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in Operations Research by (26.1k points)
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A project schedule has the following characteristics:

Activity 1-2 1-3 2-4 3-4 3-5 4-9 5-6 5-7 6-8 7-8 8-10 9-10
Time 4 1 1 1 6 5 4 8 1 2 5 7

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.

1 Answer

+1 vote
by (26.4k points)
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Best answer

Forward pass:

E1 = 0

E2 = 0 + 4 = 4

E3 = 0 + 1 = 1

E4 = (E2 + 1) (or) (E3 + 1) = (4 + 1) (or) (1 + 1) = 5 (or) 2

[whichever is maximum we must select forward pass]

∴ E4 = 5

E5 = 1 + 6 = 7

E6 = 7 + 4 = 11

E7 = 8 + 7 = 15

E8 = (E7 + 2) (or) (E6 + 1)

= (15 + 2) or (11 + 1)

= 17 or 12 [whichever is maximum]

∴ E8 = 17

E9 = 5 + 5 = 10

E10 = (E9 + 7) (or) (E8 + 5)

= (10 + 7) (or) (17 + 5)

= 17 (or) 22 [Which is maximum]

E10 = 22

Backward pass:

L10 = 22

L9 = 22 – 7 = 15

L8 = 22 – 5 = 17

L7 = 17 – 2 = 15

L6 = 17 – 1 = 16

L5 = (16 – 4) (or) (15 – 8) [whichever is minimum]

L5 = 7

L4 = 15 – 5 = 10

L3 = (10 – 1) (or) (7 – 6) [whichever is minimum]

L3 = 1

L2 = 10 – 1 = 9

L1 = 0

We can also find the critical path by this method, which also helps us to counter check the solution obtained by the table method.

Path Time
1 - 2 - 4 - 9 - 10 4 + 1 + 5 + 7 = 17
1 - 3 - 4 - 9 - 10 1 + 1 + 5 + 7 = 14
1 - 3 - 5 - 6 - 8 - 10 1 + 6 + 4 + 1 + 5 = 17 
1 - 3 - 5 - 7 - 8 - 10 1 + 6 + 8 + 2 + 5 = 22

So critical path is 1-3-5-7-8-10 as it takes 22 units to complete the project.

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