考虑恢复依赖的基础设施网络应急恢复决策

doi:10.16381/j.cnki.issn1003-207x.2019.0137

摘要/Abstract

摘要： 在大规模突发事件发生后，基础设施恢复任务之间会形成复杂的依赖关系，本文考虑了在此条件下基础设施系统的恢复设计与调度决策问题。基于网络流理论，以累积恢复效能最大化与成本最小化为目标，构建了涵盖阻塞依赖、选项依赖和效率依赖三类恢复依赖关系的集成恢复设计与调度决策混合整数规划模型，并且设计了求解模型的启发式算法。最后，以长沙市真实基础设施数据集为基础，构造了突发事件后的损毁场景实例，利用模型求解得出了受损基础设施的恢复设计与调度决策方案，并且分析了决策周期长度与工作组数量对累积恢复效能和成本的影响。结果表明：(1)该模型在突发事件后的基础设施恢复决策中具有应用可行性；(2)决策周期长度显著影响累积恢复效能，随着决策周期长度与恢复过程中各组件恢复耗时契合度的提升，累积恢复效能获得有效增长，并且，在决策周期长度的取值范围内，总成本存在最小值；(3)随工作组数量的增加，累积恢复效能呈增长趋势，增长率逐渐减小，同时，总成本呈减少趋势，减少率也逐渐减小。

关键词: 基础设施；网络流；恢复依赖；恢复效能；决策

Abstract: Modern developed social systems rely heavily on the complex infrastructure networks, after a large scale extreme event, restoration interdependencies which added the high complication to restoration decision occur among tasks during the restoration efforts. The restoration design and scheduling decision of infrastructure system are studied in the condition of the coexistence of several kinds of restoration interdependencies after a large scale extreme event. Based on network flow theory, a mixed integer programming formulation is developed integrating restoration design and scheduling decision with the goals of cumulative restoration performance maximization and cost minimum, it incorporates the three distinct restoration interdependency classes: sequence precedence, effectiveness precedence, and options precedence. And a heuristic algorithm for solving the model with NP-Hard complexity is proposed, it converts infrastructure network in the original problem into connected graph, then induced subgraphs are generated for each vertex corresponding to the node of unsatisfied demand based on the connected graph, and each induced subgraph contains the network nodes. Finally, a data set of damaged components coming from the real infrastructures in Changsha is generated based upon ice and snow disaster, then, the solution about restoration design and scheduling decision of the damaged components of infrastructure system is obtained through solving the model, and further the effect of decision period length on the overall cumulative restoration performance is analyzed. The results show that: (1) the model has the feasibility of the application in the restoration decision of infrastructures after an emergency, (2) the length of decision period has a significant impact on the overall cumulative restoration performance which is greatly enhanced as the difference of the length of decision period and restoration time reduces, and the total cost exists a minimum within the range of the length of the decision period, (3) as the number of work groups increases, the overall cumulative restoration performance maintains growth with the rate of growth decreasing, while the total cost decreases with the rate of decreasing reduction.

Key words: infrastructure; network flow; restoration interdependency; recovery performance; decision

中图分类号:

C934

任爱俊,冯耕中,田军. 考虑恢复依赖的基础设施网络应急恢复决策[J]. 中国管理科学, 2022, 30(1): 154-164.

REN Ai-jun,FENG Geng-zhong,TIAN Jun. Infrastructure Network Restoration Decision Considering Restoration Interdependency after Emergency[J]. Chinese Journal of Management Science, 2022, 30(1): 154-164.

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