2. PERT (Program Evaluation & Review Technique)
PERT was evolved by navy engineers James E. Casie &
Margan E. Walter, in charge of special projects of United States Navy. It was
formally applied to planning & control of missile program, in October 1958.
PERT deals with the problem of uncertain activities times by the
application of statistical analysis to determination of estimated time for each
activity concerning the project. In order to arrive at most reliable estimate of time,
“Three Time Estimates”.
1. The Optimistic Time – It is the shortest time possible if everything goes
perfectly with no complications, the chance of this optimum actually
occurring might be in 1 in 100.
2. The Pessimistic Time – It is the longest time considerable, it includes time
for unusual delay and thus the change of its happening might be in 1 in 100.
3. The Most Likely Time – It would be the best estimate of what normally
would occur.
METHODOLOGY / STEPS OF PERT
The steps involved in PERT are:-
A. Preparing the network: - First of all a list of activities that constitute the
project is prepared. The predecessor and successor activities are
determined. A network diagram is prepared on the basis of dependence
between different activities and events. This is project planning phase of
PERT. Events are numbered in ascending order from left to right.
B. Network Analysis: - Estimates of time required to perform each activities
are made.
3. C. Scheduling: - Expected time for each activity is computed from the three
time estimates. Earliest and latest start time and finished time for each
activity are determined. Then the critical path through the network is
determined. The slack times associated with the non critical activities are
also computed.
D. Time-Cost-Trade off: - If management wants to reduce the project
completion time, crashing or compressing the project is done. The cost of
reducing project completion time is computed.
E. Resources Allocation: - The feasibility of each schedule is checked with
respect to manpower and equipment requirements.
F. Project Control: - The project is controlled by checking programs against the
schedule, assigning and scheduling manpower and equipment and
analysing the effects of delay. Whenever major changes are made in the
schedule, the network is revised accordingly, and a new schedule is
prepared. Thus, monitoring of program may require periodic updating of
project and rescheduling to ensure completion of the project in time.
Latest Finished Time (LFT)
It is calculated by moving backward i.e. from last event to first
event of the network diagram.
Latest Start Time (LST)
It is the latest possible time by which an activity can start.
LST = LFT – Duration of that activity
4. Earliest Start Time (EST)
It is the earliest possible time by which an activity can start.
Earliest Finished Time (EFT)
It is the earliest time of an activity.
FLOAT / SLACK
It means spare time, a margin of extra time over and above its duration
which a non-critical activity can consume without delaying the project.
Float is the difference between the time available for completing an
activity and the time necessary to complete the same.
Total Float = LST – EST
OR
Total Float = LFT - EFT
Free Float If all the non critical activities start as early as possible the
surplus time is the free flow. If an activity is delayed by the free flow period, the
succeeding activity will not be delayed.
5. Free Float = EST of tail event
– EST of head event
– Activity duration
Independent Float The use of independent float of an activity does not change
the float in other activities.
Independent Float = EST of tail event
- LFT of head event
- Activity duration
(*Note: - Independent float, if it turns out to be negative, it is taken as zero.)
6. NUMERICAL
Activity Optimistic Time Most Expected Time Pessimistic Time Expected Variance
(to) (tm) (tp) Time
1-2 4 8 12 8 1.78
2-3 1 4 7 4 1.00
2-4 8 12 16 12 1.78
3-5 3 5 7 5 0.44
4-5 0 0 0 0 0.00
4-6 3 6 9 6 1.00
5-7 3 6 9 6 1.00
5-8 4 6 8 6 0.44
7-9 4 8 12 8 1.78
8-9 2 5 8 5 1.00
9-10 4 10 16 10 4.00
6-10 4 6 8 6 0.44
Expected Time=[(to+4tm+tp)/6]2
Varience=[(tp-to)%6]2
Q.Present the activity in the form of a PERT network and determine-
a.Critical path
b.Earliest and latest expected time
c.Probability of computing the project within schedule completion of 48 days.
9. Critical Path=(1-2-4-5-7-9-10)
B. The earliest expected time [E(U1)]=0
E (U2)=0+8=8
E (U3)=8+4=12
E (U4)=12+8=20
E (U5)=(12+5,20+0)=20
E (U6)=20+6=26
E (U7)=26
E (U8)=20+6=26
E (U9)=34
E (U10)=34
Latest expected time are-
E(L10)=44
E(L9)=34
E(L8)=29
E(L7)=20
E(L6)=38
E(L5)=20
E(L4)=20
E(L3)=15
E(L2)=8
10. E(L1)=0
C. Expected Project Completion time
8+12+0+6+8=44 days
Project variance=(∂T)2 =1.78+1.78+0+1+1.78+4=10.34
Varience=∂T=3.216
If due date of completion of the project is 48 days then=(48-44)/3.216=1.24
From the Standard normal table, probability of meeting the due date is 0.3925
