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LECTURE 10 LECTURER ENGR
DEPARTMENT OF ENGINEERING MANAGEMENTCOLLEGE OF E & ME, NUST
DEPARTMENT OF ENGINEERING MANAGEMENTCOLLEGE OF E & ME, NUST
PLANNING ENGINEERING AND
PROJECT MANAGEMENT
Topics Covered
Program Evaluation and Review Technique (Pert)
Project Crashing
Sample Problems
Pert calculates the expected durations for all activities and then does an ordinary CPM calculation of the network using these expected values as durations. The expected value and variance can be calculated as:
TE=(a + b + 4m)/6 (already discussed)
Var=V= 1/36 (b - a)
The variance is a measure of uncertainty of the duration. The larger variance, the larger is the uncertainty.
Program Evaluation and Review Technique
2
Standard deviation = = = = ( V )
ProbabilityPr = Φ (D – T) /
D= deadline / desired completion time
T= project completion time
Φ= normal distribution (from table)
Program Evaluation and Review Technique
1/2
Problem 09Problem 09
Activity Preceding Activity
Duration (weeks)
A - 10
B - 07
C - 12
D A 18
E B 14
F B 13
G C 16
H D, E 12
I F, G 06
(Use Pert Technique on P-04)
Problem 09 (Pert Solution)Problem 09 (Pert Solution)
Activity
m a b
AA 1010 99 1717
BB 77 55 99
CC 1212 1010 2020
DD 1818 1616 3232
EE 1414 1313 2121
FF 1313 1010 1616
GG 1616 1515 2323
HH 1212 1111 1919
II 66 55 77
Problem 09 (Pert Solution)Problem 09 (Pert Solution)
Activity
m a b TE
AA 1010 99 1717 1111
BB 77 55 99 77
CC 1212 1010 2020 1313
DD 1818 1616 3232 2020
EE 1414 1313 2121 1515
FF 1313 1010 1616 1313
GG 1616 1515 2323 1717
HH 1212 1111 1919 1313
II 66 55 77 66
Problem 09 (Pert Solution)Problem 09 (Pert Solution)
Activity
m a b TE Var
AA 1010 99 1717 1111 1.781.78
BB 77 55 99 77 .44.44
CC 1212 1010 2020 1313 2.782.78
DD 1818 1616 3232 2020 7.117.11
EE 1414 1313 2121 1515 1.781.78
FF 1313 1010 1616 1313 11
GG 1616 1515 2323 1717 1.781.78
HH 1212 1111 1919 1313 1.781.78
II 66 55 77 66 .11.11
Problem 09 (Pert Solution)Problem 09 (Pert Solution)
The network is calculated using the expected
values (TE). The critical path is A-D-H.
Project completion time T= Ta+Td+Th
= 11+20+13 = 44
Variance V= Va + Vd + Vh
= 1.78+7.11+1.78= 10.67
The variance as such does not provide much practically useful information about uncertainty. It is used to calculate probability, which can then be used as a decision parameter.
For example, project manager would like to know what is the probability of reaching the 40-days deadline calculated by CPM method.
Problem 09 (Pert Solution)Problem 09 (Pert Solution)
Standard deviation= = (V) = (10.67) =
3.266
ProbabilityPr = Φ (D – T) /
D= deadline / desired completion time=40
T= project completion time=44
Problem 09 (Pert Solution)Problem 09 (Pert Solution)
1/2 1/2
Pr = Φ (40 – 44) / 3.266
= Φ (-1.23) = 0.11
The chance of meeting the
deadline is 11 percent only.
What deadline project manager should give if he/she wants 90 percent probability of finishing on or before the deadline?
If this deadline is D, using the formula
Problem 09 (Pert Solution)Problem 09 (Pert Solution)
0.90 = 0.90 = ΦΦ (D – 44) / 3.266 (D – 44) / 3.266
ΦΦ(1.28)= (1.28)= ΦΦ (D – 44) / 3.266 (D – 44) / 3.266
D= 48.2D= 48.2In order to have 90 percentguarantee against a delay, the deadline should be 49 days.
