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The purpose of this paper is to focus on disruption management responding to large‐area flight delays (LFD). It is urgent for airways to reschedule the disrupted flights so as to relieve the negative influence and minimize losses. The authors try to reduce the risk of airline company's credit and economic losses by rescheduling flights with mathematic models and algorithm.

Based on flight classifications of real‐time statuses and priority indicators, all flights are prioritized. In this paper, two mathematic programming models of flight rescheduling are proposed. For the second model, an optimum polynomial algorithm is designed.

In practice, when LFD happens, it is very important for the airline company to pay attention to real‐time statuses of all the flights. At the same time, the disruption management should consider not only the economic loss but also other non‐quantitative loss such as passengers' satisfaction, etc.

In this paper, two mathematic programming models of flight rescheduling are built. An algorithm is designed and it is proved to be an optimum polynomial algorithm and a case study is given to illustrate the algorithm. The paper provides a theory support for airways to reduce the risk brought by LFD.

It is the complexity and the calculated quantities which require the use of the general algorithm for evaluating the maximum flow of the network. The logical cutting tree algorithm model of the network maximum flow is built using both the logical thought of the fault tree method and cutting set theories of the graphics. Therefore, the problem is resolved well and its calculation process is simpler and its logic is better than the original algorithm method.