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

Forward pass:

E₁ = 0 + 3 = 3

E₂ = E₁ + t₁₂ = 8 + 3 = 11

E₃ = 3 + 12 = 15

E₄ = E₂ + 6 (or) E₃ + 3 = 11 + 6 (or) 15 + 3 = 18

[We must select a maximum value for forwarding pass]

E₄ = 15 + 3 = 18

E₂ = E₂ + 3 = 11 + 3 = 14

E₆ = E₃ + 8 = 15 + 8 = 23

E₇ = E₆ + 8 = 23 + 8 = 31

Backward pass:

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 – 6 = (28 – 3) (or) (26 – 6) = 25 (or) 20

[We must select a minimum value for a backward pass and maximum value for forwarding pass]

L₁ = L₂ – 8 (or) L₃ – 12 = 20 – 8 (or) 15 – 12 = 12 (or) 3 = 3

L₀ = 0

Activity	Duration	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	17	31 - 8 = 28	31
6-7	8	23	31	31 - 8 = 23	31

Critical path 0-1-3-6-7 and the duration is 31 works.