Page 246 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 12: Critical Path Method and PERT

Total float TF : The total float of an activity is the difference between the latest start time and the Notes
ij
earliest start time of that activity.
TF = LS – ES (1)
ij ij ij
or
TF = (T – T ) – t (2)
ij L E ij
Free Float FF : The time by which the completion of an activity can be delayed from its earliest
ij
finish time without affecting the earliest start time of the succeeding activity is called free float.
FF = (E – E ) – t (3)
ij j i ij
FF = Total float – Head event slack
ij
Independent Float IF : The amount of time by which the start of an activity can be delayed
ij
without affecting the earliest start time of any immediately following activities, assuming that
the preceding activity has finished at its latest finish time.

IF = (E – L ) – t (4)
ij j i ij
IF = Free float – Tail event slack
ij
Where tail event slack = L-E
i i

!
Caution The negative value of independent float is considered to be zero.
Critical Path: After determining the earliest and the latest scheduled times for various activities,
the minimum time required to complete the project is calculated. In a network, among various
paths, the longest path which determines the total time duration of the project is called the
critical path. The following conditions must be satisfied in locating the critical path of a network.

An activity is said to be critical only if both the conditions are satisfied.
1. T – T = 0
L E
2. T – t – T = 0
Lj ij Ej

Example: A project schedule has the following characteristics as shown in Table 12.4

Table 12.4: Project Schedule

Activity Name Time Activity Name Time (days)
1-2 A 4 5-6 G 4
1-3 B 1 5-7 H 8
2-4 C 1 6-8 I 1
3-4 D 1 7-8 J 2
3-5 E 6 8-10 K 5
4-9 F 5 9-10 L 7

1. Construct a network diagram.
2. Compute T and T for each activity.
E L
3. Find the critical path.

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