Schedule variance early-warning control model for project critical chain resource plan

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1 JOURNAL OF SYSTEMS ENGINEERING Vol.29 No.6 Dec , 2, 3 (1. ( ), ; 2., ; 3., ) :, Weibull, Bayes.,,.,. : ; Bayes ; ; : F272.3 : A : (2014) Schedule variance early-warning control model for project crical chain resource plan Xu Xiaofeng 1, Li Xiang 2, Liu Jiaguo 3 (1. School of Economics and Management, China University of Petroleum, Qingdao , China; 2. School of Economics and Management Science, Beijing University of Chemical Technology, Beijing , China; 3. Shipbuilding Industry Management Research Instuon, Harbin Engineering University, Harbin , China ) Abstract: In order to solve the problem that the project crical chain resource plan is easier influenced by uncertain risks of the construcon process and deviate, the paper presents a modeling of schedule variance early-warning control where value analysis is embedded into Weibull distribuon, and is integrated with Bayes esmaon. The main purpose is to solve the hierarchical informaon conversion of resource plan cohesive tasks, improve the uncertain predicon ability of schedule variance, and take correcve measures for project managers and decision makers to ensure the plan s normal proceeding. Finally, a case analysis shows that the proposed model is correct and effecve. Key words: project management; Bayes esmaon; earned value analysis; schedule early-warning 1 ( ), [1]. : ; : : ( ); (J13WG67); (2013EI228); (QDSKL130415); (14CX04047B).

2 846 29,, /.,,,,.,,., Goldratt [2] (theory of constraint, TOC),,. Wei [3], TOC,. [4] Goldratt,,., [5]. [6], GM(1,1),. Nassar [7] Weibull earning value analysis, EVA, /. [8],,,. Kim [9] (crical path method, CPM) EVA, Kalman Bayesian,. [10], /,.,,.,.,, Bayes Weibull,. EVA / (schedule/cost performance index, SPI/CPI) Weibull ; Bayes,. 2., /,. CPM/PERT,,,. ( 1). t 1,t 2,...,t m, [,+1 ) i, n i i, d i i, (n i,d i ) i.,. BCWS i i, ACWP i i, BCWP i i. i,, : 1) i, ( )R i ; 2) i p i, i + 1

3 6 : 847. t 1 t 2 t 3 t 4 +1 n 1, d 1 n 2, d 2 n 3, d 3 n 4, d 4 n i, d i n i+1, d i+1 t m 1/Z 1 /t z11 5/Z 4 /t z45 6/Z 5 /t z56 2/Z 2 /t z22 4/Z 2 /t z24 8/Z 4 /t z48 y/z x /t zxy 3/Z 3 /t z33 7/Z 4 /t z47 y/z x /t zxy 表示任务 y 需要资源 Z x, 执行时间为 t zxy ; 表示该任务为关键链上任务 t 1 BCWS 1 ACWP 1 BCWP 1 t 2 BCWS 2 ACWP 2 BCWP 2 t 3 BCWS 3 ACWP 3 BCWP 3 t 4 BCWS 4 ACWP 4 BCWP 4 BCWS i ACWP i BCWP i +1 BCWS i+1 ACWP i+1 BCWP i+1 t m 1 Fig. 1 Network diagram of crical chain resource plan, : 1) m, i [,+1 ),i = 1,2,...,m 1,,,, 0 p 1 p 2 p m < 1; 2) Weibull, i p i (t α,β) = 1 e ( α ) β, 0,α,β > 0,i = 1,2,...,m 1;α,β, R i = 1 p i = e ( α ) β ; 3),,,,,., i R i, Weibull R i β. i 1 R i 1, i R i α =, t ( ln R i 1 ) 1 i 0, β > 0, i = 2,3,...,m, (1) β R i ( R i,β) = e ln Ri 1 ( ) β, 0,β > 0, i = 2,3,...,m. (2) Weibull φ i ( α,β) = β ( ) β 1 e ( α) β, 0, α, β > 0, i = 1,2,...,m 1, (3) α α R i β Weibull φ i ( R i,β) = β ( ln R i 1 ) ( ) e ln Ri 1( ) β, 0, β > 0, i = 2,3,...,m. (4), t β, R., t β, φ i ( R i,β) R i, R i = 1 p i, φ i ( R i,β) p i π i (p i,β) π i (p i,β) = β ( ) β ( ) ln(1 p i ) e ln(1 pi 1) β, 0,β > 0, i = 2,3,...,m. (5)

