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.

参考文献

［1］ Zio E. Challenges in the vulnerability and risk analysis of critical infrastructures［J］. Reliability Engineering & System Safety, 2016, 152: 137-150.
［2］ Holden R, Val D V, Burkhard R, et al. A network flow model for interdependent infrastructures at the local scale［J］. Safety Science, 2013, 53: 51-60.
［3］ Matisziw T C, Murray A T, Grubesic T H. Strategic network restoration［J］. Networks and Spatial Economics, 2010, 10(3): 345-361.
［4］ Ouyang Min, Wang Zhenghua. Resilience assessment of interdependent infrastructure systems: With a focus on joint restoration modeling and analysis［J］. Reliability Engineering & System Safety, 2015, 141: 74-82.
［5］ Sharkey T C, Nurre S G, Nguyen H, et al. Identification and classification of restoration interdependencies in the wake of Hurricane Sandy［J］. Journal of Infrastructure Systems, 2015, 22(1): 04015007.
［6］张翼. 五部委多项措施应对雪灾保煤电油运［N］.光明日报，2008-02-02(3).Zhang Yi. Five ministries and commissions have multiple measures to deal with the snow disaster to ensure coal, electricity, oil and transportation ［N］. Guangming Daily, 2008-02-02(3).
［7］王伟健,周立耘,丁文杰.罕见冰雪，我们如何更好应对［N］.人民日报,2008-01-24 (5).Wang Weijian, Zhou Liyun, Ding Wenjie. How can we better deal with rare ice and snow［N］. People’s Daily, 2008-01-24(5).
［8］张志峰,孙海涛,刘学渊,等.各地全力抗击罕见雪灾［N］.人民日报,2008-01-22(2).Zhang Zhifeng, Sun Haitao, Liu Xueyuan, et al. Fight against rare snow disasters everywhere［N］. People’s Daily, 2008-01-22(2).
［9］ Lee E E, Mitchell J E, Wallace W A. Assessing vulnerability of proposed designs for interdependent infrastructure systems［C］//Proceedings of the 37th Annual Hawaii International Conference on System Sciences, Hawaii, January 5, IEEE, 2004: 8 pp.
［10］ Ouyang Min, Dueas-Osorio L, Min Xing. A three-stage resilience analysis framework for urban infrastructure systems［J］. Structural Safety, 2012, 36-37(2):23-31.
［11］张雷, 元昌安, 马璐. 考虑优先权的地震灾害时限应急救援指派模型［J］. 计算机应用研究, 2013, 30(5):1439-1442.Zhang Lei, Yuan Changan, Ma Lu. Time limit emergency rescue assignment model of earthquake disaster based on rescue priority ［J］. Application Research of Computers, 2013, 30(5):1439-1442.
［12］ Permann M R. Genetic algorithms for agent-based infrastructure interdependency modeling and analysis［C］//Proceedings of the 2007 spring simulation multiconference-Volume 2. Norfolk, March 25-29, 2007.
［13］ Shen Siqian. Optimizing designs and operations of a single network or multiple interdependent infrastructures under stochastic arc disruption［J］. Computers & Operations Research, 2013, 40(11): 2677-2688.
［14］ González A D, Dueas-Osorio L, Sánchez-Silva M, et al. The interdependent network design problem for optimal infrastructure system restoration［J］. Computer-Aided Civil and Infrastructure Engineering, 2016, 31(5): 334-350.
［15］ Fang Y P, Pedroni N, Zio E. Resilience-based component importance measures for critical infrastructure network systems［J］. IEEE Transactions on Reliability, 2016, 65(2): 502-512.
［16］ Nurre S G, Cavdaroglu B, Mitchell J E, et al. Restoring infrastructure systems: An integrated network design and scheduling (INDS) problem［J］. European Journal of Operational Research, 2012, 223(3): 794-806.
［17］ Cavdaroglu B, Hammel E, Mitchell J E, et al. Integrating restoration and scheduling decisions for disrupted interdependent infrastructure systems［J］. Annals of Operations Research, 2013, 203(1): 279-294.
［18］ Sharkey T C, Cavdaroglu B, Nguyen H, et al. Interdependent network restoration: On the value of information-sharing［J］. European Journal of Operational Research, 2015, 244(1): 309-321.
［19］代颖, 马祖军, 郑斌. 突发公共事件应急系统中的模糊多目标定位-路径问题研究［J］. 管理评论, 2010, 22(1): 121-128.Dai Ying, Ma Zujun, Zheng Bin. Fuzzy multi-objective location-routing problem in emergency systems for unexpected public emergency［J］. Management Review, 2010, 22(1): 121-128.
［20］王海军, 王婧, 马士华, 等. 模糊供求条件下应急物资动态调度决策研究［J］. 中国管理科学, 2014, 22(1): 55-64.Wang Haijun, Wang Jing, Ma Shihua, et al. Decision-making for emergency materials dynamic dispatching based on fuzzy demand and supply［J］. Chinese Journal of Management Science, 2014, 22(1): 55-64.
［21］祁明亮, 秦凯杰, 赵琰. 雪灾救援物资车辆一直升机联合运送的调度问题研究［J］. 中国管理科学, 2014, 22(3): 59-67.Qi Mingliang, Qin Kaijie, Zhao Yan. Research on problem of scheduling of helicopter coordinated with vehicle for resources distribution in snowstorm［J］. Chinese Journal of Management Science, 2014, 22(3): 59-67.
［22］刘长石, 彭怡, 寇纲. 震后应急物资配送的模糊定位一路径问题研究［J］. 中国管理科学, 2016, 24(5): 111-118.Liu Changshi, Peng Yi, Kou Gang. Research on fuzzy location-routing problem in post-earthquake［J］. Chinese Journal of Management Science, 2016, 24(5): 111-118.
［23］杨继君, 佘廉. 面向多灾点需求的应急资源调度博弈模型及优化［J］. 中国管理科学, 2016, 24(8): 154-163.Yang Jijun, She Lian. Game Model and optimization based on resource requirements of multiple crisis locations［J］. Chinese Journal of Management Science, 2016, 24(8): 154-163.
［24］刘波, 李砚. 应急物资车辆调度的鲁棒双层优化模型［J］. 系统工程, 2016, 34(5): 77-81.Liu Bo, Li Yan. Robust bi-level optimization model for vehicle routing of emergency commodities［J］. Systems Engineering, 2016, 34(5): 77-81.
［25］朱佳翔, 谭清美, 蔡建飞, 等. 基于双重不确定性的应急物流配送策略［J］. 系统工程, 2016, 34(3): 1-8.Zhu Jiaxiang, Tan Qingmei, Cai Jianfei, et al. Emergency logistics distribution strategy based on double uncertainty ［J］. Systems Engineering, 2016, 34(3): 1-8.
［26］李双琳, 马祖军, 郑斌, 等. 震后初期应急物资配送的模糊多目标选址-多式联运问题［J］. 中国管理科学, 2013, 21(2): 144-151.Li Shuanglin, Ma Zujun, Zheng Bin, et al. Fuzzy multi-objective location-multimodal transportation problem for relief delivery during the initial post-earthquake period ［J］. Chinese Journal of Management Science, 2013, 21(2): 144-151.
［27］ Peng Min, Peng Yi, Chen Hong. Post-seismic supply chain risk management: A system dynamics disruption analysis approach for inventory and logistics planning［J］. Computers & Operations Research, 2014, 42: 14-24.
［28］王熹徽, 李峰, 梁樑. 救灾物资供应网络解构及结构优化模型［J］. 中国管理科学, 2017,25(1): 139-150.Wang Xihui, Li Feng, Liang Liang. The deconstruction of a relief material supply network and corresponding structure optimization model［J］. Chinese Journal of Management Science, 2017,25(1): 139-150.
［29］ Hong Sheng, Lv Chuan, Zhao Tingdi, et al. Cascading failure analysis and restoration strategy in an interdependent network［J］. Journal of Physics A: Mathematical and Theoretical, 2016, 49(19): 195101.
［30］ Lee II E E, Mitchell J E, Wallace W A. Restoration of services in interdependent infrastructure systems: A network flows approach［J］. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 2007, 37(6): 1303-1317.
［31］ Schneider P J, Schauer B A. HAZUS—its development and its future［J］. Natural Hazards Review, 2006, 7(2): 40-44.

