Page 248 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 12: Critical Path Method and PERT

To calculate T for all activities Notes
L
T = T = 22
L10 E10
T = T – t , 10 = 22 – 7 = 15
L9 E10 9
T = T – t = 22 – 5 = 17
L8 E10 8, 10
T = T – t = 17 – 2 = 15
L7 E8 7, 8
T = T – t = 17 – 1 = 16
L6 E8 6, 8
T = min (T – t and T – t )
L5 E6 5, 6 E7 5, 7
= min (16 – 4 and 15 -8) = min (12, 7)

= 7 days
T = T – t = 15 – 5 =10
L4 L9 4, 9
T = min (T – t and T – t )
L3 L4 3, 4 L5 3, 5
= min (10 – 1 and 7 – 6) = min (9, 1)
= 1 day
T = T – t = 10 – 1 = 9
L2 L4 2, 4
T = Min (T – t and T – t )
L1 L2 1, 2 L3 1, 3
= Min (9 – 4 and 1 – 1) = 0

Table 12.5: Various Activities and their Floats

Activity Activity Normal Earliest Time Latest Time Total Float
Name Time
Start Finish Start Finish
1-2 A 4 0 4 5 9 5
1-3 B 1 0 1 0 1 0
2-4 C 1 4 5 9 10 5

3-4 D 1 1 2 9 10 8
3-5 E 6 1 7 1 7 0
4-9 F 5 5 10 10 15 5
5-6 G 4 7 11 12 16 5
5-7 H 8 7 15 7 15 0
6-8 I 1 11 12 16 17 5
7-8 J 2 15 17 15 17 0
8-10 K 5 17 22 19 22 0
9-10 L 7 10 17 15 22 5

3. From the table 12.5, we observe that the activities 1 – 3, 3 – 5, 5 – 7,7 – 8 and 8 – 10 are critical
activities as their floats are zero.

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