基于Clayton Copula函数的PERT模型优化及应用研究  

Research on Optimization and Application of PERT Model Based on Clayton Copula Function

作　　者：谢湖 万晨 郑龙 杨葛 刘华青 黄建文[1] XIE Hu;WAN Chen;ZHENG Long;YANG Ge;LIU Hua-qing;HUANG Jian-wen(Hubei Key Laboratory of Construction and Management in Hydropower Engineering,China Three Gorges University,Yichang 443002,China;College of Computer and Information Technology,China Three Gorges University,Yichang 443002,China;China Gezhouba Group Three Gorges Construction Engineering Co.,Ltd.,Yichang 443000,China;China Three Gorges Construction Engineering Corporation,Chengdu 610095,China)

机构地区：[1]三峡大学水电工程施工与管理湖北省重点实验室,湖北宜昌443002 [2]三峡大学计算机与信息学院,湖北宜昌443002 [3]中国葛洲坝集团三峡建设工程有限公司,湖北宜昌443000 [4]中国三峡建工(集团)有限公司,四川成都610095

出　　处：《水电能源科学》2025年第3期114-118,共5页Water Resources and Power

基　　金：国家自然科学基金项目(51879147,52009069)。

摘　　要：计划评审技术(PERT)作为一种重要的项目管理方法,已广泛应用于各种复杂项目的进度管理中。传统PERT模型假设工序持续时间同分布(均服从Beta分布)、工序间相互独立、关键线路固定,与工程实际存在偏差,导致工期模拟精度受限。为此,建立了基于Clayton Copula函数的PERT优化模型。首先,通过历史数据拟合并确定不同类别工序持续时间的分布形式,揭示工序持续时间分布的多样性;其次,针对相邻工序之间普遍存在的依赖关系,采用Spearman秩相关系数定量描述相邻工序间的相关性;在此基础上,运用Clayton Copula函数构建相邻工序持续时间的联合分布,并利用蒙特卡罗(MC)法对工序持续时间、关键线路及工期分布进行模拟,确定关键线路及各工序的关键度指标。实例应用结果表明,该模型能真实反映工序持续时间的分布特征和相邻工序间的相关性,有效识别了关键线路,精准模拟项目工期分布,可以为项目进度管理提供可靠的决策支持。The program evaluation review technique(PERT)is a key project management tool frequently used for scheduling in complex projects.However,the traditional PERT model assumes that all process durations follow a single distribution(the Beta distribution),that processes are independent of each other,and that critical paths are fixed.These assumptions diverge from actual engineering conditions,limiting the accuracy of construction period simulations.To address these limitations,this paper introduces an optimized PERT model based on the Clayton Copula function.Firstly,the model identifies the distribution forms of various types of processes by fitting historical data,thus revealing the diversity in process duration distributions.Secondly,for the dependency relationships that exist between adjacent processes,Spearman's rank correlation coefficient is used to quantitatively describe the correlations between them.On this basis,the joint distribution of adjacent process durations is constructed using the Clayton Copula function.The Monte Carlo(MC)method is applied to simulate process durations,critical paths,and construction period distributions,enabling the identification of criticality indicators for both critical paths and processes.Case studies have shown that the model can accurately reflect the distribution characteristics of process durations and the correlations between adjacent processes,effectively identify critical paths,and accurately simulate the distribution of project construction periods,which can provide reliable decision support for project schedule management.

关 键 词：PERT Clayton Copula 关键线路 完工概率 蒙特卡罗模拟 

分 类 号：TV512[水利工程—水利水电工程]