班序列 总服务时间/min 1 1→18 31 73 9 9→26 None 42 2 3→20 33 69 10 11→22 None 34 3 2→17 34 96 11 13→28 None 37 4 5→25 32 101 12 10→30 None 41 5 4→24 39 108 13 12→27 None 34 6 6→19 29 90 14 15 36 45 7 8→23 35 89 15 16→37 None 34
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