Question

For the following network determine:

a) The activities on the critical path

b) The time for the critical path

c) The slack for EVERY activity

Activity	Immediate Predecessors	Time
A	-	5
B	-	4
C	A,B	3
D	A,B	6
E	A,B	2
F	C,D,E	8
G	C,D,E	5

Answer 1

To answer the above question, we'll have to make a network diagram first.

A, B activities are independent and can be started right away.

C, D, E are dependent on A and B and will start only after completion of A and B.

F and G are dependent on C, D & E and will start only after completion of C, D, & E

The project will be completed after completion of activities E and F.

The above details give us the following network diagram.

We now perform forward pass on Activity on Node network diagram.

In the forward pass,

The early start for independent activities is always 0. Early start for activities A, B is 0.

Early finish (EF) = Early start (ES) + Duration of the task

For task A, Early finish = 0 + 5 = 5

For task B, Early finish = 0 + 4 = 4

Early start any activity is the lastest Early finish value for any predecessor.

For activity C, D, & E, Early start is 5, Latest early finish value of its predecessors A(5) and B(4).

For task C, Early finish = 5 + 3 = 8

For task D, Early finish = 5 + 6 = 11

For task E, Early finish = 5 + 2 = 7

For activity E& F, an early start is 11, Latest early finish value of its predecessors C(8) and D(11) & E(7).

For task F, Early finish = 11 + 8 = 19

For task G, Early finish = 11 + 5 = 16

Project completion time is the highest time required for activity with no dependent activity. In this case, F takes 19 time period to finish which is more than 3 weeks taken by G. G and F are only 2 activities without any dependents.

Project completion time = 19

In the backward pass,

Late finish (LF) for activities without dependents is always equal to project completion time.

Late finish for F =19

Late finish for G =19

Late start (LS) = Lates finish - Duration of the task

For task F, Late start = 19 - 8= 11

For task G, Late start = 19 - 5= 14

Late finish for C, D & E is 11 the earliest of late start value from its dependents F(11) and G(14).

Late finish for C = 11

Late finish for D = 11

Late finish for E = 11

For task C, Late start = 11 - 3= 8

For task D, Late start = 11 - 6= 5

For task D, Late start = 11 - 2= 9

Late finish for A & B  is 5 the earliest of late start value from its dependents C(8) and D(5) & E(9).

For task A, Late start = 5 - 5= 0

For task B, Late start = 5- 4= 1

Following is the completed Network diagram.

Now slack for the activity is given by Late start (LS) of activity minus Early start (ES) of activity.

Slack = LS - ES

Slack for A = 0-0 = 0

Slack for B = 1-0 = 1

Slack for C = 8-5 = 3

Slack for D = 5-5 = 0

Slack for E = 9-5 = 4

Slack for F = 11-11 = 0

Slack for G = 14-11 = 3

a. Activities which has 0 slack cannot be delayed and hence called critical activities. The string of critical activities is called critics path.

Activities on the critical path are A, D, F.

b. The critical path determines completion time of the Project.

Time for critical path = Project completion time = 5 + 6 + 8 = 19

c.

Slack for A, D, F is 0.

Slack for B is 1

Slack for C & G is 3.

Slack for E is 4.