Question

The following table gives the activities of a project and their duration in days

Activity	1 - 2	1 - 3	2 - 3	2 - 4	3 - 4	3 - 5	4 - 5
Duration	5	8	6	7	5	4	8

Construct the network and calculate the earliest start time, earliest finish time, latest start time and latest finish time of each activity and determine the Critical path of the project and duration to complete the project.

Answer 1

E₁ = 0

E₂ = 0 + 5 = 5

E₃ = (0 + 8) or (5 + 6)

Whichever is maximum

= 11

E₄ = (11 + 5) or (5 + 7)

Whichever is maximum

= 16

E₅ = (11 + 4) or (16 + 8)

Whichever is maximum

= 24

L₅ = 24

L₄ = 24 – 8 = 16

L₃ = (24 – 4) or (16 – 5)

whichever is minimum

= 11

L₂ = (16 – 6) or (16 – 7)

whichever is minimum

= 5

L₁ = (5 – 5) or (11 – 8)

whichever is minimum

L₁ = 0

Activity	Duration tij	EST	EFT = EST + tij	LST = LFT – tij	LFT
1 - 2	5	0	5	5 – 5 = 0	5
1 - 3	8	0	8	11 – 8 = 3	11
2 - 3	6	5	11	11 – 6 = 5	11
2 - 4	7	5	12	16 – 7 = 9	16
3 - 4	5	11	16	16 – 5 = 11	16
3 - 5	4	11	15	24 – 4 = 20	24
4 - 5	8	16	24	24 – 8 = 16	24

Since EFT and LFT are same in 1 - 2, 2 - 3, 3 - 4 and 4 - 5.

Hence the critical path is 1 - 2 - 3 - 4 - 5 and the duration time taken is 24 days.