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运筹学. 之. 第六章 网络计划技术. ( Program Evaluation and Review Technique ). §6.4 网络计划技术( PERT ). 6.4.1 前 言 6.4.2 网络图 6.4.3 网络时间与关键路线 6.4.4 网络优化 6.4.5 网络计划的实施控制 作业. 6.4.1 前 言. 用网络分析的方法编制的计划称为网络计划。它 是二十世纪五十年代末发展起来的一种编制大型工程 进度计划的有效方法。 1956 年,美国杜邦公司在制定 企业不同业务部门的系统规划时,制定了第一套网络

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6469219

Program Evaluation and Review Technique


6 4 pert

6.4 PERT

  • 6.4.1

  • 6.4.2

  • 6.4.3

  • 6.4.4

  • 6.4.5


6 4 1

6.4.1

1956

Critical Path MethodCPM


6469219

1958Program Evaluation and Review TechniquePERTCPMPERT


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CPMPERTCPMPERT


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6.4.2

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(2)

,

  • (Tij )Tij

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    TE (j)


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,TE (j),TE (1) = 0TE (1) = 0

TE (j)= max{TE (i)+Tij)} ( j = 2n)

TE (j)

TE (i)


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b

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41

TE (1) = 0

TE (2) = TE (1)+T(12) = 0+60 = 60

TE (3) = TE (2)+T(23) = 60+10 = 70

TE (4) = TE (2)+T(24) = 60+20 = 80

TE (5) = max {TE (2)+T(25) TE (4)+T(45) }

= max { 60+40 80+0 } = 100

TE (6) = TE (4)+T(46) = 80+30 = 110


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TE (7) = max {TE (2) + T(2,7) TE (3) + T(3,7)

TE (6) + T(6,7) TE (5) + T(5,7) }=

max { 60 + 45 ,70 + 18 ,110 + 25 ,100 + 15 } = 135

TE (8) = TE (7) + T(78) = 135 + 35 = 170

4-5


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b(45)

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TL(i)

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TL (n) = TE (n) n

TL ( i ) = min { TL (j) T(i , j) } ( i = n12, 1)

TL (i )

TL (j )

41

TL (8) = TE (8) = 170

TL (7) = TL (8) T(7,8) = 170 = 135


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b(45)

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TL (6) = TL (7) T(6,7) = 135 25 = 110

TL (5) = TL (7) T(5,7) = 135 20 = 115

TL (4) = min {TL (6) T(4,6) TL (5) T(4,5) }

= min { 110 30 120 0 } = 80

TL (3) = TL (7) T(37) = 135 18 = 117

TL (2) = min {TL (7) T(2,7) TL (3) T(2,3)

TL (4) T(2,4) TL (5) T(2,5) }

= min { 135 45 117 10 80 20

120 40 } = 60

TL (1) = TL (2) T(12) = 60 60 = 0


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45

3

TES (ij)

TES (ij)

TES (ij) = TE (i)


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4-5

TES (12) = 0

TES (2, 3) = TES (2, 4) = TES (2, 5) = TES (2, 7) = 60

TES (37) = 70

TES (46) = 80

TES (57) = 100

TES (67) = 110

TES (78) = 135


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b(45)

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TEF (ij)

TEF (ij) = TES (ij) + T( ij)

4-5

TEF (12) = 0 + 60 = 60

TEF (23) = 60 + 10 = 70

TEF (24) = 60 + 20 = 80


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TEF (25) = 60 + 40 = 100

TEF (27) = 60 + 45 = 105

TEF (37) = 70 + 18 = 88

TEF (46) = 80 + 30 = 110

TEF (57) = 100 + 15 = 115

TEF (67) = 110 + 25 = 135

TEF (78) = 135 + 35= 170


6469219

TLF (ij)

, , TLF (ij):

TLF (ij) = TL (j )

4-5

TLF (78) = 170

TLF (6, 7) = TLF (5, 7) = TLF (3, 7) = TLF (2, 7) = 135

TLF (46) = 110 TLF (25) = 120

TLF (24) = 80 TLF (23) = 117 TLF (12) = 60


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TLS (ij)

, TLS (ij): TLS (ij) = TLF (ij) T(ij)

4-5

TLS (12) = 60 60 = 0 TLS (23) = 117 10 = 107

TLS (24) = 80 20 = 60 TLS (25) = 120 40 = 80

TLS (27) = 135 45 = 90 TLS (37) = 135 18 = 117

TLS (46) = 110 30 = 80 TLS (57) = 135 15 = 120

TLS (67) = 135 25 = 110 TLS (78) = 170 35 = 135


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TF(ij)

()()

= :

TF(ij) = TLS(ij) TES(ij):

= :

TF(ij) = TLF(ij) TEF(ij)

,


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FF(ij)

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FF(ij) = TES(jk) TEF(ij)

TES(jk) ij4-6


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R(i)=tL(i)-tE(i)

(1)

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tE(j)=max{tE(i)+tij }

tL(n)= tE(n)

tL(i)=min{tL(j)- tij }

tE(i)=

tL(i)=

i

j

( tij )


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tLF(i, n)= tEF(i, n)

tLS(i, j)=min{tLS(j, k)-tij}

tLF(i, j)=tLS(i, j)+tij

tES(1, j)=0

tES(i, j)=max{tES(k, i)+tki }

tEF(i, j)=tES(i, j)+tij

(1)

(3)

(2)

(4)

()


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(6)

(5)

R(i, j)=tLS(i, j)-tES(i, j)=tLF(i, j)-tEF(i, j)

r(i, j)=tES(j, k)-tEF(i, j)

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tij

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4.4

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(2)

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  • 2)


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46: 45(), 44


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44


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,g

al(, ),

40045444517068900 170 400/ = 68000136900


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, ,adgkl , gk 10150(68900)68900+(290/10+350/10)= 75300(170400/20 400/= 680008000 = 6000075300+60000 = 135300150


6469219

201600(=136900 135300

, 10d 10h55e575300 + 400 10 + 400 5 + 500 5 = 8380060000 400 10 = 5600083800 + 56000 = 139800150


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(1)

(2)

(3)


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4.5

(1)


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ES EF R

LS LF r


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2

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()

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  • 6.2, 6.4


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