# Project What is the duration Critical Path

1. What is the duration Critical Path? In solve this, the critical path should be solved first from the work diagram. The diagram is constructed below. To compute for the critical path, one needs to only add the duration for each step for one complete path from start to finish. There are four complete paths in the diagram. Accordingly:

1. D, E, G, H, C = 4 + 8 + 5 + 7 + 8 = 32 months

2. D, F, G, H, C = 4 + 7 + 5 + 7 + 8 = 31 months

3. A, F, G, H, C = 6 + 7 + 5 + 7 + 8 = 33 months (this is the critical path because it has the highest number of months to complete. Its duration is 33 months)

4. A, F, B = 6 + 7 + 5 = 18 months

A = 6

B = 5

C = 8

D = 4

E = 8

F = 7

G = 5

H = 7

End

Start

1. What is the slack of task for B? = 33 – 18 = 15 months

2. What is the slack of task for E? = 13 – 12 = 1 month

3. What is the slack of task for D? = 5 – 4 = 1 month

The “slack” of each task (A, B, C… H) is defined as the time thatcan be delayed for each task without adversely affecting the durationof the critical path. This can be done by first computing for theearliest start (ES) and earliest finish (EF) for each task. For thecomputation of ES, at the start the ES is 0 and for the rest of theother task, the ES is the EF of the preceding task. This is shown inthe figure below. The EF is simply the ES plus the duration of eachtask.

25

18

18

13

4

12

4

0

A = 6

B = 5

D = 4

E = 8

F = 7

G = 5

H = 7

End

Start

18

13

13

6

6

0

33

25

ES

EF

0

0

C = 8

33

33

0

0

0

0

5

1

13

5

18

13

25

18

33

25

33

33

33

28

LF

LS

ES

EF

13

6

6

0

A = 6

B = 5

C = 8

D = 4

E = 8

F = 7

G = 5

H = 7

End

Start

0

4

4

12

13

18

18

25

25

33

0

6

6

13

13

18

33

33

The secondstep for computing the slack is the computation of the latest star(LS)t time and latest finish time (LF). By definition, the LF of thevery last task, Which is in this case is B and C to be the EF time ofthe last task. The LS is simply LF minus the duration of the task.All other LF will be the LS of the previous task (from end to start).The “Slack” is the computed by simple subtracting LS – ES or LF– EF. For this I used LF – EF.