3- precedence network

8/10/2019 3- Precedence Network

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Tutorial # 3Precedence Network

King Saud University

College of Engineering

GE 404 Engineering Management



Important extension to the original activity-on-nodeIncludes precedence relationships among the activities

specify a “lead/lag time” associated with any of the precedence relationships

one activity will overlap another in some fashion.Lag time can be designated on a dependency line witha positive, negative, or zero value.

Limitations and Disadvantages of Lag:Lag would complicate the scheduling process.Lags are not extensively used except where the timeeffects are substantial for special project type.

Precedence Diagramming



10

A

40

B

20

C

20

D

15

E

SS 5

SF 10

FF 10

SF 5FS 6

ES D EF

Act FF

LS TF LF

Example1Given a precedence network for small project. Find:

All times

Project duration Critical path



0 10 10

A

5 40 45

B

16 20 36

C

35 20 55

D

30 15 45

E

SS 5

SF 10

FF 10

SF 5FS 6ES D EF

Ac t FF

j j j

jiji

jiji

iji

iji

i j

D ES EF DSF ES

D FF EF SS ES

FS EF

all Max ES

]2[

TimeInitial

)(]1[

Forward Pass ComputationsActivity A

10100

0TimeInitial

A D A ES A EF A ES

Activity B

45405

550

0TimeInitial)(

B B B

AB A B

D ES EF

SS ES A Max ES

Activity C

362016

16610

0TimeInitial)(

C DC ES C EF AC FS A EF A Max ES C

Activity D

552035

120516,

352010450TimeInitial

),(

D D D ES D EF D DCDSF C ES OR D

D BD

FF B

EF C B Max D ES

Activity E

45153030151035

0TimeInitial)(

E E E

E DE D E

D ES EF DSF ES

D Max ES

Notice: Terminal Time = 55Project duration =55



0 10 10

A

0 0 10

5 40 45

B

5 0 45

16 20 36

C

35 19 55

35 20 55

D

35 0 55

30 15 45

E

40 10 55

SS 5

SF 10

FF 10

SF 5FS 6ES D EF

Ac t FF

Activity E

401555

55TimeTerminal

E D E LF E LS E LF

Activity D

352055

65201055

55TimeTerminal)(

D D D

D DE E D

D LF LS

DSF LF E Min LF

Activity A

01010

101055,

2963555TimeTerminal

),(

A D A LF A LS A D ABSS B LS OR AC

FS C

LS C B Min A LF

Backward Pass Computations

i i i

i ij j

i ij j

ij j

ij j

j i

D LF LS

D SF LF

D SS LS

F F LF

F S LS

e

al l M in LF

]4[

TimTerminal

)(]3[

Notice: Critical Path (A, B, D)Project duration =55

Activity C

352055

7020555

55TimeTerminal)(

D D D

C CD DC

D LF LS

DSF LF D Min LF

Activity B

54045451055

55TimeTerminal)(

B B B

BD D B

D LF LS FF LF

D Min LF



0 10 10

A

0 0 10

5 40 45

B

5 0 45

16 20 36

C

35 19 55

35 20 55

D

35 0 55

30 15 45

E

40 10 55

SS 5

SF 10

FF 10

SF 5FS 6

ES D EF

Act FF

LS TF LF

Notice: Critical Path (A, B, D)Project duration =55

Final solution



10

A

20

C

12

E

14

F

2

H

8

B

6

D

3

G

FS 4

SS 10

FF 2

SS 3

SF 5

FF 5

ZZ2,5

SS 3

ES D EF

Act FF

LS TF LF

Example2Given a precedence network for small project. Find:

All times

Project duration Critical path



0 10 10

A

0 20 20

C

10 12 22

E

13 14 27

F

25 2 27

H

3 8 11

B

2 6 8

D

22 3 25

G

FS 4

SS 10

FF 2

SS 3

SF 5

FF 5

ZZ2,5 SS 3

ES D EF

Act FF

LS TF LF

j j j

jiji

jiji

iji

iji

i j

D ES EF

DSF ES

D FF EF

SS ES

FS EF

all Max ES

]2[

TimeInitial

)(]1[

Forward PassComputations



0 10 10

A

0 10

0 20 20

C

7 27

10 12 22

E

10 22

13 14 27

F

13 27

25 2 27

H

25 27

3 8 11

B

8 16

2 6 8

D

7 13

22 3 25

G

22 25

FS 4

SS 10

FF 2

SS 3

SF 5

FF 5

ZZ2,5 SS 3

ES D EF

Ac t

FF

LS TF LF

Backward PassComputations

iii

iij j

iij j

ij j

ij j

ji

D LF LS DSF LF

DSS LS

FF LF

FS LS

e

all Min LF

]4[

TimTerminal

)(]3[



0 10 10

A

0 0 10

0 20 20

C

7 7 27

10 12 22

E

10 0 22

13 14 27

F

13 0 27

25 2 27

H

25 0 27

3 8 11

B

8 5 16

2 6 8

D

7 5 13

22 3 25

G

22 0 25

FS 4

SS 10

FF 2

SS 3

SF 5

FF 5

ZZ2,5

SS 3

ES D EF

Act FF

LS TF LF

Total Float Computations

Notice:Project duration =27Critical Paths (A, E, F, H; A, E, G, H)

3- precedence network

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