不确定性枢纽航线网络优化设计方法研究
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摘要
航线网络是航空公司的立足之本，航空公司的其它管理决策，例如航班计划、运行控制、收益管理等都是在航线网络的基础之上进行的，因此航线网络是否科学合理对航空公司的整体效益将产生深远的影响。航线网络设计问题中的运输需求、成本和容量等参数往往具有不确定性，本文针对枢纽航线网络随机优化的相关问题展开研究。
从航线网络的经济性角度出发，本文提出了无容量限制的多分配严格p枢纽中位随机优化模型，设计了情景分解算法，采用经典航空运输算例对模型和算法进行了测试。算例结果表明在情景数量较大的情况下，算法体现出了较高的效率，通过随机解价值指标比较了使用确定模型和随机优化模型的差异。
从风险控制角度出发，本文使用了鲁棒优化方法，综合考虑需求、成本和容量三个设计参数的不确定性，建立了航线网络的鲁棒优化模型。多种不确定因素的综合以及容量限制的加入使得整个模型的求解复杂度大大增加。针对有容量限制的枢纽网络的特点，本文设计了TreePruning算法，能够预先排除大量枢纽组合，减少计算量，提高算法效率。针对多情景下鲁棒优化模型，本文将Tree Pruning算法与对偶升算法相结合，较为快速地求解出精确解，适用于大型网络的中长期规划。
同时考虑航线网络的经济性和风险控制，本文提出了枢纽航线网络的均值-鲁棒值模型，在算例中比较了期望值模型、确定性模型以及均值-鲁棒值模型的解。鲁棒值完全取决于最差情景，并没有考虑情景的发生概率，这导致在某些极端情况下风险度量不准确。因此，本文引入了条件风险价值作为风险度量函数，建立了枢纽航线网络的均值-条件风险价值模型。目标函数中加入条件风险价值导致模型的求解复杂度大大增加，本文设计了拉格朗日松弛算法结合情景分解算法进行求解。在算例部分，采用了CAB数据算例和中国民航实际算例，分析了双惩罚参数的取值对最终求解效果的影响，比较了期望值模型、确定性模型以及均值-条件风险价值模型的解，两个算例的求解结果均表明均值-条件风险价值模型的结果优于其他模型。
本文在网络模型中考虑了旅客的时间效用的影响，提出了旅客时间价值系数。旅客的时间价值具有不确定性，因此将其离散化处理成不同情景。本文将旅客的时间效用考虑到网络总效用中，这使得所构造的航线网络能够较好地满足旅客对旅行时间的要求。我国现阶段旅客对时间敏感程度较高，在这样的条件下，与多次中转的严格枢纽式航线网络相比，所规划出的混合枢纽网络具有更强的竞争力，也更符合航线网络规划实际，能够更好地为航线网络规划实践提供理论依据和决策支持。
The airline network is the foundation of airline company. Flight scheduling, operation control,revenue management and other works are based on the airline network. Hence, the efficient andeffective airline network has far-reaching effect on airline company. However in reality, someimportant model parameters, such as future demand and cost, are often uncertain. This article studiesthe related problems on the hub-and-spoke airline network design using stochastic optimizationmethod.
Taking the economy of airline network into consideration, the restrict uncapacitated multiallocation p-hub median problem is proposed. A scenario decomposition method combined with theLagrangian relaxation method is used to solve the model. The scenario decomposition method candivide the primal problem into several independent subproblems. A case study using CAB data teststhe model and the algorithm. The results show that algorithm is effective especially when the numberof scenarios is huge. The value of stochastic shows the meaning of using stochastic optimization.
For risk management, a robust optimization model for the p-hub median problem is developed totake the risk into consideration under demand and cost uncertainties. A solution algorithm based onthe combination of dual ascent procedure and Tree pruning algorithm, is implemented. The proposedmodeling and computing methods are tested in the case study with the China airline data.
A Mean-CVaR stochastic programming model is developed for a p-hub median problem tobalance the overall system efficiency and robustness under demand and cost uncertainties. Asolution algorithm based on scenario decomposition, the progressive hedging method, is designed toovercome computational challenges brought by the large size of the problem. The proposedmodeling and computing methods are tested in two case studies using the classic CAB dataset andChina aviation data. The solutions of different models including the mean-CVaR model, thedeterministic model and the expectation model are reported in the case study part. The result suggeststhat mean-CVaR model is better than others.