R
E
S
U
L
T
Program evaluation and review technique (PERT) allows activity duration with uncertainty. It assumes that there is no underlying connection leading to simultaneous duration variation of two or more activities.
If activity X is delayed, this does not lead to a similar delay of activity Y. This is, of course, a questionable assumption. Quite often there are activities that are connected.
For example, a delay of an activity may be caused by a shortage of labor. In this case it is reasonable to believe that this is the case for other activities performed in the same region.
Comments on Pert
Crashing means reducing project time (total project completion time)
The objective of crashing is to reduce the entire project completion time by a certain amount at the least cost.
Crashing is achieved by reducing the activity (s) times in a network.
Activity time can be reduced by utilizing additional resources i-e additional labor, more equipment and so on.
Project CrashingProject Crashing
Although shortening or crashing activity times can be expensive; doing so might be worthwhile. This is also referred as cost-time trade-offs.
Project CrashingProject Crashing
Project CrashingProject Crashing
Crash Cost and Crash Duration
Crash cost is defined as the cost associated with the fastest way of doing something and results in what we call the crash duration.
Normal Cost and Normal Duration:
Normal cost is defined as the cost associated with the most economical way of doing something and results in what we call the normal duration.
Project CrashingProject Crashing
Rules:
Crash the activities on the critical path. As a result of crashing, a parallel non-critical path may become new critical path.
Start crashing with least cost of crashing per unit time, crash the most costly activity if required, last of all.
Project CrashingProject Crashing
16
4
2
3
3 4
32
Total Project
Time 07 days
Reduce it
to 06 days
Project CrashingProject Crashing
Act- Act- ivityivity
NormNormalal
TimeTime
(days)(days)
NormNormalal
CostCost
($)($)
CrasCrashh
TimeTime
(days(days))
CrasCrashh
CostCost
($)($)
CostCost
TimeTime
1-21-2 33 4040 11 8080 (80-40)/(3-1)(80-40)/(3-1)
=20=20
1-31-3 22 5050 11 120120
1-41-4 66 100100 44 140140
2-42-4 44 8080 22 130130 (130-80)/(4-2)(130-80)/(4-2)
=25=25
3-43-4 33 6060 11 140140
crash cost per unit timecrash cost per unit time
Project CrashingProject CrashingActivity 1-2 and Activity 2-4; both are on critical path. The project completion time can be reduced to six days by crashing either 1-2 or 2-4 by one day.
It costs $20 per day to crash activity 1-2
and $25 per day to crash activity 2-4.
Therefore it is less costly to crash activity 1-2 by one day in order to achieve an over all project completion time of six days.
Problem 10The data of activities, activity precedence, activity normal and crash times and costs for a pipe line renewal is given in the table on next slides.
a) Develop a network for the project.
b) Determine the project completion time with normal time of activities.
c) Crash the project to reduce the project completion time with least incremental cost.
Note: Time is given in days and cost in rupees.
Problem 10Problem 10
Activity
Prece-dence
Normal
time
Normal cost
Crash time
Crash cost
A - 3 - 1 -
B - 4 - 4 -
C A 2 900 1 1000
D C 1 300 1 300
E D 5 2500 3 3000
F D 9 900 5 1200
G E 5 3500 2 5000
H B, D 1 300 1 300
I B, D 2 900 1 1200
Go on next slide for remaining data of Problem 10
Remaining Problem 10
Activity
Prece-dence
Normal
time
Normal cost
Crash time
Crash cost
j H, I 4 1200 2 2000
K G, J 6 4200 3 5400
L K 2 800 1 1000
M F, H, I 2 500 1 800
N L, M 2 500 1 800
O N 2 400 1 600
P L, M 4 1200 2 1600
Q N, P 2 400 1 600
R O, Q 2 400 1 500
Remaining Problem 10
Discussion