Question

Consider the following statement associated with critical path:

1. Critical path is the most important sequence of activities which has no float and which determine the project completion period

2. Critical path is the largest path with shortest duration within which the project can be completed

3. The difference between early start time and late finish time must be equal to the activity duration

4. Cannot pass through dummy activity

Which is among the above are correct statements? 

1. 1, 2 and 4
2. 1, 3 and 4
3. 1, 2 and 3
4. 1, 2, 3 and 4

Answer 1

Correct Answer - Option 3 : 1, 2 and 3

Concept:

Total float:

The time span by which starting or finishing time of an activity can be delayed without delaying the completion of the project. It is the maximum available time in excess of the activity completion time.

Float is given by LST – EST or LFT – EFT

F_T = (T^j_L - Tⁱ_E) - t_ij

F_T = LFT - EST

Where,

LFT = Latest start time

EST = Earliest start time

Explanation:

Critical path:

1) In CPM analysis, the path along which total floats are zero or minimum is called critical path.

2) Critical path is the largest path with shortest duration within which the project can be completed

3) There can be more than one critical path.

4) Critical path can pass through dummy activity.

5) All activities on this path are critical.

6) For the critical path the difference between early start time and late finish time must be equal to the activity duration.

We know that FT = (TjL - TiE) - tij and FT = LFT - EST = 

Total float for critical path = 0

∴ 0 = (TjL - TiE) - tij 

∴ (TjL - TiE) = tij 

i.e Difference between early start time and late finish time is equal to the activity duration.