Robust Optimization Design And Complexity Analysis For Airline Network

Airline network is a foundation for airlines’ operations and is strategic to the development ofairlines. It is important to build an airline network which is matching the realistic of the airlines and isrobust by means of optimization designing after analyzing the situation of airlines in current and aperiod in future. The optimization theory of airline network is generally aiming at the network whichis abstracted and has special structure. It has some limitations when guiding the planning anddesigning of airline network. It is also important to explore the evolution mechanism of network andoperation characteristics on network from the aspect of system complexity analysis. This paper willfocuse on on the robust optimization of airline network design and complexity analysis with the helpof economic theory, operations research theory, classic and intelligence algorithms, statistical theory,theory of complex networks and etc.With the changes of the market environment, the traffic between the OD, unit transport costs andthe capacity of a node will have much uncertainty. These uncertainty factors will probably lead to adeviation between the existing network structure and the actual needing network structure, and willhave a great impact on the production based on the network, therefore there needs to make thedesigning network have better robustness. By analyzing the data of airline passenger traffic, unit flowtransport cost and nodes’ capacity, this paper defines a discrete scenario set, establishes a robustoptimization design model of Hub and spoke network under the capacity-limited conditions, and solvethe model with the Benders Decomposition algorithm. As the number of scenarios is limited in thediscrete scenario set, in order to analyze the problem in more wide and more complex environment,this paper defines an interval type of scenario set which contains more information, establishes twonetwork design models of uncapacitated interval absolute robust optimization and relative robustoptimization, solves the modes with the methods combining the modified shortest path algorithm andsimulation annealing algorithm, carries out some applications for the models using the classic CABdata and airlines actual data. The results show that the network designed by the models of the intervalrobust optimization has better robustness and the optimization model under the determinedcircumstances is a special case of the interval robust optimization model.The optimization design of airline network is carried out under the special structure,so theanalysis of the structure of airline network will be important to select the excellence structure.Under the conditions of node or edge having capacity limit, this paper establishes a network evolution modelwith limited capacity, solves the model with mean field theory. The theoretical solutions andsimulation results indicate that the new model can better reappear some characteristics of actualnetworks and the BBV model is just a special case of the new model when the nodes’ capacity tendesto infinity. After the network is generated, its operation characteristics need to be analyzed. Using thenew evolution model, two types of network are genetated when the nodes’ capacity tendes to finity orinfinity, and then the capacity of the networks and center-deal ability of nodes and edges is caculatedand compared. Flights delay have impacted the air transport heavily, according to the model ofexpected flow, an evolution of Chinese airline network is generated, a delay spreading model iseastablished based on the network. After then, from the aspect of macro-level, considering differentcases, such as the parameters taking different values and the initial delay happening at node withdifferent degree, the delay influences are analyzed, including the whole number of delayed nodes andthe delay spreading distance and etc. Under the recovery strategy of airports or airlines, delayspreading usually does not cause serious influence on network, this paper also analyzes someallocation strategies of the weight of the unfuncitional edges when serious malfunctions happen.Simulation results indicate that the use of appropriate allocation strategies may reduce or avoide thecascading effect.