A Hybrid network utility model is designed to extend the classic hub-and-spoke model. From thereduction of "non-essential transit" point of view, the concept of passenger time value coefficient isproposed. Finally, an instance which contains15cities is given to demonstrate the relationshipbetween the passenger time value coefficient and the scale of spider web network.
从航线网络的经济性角度出发，本文提出了无容量限制的多分配严格p枢纽中位随机优化模型，设计了情景分解算法，采用经典航空运输算例对模型和算法进行了测试。算例结果表明在情景数量较大的情况下，算法体现出了较高的效率，通过随机解价值指标比较了使用确定模型和随机优化模型的差异。
从风险控制角度出发，本文使用了鲁棒优化方法，综合考虑需求、成本和容量三个设计参数的不确定性，建立了航线网络的鲁棒优化模型。多种不确定因素的综合以及容量限制的加入使得整个模型的求解复杂度大大增加。针对有容量限制的枢纽网络的特点，本文设计了TreePruning算法，能够预先排除大量枢纽组合，减少计算量，提高算法效率。针对多情景下鲁棒优化模型，本文将Tree Pruning算法与对偶升算法相结合，较为快速地求解出精确解，适用于大型网络的中长期规划。
同时考虑航线网络的经济性和风险控制，本文提出了枢纽航线网络的均值-鲁棒值模型，在算例中比较了期望值模型、确定性模型以及均值-鲁棒值模型的解。鲁棒值完全取决于最差情景，并没有考虑情景的发生概率，这导致在某些极端情况下风险度量不准确。因此，本文引入了条件风险价值作为风险度量函数，建立了枢纽航线网络的均值-条件风险价值模型。目标函数中加入条件风险价值导致模型的求解复杂度大大增加，本文设计了拉格朗日松弛算法结合情景分解算法进行求解。在算例部分，采用了CAB数据算例和中国民航实际算例，分析了双惩罚参数的取值对最终求解效果的影响，比较了期望值模型、确定性模型以及均值-条件风险价值模型的解，两个算例的求解结果均表明均值-条件风险价值模型的结果优于其他模型。
本文在网络模型中考虑了旅客的时间效用的影响，提出了旅客时间价值系数。旅客的时间价值具有不确定性，因此将其离散化处理成不同情景。本文将旅客的时间效用考虑到网络总效用中，这使得所构造的航线网络能够较好地满足旅客对旅行时间的要求。我国现阶段旅客对时间敏感程度较高，在这样的条件下，与多次中转的严格枢纽式航线网络相比，所规划出的混合枢纽网络具有更强的竞争力，也更符合航线网络规划实际，能够更好地为航线网络规划实践提供理论依据和决策支持。
The airline network is the foundation of airline company. Flight scheduling, operation control,revenue management and other works are based on the airline network. Hence, the efficient andeffective airline network has far-reaching effect on airline company. However in reality, someimportant model parameters, such as future demand and cost, are often uncertain. This article studiesthe related problems on the hub-and-spoke airline network design using stochastic optimizationmethod.
Taking the economy of airline network into consideration, the restrict uncapacitated multiallocation p-hub median problem is proposed. A scenario decomposition method combined with theLagrangian relaxation method is used to solve the model. The scenario decomposition method candivide the primal problem into several independent subproblems. A case study using CAB data teststhe model and the algorithm. The results show that algorithm is effective especially when the numberof scenarios is huge. The value of stochastic shows the meaning of using stochastic optimization.
For risk management, a robust optimization model for the p-hub median problem is developed totake the risk into consideration under demand and cost uncertainties. A solution algorithm based onthe combination of dual ascent procedure and Tree pruning algorithm, is implemented. The proposedmodeling and computing methods are tested in the case study with the China airline data.
A Mean-CVaR stochastic programming model is developed for a p-hub median problem tobalance the overall system efficiency and robustness under demand and cost uncertainties. Asolution algorithm based on scenario decomposition, the progressive hedging method, is designed toovercome computational challenges brought by the large size of the problem. The proposedmodeling and computing methods are tested in two case studies using the classic CAB dataset andChina aviation data. The solutions of different models including the mean-CVaR model, thedeterministic model and the expectation model are reported in the case study part. The result suggeststhat mean-CVaR model is better than others.
A Hybrid network utility model is designed to extend the classic hub-and-spoke model. From thereduction of "non-essential transit" point of view, the concept of passenger time value coefficient isproposed. Finally, an instance which contains15cities is given to demonstrate the relationshipbetween the passenger time value coefficient and the scale of spider web network.
引文
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