[1]	聂慧芳, 朱建军. 考虑情绪演化下突发事件所致舆情危机的两阶段响应决策方法[J]. 中国管理科学, 2025, 33(10): 112-125.
[2]	张恒杰, 刘娟, 朱文凤, 董玉成. 基于最小成本反向图模型的双渠道供应链碳减排冲突研究[J]. 中国管理科学, 2025, 33(10): 212-224.
[3]	景熠, 刘威, 刘芹芹, 程凤娇, 张华荣. 突发事件冲击下应对供应中断的供应链响应计划研究[J]. 中国管理科学, 2025, 33(10): 57-66.
[4]	张发明, 韩江涛, 张淋茜, 朱姝琪. 社会信任网络下基于T₂PLD算子的多属性大群体决策方法[J]. 中国管理科学, 2025, 33(9): 177-188.
[5]	李聪聪, 梁海明, 董玉成. 多粒度语言环境下基于持续学习和行为建模的个性化语义共识决策模型[J]. 中国管理科学, 2025, 33(9): 201-212.
[6]	景熠, 张闻秋, 曹柳. 电商购物平台与回收平台的“以旧换新”合作策略研究[J]. 中国管理科学, 2025, 33(8): 289-297.
[7]	代业明, 于双. 碳税政策下考虑零售商双重行为偏好的再制造闭环供应链决策[J]. 中国管理科学, 2025, 33(8): 308-320.
[8]	张侃, 刘思施, 魏华, 余鹏, 梁新. 基于CPSO改进的TOPSIS三维空间组合定权投影动态综合评价研究[J]. 中国管理科学, 2025, 33(7): 117-127.
[9]	董乾坤, 易平涛, 李伟伟, 王露. 基于多源混合评价信息的随机聚合指数及应用[J]. 中国管理科学, 2025, 33(7): 128-138.
[10]	李进, 江赫奇, 丁圣琪, 张海霞, 伍蓓. 碳交易机制下竞争型供应链最优减排与规制政策研究[J]. 中国管理科学, 2025, 33(7): 360-368.
[11]	缑迅杰, 徐鑫茹, 徐泽水. 基于动态社会网络的能源转型路径评估多属性群决策建模研究[J]. 中国管理科学, 2025, 33(6): 346-359.
[12]	罗世华, 刘俊. 拓展区间Fermatean模糊前景理论综合评价方法[J]. 中国管理科学, 2025, 33(6): 129-139.
[13]	张磊, 韩可可, 叶鑫. 广义Z-numbers证据下考虑专家影响力和评价值一致性的应急决策方法[J]. 中国管理科学, 2025, 33(6): 160-170.
[14]	常志朋, 王治莹, 陈闻鹤. 基于模糊影响图和前景理论的重大疫情防控策略决策方法[J]. 中国管理科学, 2025, 33(6): 171-181.
[15]	赵程伟, 徐选华, 刘瑞环, 何继善. 模糊异构环境下考虑双重交互及不完全理性心理的多属性群决策及应用[J]. 中国管理科学, 2025, 33(6): 182-195.