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

Forward pass:

E₁ = 0

E₂ = 0 + 6 = 6

E₃ = 0 + 5 = 5

E₄ = 6 + 10 = 16

E₅ = (E₄ + 6) (or) (E₃ + 4)

E₅ = (16 + 6) (or) (5 + 4) [whichever is maximum]

E₅ = 22

E₆ = (E₅ + 9) (or) (E₄ + 2)

E₆ = (22 + 9) (or) (4 + 2) [whichever is maximum]

E₆ = 31

Backward pass:

L₆ = 31

L₅ = 31 – 9 = 22

L₄ = 22 – 6 (or) 31 – 2 [whichever is minimum]

L₄ = 16

L₃ = 22 – 4 = 18

L₂ = 16 – 10 = 6

L₁ = 6 – 6 = 0

EFT and LFT are the same on 1-2, 2-3, 3-4, and 4-5 

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