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摘要: 为解决缓冲区设置不合理带来的项目间工序松弛、工期延误等问题, 基于信息熵理论提出了一种关键链缓冲区设置方法. 首先, 提出了复杂熵、资源熵和人因熵的概念及其度量方法, 运用熵的概念量化诸多不确定因素对工序造成的影响; 其次, 提出了基于区间直觉梯形模糊数的人因熵度量步骤与方法; 最后, 给出了工序工期、项目缓冲和汇入缓冲的熵模型与修正模型, 充分考虑了人的行为因素对项目进度的影响, 并通过算例验证了模型的实用性.Abstract: In order to solve the problems caused by unreasonable buffer setting, such as process slacking and project delaying, this paper proposes a buffer setting method of critical chain based on information entropy. Firstly, it presents concepts and measurement method of complex entropy, resource entropy and human factor entropy, which are used to quantify the influence of uncertain factors on the process. Secondly, the steps and methods of human factor entropy based on interval-valued intuitionistic trapezoidal fuzzy numbers are proposed. Finally, fully considering the influence to project schedule of human behavior, it presents entropy models and modification models of procedure duration, project buffer and feeding buffer. The examples given in the end vividly convey the practicability.
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表 1 项目中各工序基本信息
Table 1 Information of process in the program
工序编号 紧前工序 紧后工序 最乐观时间 (d) 最可能时间 (d) 最悲观时间 (d) 所需资源数量 p1 p2 p3 A − C, D 6 8 12 4 5 2 B − C, D 3 6 8 3 2 1 C A, B E, F 7 10 12 4 4 1 D A, B E, F 5 6 9 4 3 2 E G G 8 10 11 3 2 1 F H H 4 6 7 5 3 1 G E I, J 8 9 12 4 3 2 H F I, J 4 6 9 5 2 1 I G, H K 2 4 5 5 3 0 J G, H L 10 12 16 3 2 1 K I L 9 11 13 3 4 3 L J, K M, N, O 8 9 12 4 2 2 M L P, Q, R 15 20 22 6 1 1 N L P, Q, R 7 10 12 4 3 0 O L P, Q, R 4 5 6 4 3 2 P M, N, O S 8 9 12 4 4 2 Q M, N, O S 6 8 9 7 5 1 R M, N, O S 3 5 6 4 3 1 S P, Q, R − 4 5 8 7 3 1 资源限量 8 7 3 
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表 2 缓冲区参数计算
Table 2 Value of buffer parameters
类型 编号 三角分布 $T_{50 {\text{%} } }$ $T_{95 {\text{%} } }$ $\sigma_{i}$ $H_{f}$ $H_{z_{i}}$ $H_{r_{i}}$ $d_{i}^{X}$ ${ FB}$ $PB$ ${ FB}^{X}$ ${ PB}^{X}$ 关键链工序 A (6, 8, 12) 8.35 11.19 2.84 0.13 0.13 0.15 7.10 − 7.50 − 8.02 C (7, 10, 12) 10.38 11.42 1.04 0.12 0.18 8.51 − − E (8, 10, 11) 10.22 10.64 0.42 0.08 0.20 8.18 − − G (8, 9, 12) 9.48 11.04 1.56 0.13 0.21 7.49 − − H (4, 6, 9) 6.25 8.45 2.20 0.10 0.10 5.63 − − I (2, 4, 5) 4.54 4.83 0.29 0.08 0.13 3.85 − − K (9, 11, 13) 11.00 12.28 1.28 0.22 0.05 10.15 − − L (8, 9, 12) 9.16 11.25 2.09 0.13 0.14 7.88 − − N (6, 10, 12) 10.42 11.72 1.30 0.10 0.08 9.59 − − M (15, 20, 22) 20.08 21.16 1.08 0.22 0.27 14.66 − − Q (6, 8, 9) 8.35 8.78 0.43 0.16 0.08 7.68 − − P (8, 9, 12) 9.38 11.12 1.74 0.13 0.15 7.97 − − S (4, 5, 8) 4.92 7.34 2.42 0.11 0.23 3.79 − − 非关键链工序 B (3, 6, 8) 6.26 7.68 1.42 0 0.11 0.14 5.38 4.17 − 4.17 − D (5, 6, 9) 5.86 8.26 2.40 0.35 0.19 0.09 5.33 − − F (4, 6,7) 6.15 6.71 0.56 0 0.18 0.28 4.43 0.66 − 0.66 − J (10, 12, 16) 12.12 14.98 2.86 0 0.14 0.13 10.54 3.98 − 3.46 − O (4, 5, 6) 5.08 6.62 1.54 0 0.17 0.11 4.52 1.80 − 1.80 − R (3, 5, 6) 5.14 6.68 1.54 0 0.13 0.08 4.73 1.74 − 1.74 −
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表 3 不同方法缓冲区消耗对比
Table 3 Comparison of buffer consumption by different methods
方法名称 汇入缓冲 (d)/汇入缓冲平均消耗率 (%) 项目缓冲 (d) 项目缓冲平均消耗率 (%) ${ FB}_{BD}$ ${ FB}_{F}$ ${ FB}_{J}$ ${ FB}_{O}$ ${ FB}_{R}$ 1) 关键路线法 − − − − − − − 2) 根方差法 2.79/8.73 0.56/10.82 2.86/2.93 1.54/8.24 1.54/9.55 5.84 91.62 3) APRT法 6.64/2.24 1.31/3.18 5.78/0.10 3.91/1.35 3.74/1.02 12.96 26.98 4) 胡晨 3.06/8.14 0.58/10.62 2.98/2.13 1.58/6.98 1.59/7.54 6.75 88.54 5) 蒋红妍 3.78/5.08 0.60/7.95 3.24/1.09 1.75/2.68 1.62/3.40 7.58 75.76 6) 张俊光 4.04/4.86 0.64/6.76 3.31/0.72 1.72/3.35 1.66/2.08 7.89 69.20 7) 本文方法 4.17/4.68 0.66/6.79 3.46/0.36 1.80/1.95 1.74/1.26 8.02 57.03
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表 4 不同方法完工情况对比
Table 4 Completion comparison of different methods
方法名称 缓冲区主要考虑因素 计划总工期 (d) 项目平均完工率 (%) 1) 关键路线法 − 90.50 15.14 2) 根方差法 工序方差 112.76 89.62 3) APRT法 资源紧张度 124.58 98.98 4) 胡晨 活动工期分布、资源紧张度 115.82 93.56 5) 蒋红妍 工期分布、信息综合约束、资源受限程度等 118.35 96.45 6) 张俊光 资源紧张度、工序复杂度、位置系数、技术与需求不确定性等 120.30 97.68 7) 本文方法 网络复杂度、资源约束、人的行为因素 110.50 95.20
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