Question

In: Operations Management

The network below represents a project being analyzed by the critical path method. Activity durations are indicated on the network.

a. Identify the activities on the critical path. b. What is the duration of the critical path? c. Calculate the amount of slack time at activity H. d. If activity I were delayed by ten time units, what would be the impact on the project duration?

Expert Solution

a.

Critical path is the path with longest time for completion. We will assess time for all possible paths to arrive at critical path.

Path 1. A-C-J-K: 5 +11+6+4 =26

Path 2. B-E-J-K: 3+7+6+4 = 20

Path 3. B-G-I: 3+4+5 = 12

Path 4. D-F-I: 4+6+5 = 15

Path 5: D-H-J-K: 4+3+6+4=17

Hence the critical path is Path 1. A-C-J-K with longest completion time of 26 units.

b.

Duration of critical path is 26 units.

c.

For calculating slack time for activity H, we need earliest start (ES) and Latest start (LS).

Earliest start (ES) for H = Earliest finish (EF) for D = 0 + Duration for D = 0 + 4 = 4 units

ES for H is 4 units.

Latest start (LS) for K = Latest finish (LF) for K - Duration of K = 26 - 4 = 22

Latest start (LS) for J = Latest finish (LF) for J - Duration of J = Latest start (LS) for K - Duration of J = 22 - 6 = 16

Latest start (LS) for H = Latest start (LS) for J - Duration of H = 16 - 3 = 13 units

Hence, slack for H = Latest start (LS) for H - Earliest start (ES) for H = 13 - 4 = 9 units

d.

If I is delayed by 10 units, then the impact on possible paths given in a

Path 3. B-G-I: 12 + 10 = 22

Path 4. D-F-I: 15 + 10 = 25

Completion time for both paths is still less than Path 1. A-C-J-K.

Hence, the project duration will not be impacted and remain same as 26 units.

keosha answered 2 years ago

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