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摘要:
为了帮助航空公司合理规划航线网络，降低运输成本，从航空公司的角度出发，将机场容量看作到港和离港航班的函数，绘制了机场容量包络曲线。基于机场容量包络曲线构建了随机需求下多分配、非严格的两阶段混合整数随机规划模型，第1阶段确定网络的枢纽位置，第2阶段确定不同需求情形下城市对的运输路径和不同路径上的流量比例。当需求情形是离散变量时将两阶段模型转化为确定的等价规划。继而以东航为例选取13个机场对模型进行验证，并对运输成本折扣因子进行灵敏度分析。结果表明：在不同的折扣因子情形下选择的枢纽机场不同，折扣越大，选择的枢纽越多，网络总成本越低，且3种折扣因子情形下的枢纽选择与实际比较吻合；每种折扣因子情形下，当需求不同时航线网络的布局有所差异；对比需求确定和不确定下的模型结果差异，得出需求不确定下的网络总成本更低。可见需求不确定下的随机规划模型更加贴近实际，能够帮助航空公司规划符合实际情形的枢纽航线网络，并确定其在枢纽机场的容量份额。
Abstract:In order to help airlines plan route network reasonably and reduce operation cost, from the perspective of airlines, airport capacity is regarded as a function of arrival and departure flights to draw airport capacity envelope curve. Based on airport capacity envelope curve, a two-stage mixed integer stochastic programming model with multi-allocation and non-strictness under stochastic demand is established. In the first stage, the hub location of the network is determined, and in the second stage, the transportation routes of each city pair and the flow ratios of different routes under different demand scenarios are determined. When demand scenario is a discrete variable, the model is transformed into a deterministic equivalent programming. Then taking China Eastern Airlines as an example, 13 airports are selected to validate the model, and the sensitivity analysis of transportation cost discount factor is carried out. The results show that the hub airports selected under different discount factors are different, the larger the discount, the more the hub selected, the lower the total network cost, and the hub selected under three discount factor scenarios is in good agreement with the actual situation; in each discount factor case, when the demand is different, the layout of the route network is different; by comparing the model results between certain and uncertain demand, it is concluded that the total cost of the network is lower when the demand is uncertain. Therefore, the proposed stochastic programming model under uncertain demand is closer to reality, which can help airlines plan hub-and-spoke network that is in line with the actual situation, and determine their capacity share in hub airports.
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Key words:
- airline /
- hub location /
- uncertain demand /
- airport capacity /
- stochastic planning
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图 3 西安机场单位小时进离港航班数
Figure 3. Number of arrival and departure flights per hour at Xi'an Airport
图 5 不同需求和折扣因子情形下的航线网络布局
Figure 5. Route network layout with different demand scenarios and different discount factors
图 6 需求不确定和确定下的结果差异
Figure 6. Differences in results under uncertain and certain demand
表 1 机场容量包络曲线系数
Table 1. Airport capacity envelope curve coefficient
机场
所在地机场
