Question

Construct the network for the project whose activities are given below.

Activity	0 - 1	1 - 2	1 - 3	2 - 4	2 - 5	3 - 4	3 - 6	4 - 7	5 - 7	6 - 7
Duration (in week)	3	8	12	6	3	3	8	5	3	8

Calculate the earliest start time, earliest finish time, latest start time and latest finish time of each activity. Determine the critical path and the project completion time.

Answer 1

E₁ = 0 + 3 = 3

E₂ = E₁ + t₁₂ = 8 + 3 = 11

E₃ = 3 + 12 = 15

E₄ = 15 + 3 = 18

E₅ = E₂ + 3 = 11 + 3 = 14

E₆ = E₃ + 8 = 15 + 8 = 23

E₇ = E₆ + 8 = 23 + 8 = 31

L₇ = 31

L₆ = L₇ – 8 = 31 – 8 = 23

L₅ = L₇ – 3 = 31 – 3 = 28

L₄ = L₇ – 5 = 31 – 5 = 26

L₃ = L₆ – 8 = 23 – 8 = 15

L₂ = L₅ – 3 or L₄ which is minimum

= (28 – 3) or (26 – 6)

= 25 or 20

= 20 (which is minimum)

L₁ = L₂ – 8 or L₃ – 12

whichever is minimum

= (20 – 8) or (15 – 12)

= 12 or 3

= 3

L₀ = 0

Activity	Duration tij	EST	EFT = EST + tij	LST = LFT – tij	LFT
0 - 1	3	0	3	3	3
1 - 2	8	3	11	20 – 8 = 12	20
1 - 3	12	3	15	15 – 12 = 3	15
2 - 4	6	11	17	26 – 6= 20	26
2 - 5	3	11	14	28 – 3 = 25	28
3 - 4	3	15	18	26 – 3 = 23	26
3 - 6	8	15	23	23 – 8 = 15	23
4 - 7	5	18	23	31 – 5 = 26	31
5 - 7	3	14	14	31 – 3 = 28	31
6 - 7	8	23	31	31 – 8 = 23	31

The critical path is 0 - 1 - 3 - 6 - 7 and the project completion time is 31 weeks.