4 π i (p i ) i, i, Bayes f i (p i (n i,d i )) = pi 1 Pr{(n i,d i ) p i } = ( n i ) d i p d i i (1 p i ) ni di,m{(n i,d i ) p i } =. 0 π i (p i )Pr{(n i,d i ) p i }, i = 2,3,...,m, (6) π i (p i )Pr{(n i,d i ) p i }dp i pi 1 0 π i (p i )Pr{(n i,d i ) p i }dp i p i, t β, i π i (p i,β) Weibull φ i ( R i,β)., (n i,d i ), i f i (p i (n i,d i )), i + 1 π i+1 (p i+1 ),. β, π(p). 2.1 SPI/CPI (α,β) Weibull, (median ranking method MRM). MRM Weibull y = kx + b, α β [11,12]. : 1 i, SPI i /CPI i,, SPI i = BCWP i /BCWS i,cpi i = BCWP i /ACWP i ; 2 SPI i /CPI i i = 1,2,...,n, M i, M i = (i 0.3)/(n + 0.4),i = 1,2,...,n; 3 ln (ln(1/(1 M i ))), ln(spi i ) ln(cpi i ) y = kx + b ; 4 β = k SPI k CPI, α = e b β SPI e b β CPI. 2.2 Bayes,,.,, [13,14]. i, (n i,d i ),, i p i Bayes f i (p i (n i,d i )), (5) i + 1 π i+1 (p i+1 +1,β) = β +1 ( ln(1 l i p i )) ( +1 ) β e ln(1 lipi)( +1 ) β, 0,β > 0, i = 1,2,...,m 1, (7) l i., t β, l i, i + 1. ML-II,, l i. (n i+1,d i+1 ) i + 1, m(n i+1,d i+1 ) p i+1. i, i + 1, n i+1, d i+1.,, Monte Carlo

5 6 : 849 m(n i+1,d i+1 = Max) l i ˆl i, i + 1 p i+1 π i+1 (p i+1 +1,β) = β ( ) β ln(1 t ˆl +1 i p i ) e ln(1 ˆl ip i)( +1 ) β, i+1 0,β > 0, i = 1,2,...,m 1. (8),. 3,, MATLAB. / SPI/CPI,, 1. 1 Table 1 Project progress informaon stascs i SPI i CPI i n i d i SPI/CPI, ln SPI ln CPI. MRM M i, ln (ln (1/(1 M i ))), 2. 2 Table 2 MRM MRM-based data processing i SPI i ln SPI i CPI i lncpi i M i ln(ln(1/(1 M i ))) ln SPI i /ln CPI i ln (ln (1/(1 M i ))) y = kx + b, β = k,α = e b β, 3. 3 β, li ˆl i. ˆl i [0,n i ],. f i, [0,n i ],.

6 / 0 I , Monte Carlo , m i (n i,d i ) ˆl i., 1, π 0 (p 0 ) = 1, p 0 = Table 3 3 Parameter esmaon based on regression analysis (SPI) (CPI) k b β α S P C P I / Fig. 2 Resource plan schedule/cost variance appear probability curve 2,, /. /,,., p < 0.15, 8.,, p i [0.15,0.20),, 9,,,. /,, p 0.20, 10,,,. 4,,. Weibull, Bayes. EVA Weibull, Bayes,,

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