不确定需求下航空公司枢纽网络优化设计

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。 

Airline hub network optimization design under uncertain demand

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.