代码ask bsk Uskmax/(106人) a1k a2k a3k b1k b2k b3k U1kmax U2kmax U3kmax 深圳 SZX 1 0 1 0 1 0.882 40.64 39.29 63.69 西安 XIY 1 0 1 0 1 1.034 41.37 40.33 64.43 郑州 CGO 1 0 1 0 1 1.029 24.16 24.88 38.24 乌鲁木齐 URC 1 0 1 0 1 1.001 29.45 28.51 43.77 长沙 CSX 1 0 1 0 1 0.906 21.77 21.36 34.08 武汉 WUH 1 0 1 0 1 1.167 22.71 21.88 38.80 成都 CTU 1 0 1 0 1 0.862 40.54 39.19 58.77 浦东 PVG 1 0 1 0 1 1.013 55.88 54.64 80.25 南京 NKG 1 0 1 0 1 0.548 25.61 26.85 34.42 沈阳 SHE 1 0 1 0 1 0.618 25.51 23.43 32.95 北京 PEK 1 0 1 0 1 0.717 85.74 56.71 92.80 太原 TYN 1 0 1 0 1 0.530 15.86 13.69 19.60 昆明 KMG 1 0 1 0 1 0.713 48.52 43.34 64.20 
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表 2 不同容量情形下的枢纽建设成本
Table 2. Hub construction cost under different capacity scenarios
107元 机场代码 pk1=0.05 pk2=0.1 pk3=0.15 pk4=0.2 SZX 89 195.8 323.1 473.8 XIY 85 187 308.6 452.5 CGO 80 144 194.4 233.3 URC 68 149.6 246.8 362 CSX 73 160.6 265.0 388.7 WUH 82 180.4 297.7 436.6 CTU 88 193.6 319.4 468.5 PVG 90 198 326.7 479.2 NKG 78 171.6 283.1 415.3 SHE 75 135 182.3 218.7 PEK 95 209 344.9 505.8 TYN 73 131.4 177.4 212.9 KMG 88 193.6 319.4 468.5
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表 3 不同需求情形下的折扣因子
Table 3. Discount factors for different demand scenarios
需求
情形情形1 情形2 情形3 α1, γ1 β1 α2, γ2 β2 α3, γ3 β3 低 0.95 0.85 0.85 0.75 0.75 0.65 中 0.9 0.8 0.8 0.7 0.7 0.6 高 0.85 0.75 0.75 0.65 0.65 0.55
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表 4 折扣灵敏度下的枢纽选址结果
Table 4. Results of hub location under discount sensitivity
折扣因子
情形枢纽点
(容量水平)目标函数值/
(1010元)情形1 无 2.31 情形2 XIY(10%)、PVG(5%) 2.27 情形3 XIY(10%)、PVG(5%)、KMG(10%) 2.11
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表 5 折扣因子情形2下的中转情况
Table 5. Transit in discount factor Case 2
需求情形 OD 中转点 路径流比例 高 KMG-TYN XIY 0.3756 无 0.6244 KMG-SHE XIY 0.9825 PVG 0.0175 WUH-URC XIY 1 KMG-PEK XIY 1 NKG-URC XIY 1 SHE-CTU XIY 1 中 TYN-SZX XIY 1 WUH-URC XIY 1 KMG-PEK XIY 1 NKG-URC XIY 1 SHE-CTU XIY 1 KMG-TYN XIY 1 PEK-CTU XIY 1 TUN-CTU XIY 1 SHE-NKG XIY 1 KMG-SHE XIY 1 SZX-TYN XIY 0.2678 无 0.7322 低 TYN-SZX XIY 1 URC-CGO XIY 1 KMG-TYN XIY 1 WUH-URC XIY 1 NKG-URC XIY 1 NKG-CTU XIY 1 SHE-CTU XIY 1 PEK-CTU XIY 1 TYN-CTU XIY 1 KMG-SHE XIY 1 KMG-PEK XIY 1
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表 6 折扣因子情形3下的中转情况
Table 6. Transit in discount factor Case 3
需求情形 OD 中转点 路径流比例 高 WUH-SHE PVG 0.2179 无 0.7821 SHE-CTU XIY 1 URC-CGO XIY 1 WUH-URC XIY 1 PEK-CTU XIY 1 CTU-SZX KMG 1 TYN-SZX XIY 1 TUN-CTU XIY 1 NKG-URC XIY 1 TYN-URC XIY 1 SHE-WUH PVG 1 NKG-CTU XIY 1 中 CTU-SZX KMG 1 TYN-SZX XIY 1 WUH-URC XIY 1 NKG-CTU XIY 1 URC-CGO XIY 1 PVG-URC XIY 0.6745 无 0.3255 SHE-CTU XIY 1 NKG-URC XIY 1 TYN-CTU XIY 1 TYN-CSX XIY 1 PEK-CTU XIY 1 CTU-WUH XIY 0.9383 无 0.0617 SHE-WUH PVG 1 TYN-CTU XIY 1 SZX-NKG PVG 0.5016 无 0.4984 SHE-NKG PVG 1 低 TYN-SZX XIY 1 URC-CGO XIY 1 TYN-URC XIY 1 WUH-URC XIY 1 PVG-URC XIY 1 NKG-URC XIY 1 TYN-CSX XIY 1 CTU-WUH XIY 1 SHE-WUH PVG 1 NKG-CTU XIY 1 SHE-CTU XIY 1 PEK-CTU XIY 1 TYN-CTU XIY 1 SHE-NKG PVG 1
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