17-1 maintenance

Project Management

PERT and CPM

PERT: Program Evaluation
and Review Technique
CPM: Critical Path Method

Graphically displays project

activities
Estimates how long the
project will take
Indicates most critical
activities
Show where delays will not
affect project

Arranged by Dr. Syed Hassan Javed

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Project Management

Developed in 1950s
CPM by DuPont for
chemical plants
PERT by U.S. Navy for
Polaris missile
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maintenance

The Network Diagram

Network (precedence)
diagram
Activity-on-arrow (AOA)
Activity-on-node (AON)
Activities
Events
Slack is the amount of time
an activity can be delayed
without delaying the project
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The Network Diagram (contd)

Path
Sequence of activities that leads from the
starting node to the finishing node
Critical path
The longest path; determines expected project
duration
Critical activities
Activities on the critical path
Slack
Allowable slippage for path; the difference the
length of path and the length of critical path
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Project Network Activity on Arrow

Order
AOA furniture 4
Furniture
Locate 2 setup
facilities
Remodel
1 5 6
Move
in
Interview
Hire and
train
3
17-6 Project Management

Project Network Activity on Node

Order
furniture
Locate Furniture
2 setup
facilities
AON
1 6
Move
Remodel
in

S 5 7

Hire and
Interview
train

3 4
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Network Conventions
a
b
c a

c
b

a c
a c

b Dummy
activity
b d
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Time Estimates
Deterministic
Time estimates that are fairly certain

Probabilistic
Estimates of times that allow for variation
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6 weeks
Deterministic 4
time estimates
3 weeks
8 weeks 2

11 weeks Move
in
1 5 6
1 week

4 weeks
9 weeks

3
17-10 Project Management

Routs to reach from 1 to 6

1) 1-2-4-5-6 (16weeks )

2) 1-2-5-6 ( 20 weeks )

3) 1-3-5-6 ( 14 weeks )
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6 weeks
Deterministic 4
time estimates
3 weeks
8 weeks 2

11 weeks Move
in
1 5 6
1 week

4 weeks
9 weeks

3
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Example 1 Solution
Critical Path

Path Length Slack

(weeks)
1-2-3-4-5-6 18 2
1-2-5-6 20 0
1-3-5-6 14 6
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Computing Algorithm
Network activities
ES: early start (As soon as you can start the activity)
EF: early finish (As soon you can finish the activity)
LS: late start ( For back calculations)
LF: late finish ( For back calculations)
Used to determine
Expected project duration
Slack time
Critical path
17-14 Project Management

Computing ES, EF, LF, LS

Slack (LS-ES)

Activity duration ES EF LF LS LS-ES

1-2 8 0 8 8 0 0
1-3 4 0 4 10 6 6
2-4 6 8 14 16 10 2
2-5 11 8 19 19 8 0
3-5 9 4 13 19 10 6
4-5 3 14 17 19 16 2
5-6 1 19 20 20 19 0
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CPM

EXAMPLES OF CRITICAL
PATH METHOD
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Picnic program
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REQUIREMENTS OF NODE
DIAGRAM
1) DEFINE ACTIVITIES

2) DEFINE TIME ASSOCIATED WITH EACH

ACTIVITY

3) DEFINE PRECEDENCE ORDER

17-18 Project Management Without precedence

Picnic program
Activities Time in min
A PREPARE TEA 20
B PREPARE FRUITS 5
C PREPARE SANDWICHES 10
D PREPARE BASKET 10
E DRESS UP 15
F COLECT BLANKETS 5
G PREPARE SUIT CASE 20
H LOAD CAR 10
I GET GAS 10
J GET SPARES 15
K DRIVE 30
17-19 Project Management HOW TO ARRANGE IT

6
2 7
8

1
3
10

9
4

5
17-20 Project Management

Picnic program
Activities Time in min
A 1,3 PREPARE TEA 20
B 1,2 PREPARE FRUITS 5
C 2,3 PREPARE SANDWICHES 10
D 3,4 PREPARE BASKET 10
E 4,6 DRESS UP 15
F 4,5 COLECT BLANKETS 5
G 5,6 PREPARE SUIT CASE 20
H 6,7 LOAD CAR 10
I 7,8 GET GAS 10
J 8,9 GET SPARES 15
K 9,10 DRIVE 30
17-21 Project Management

NODE DIAGRAM

`A D E H I J K
20 10 15 10 10 15 30

1 3 4 6 7 8 9 10

5B 10 C 5F 20 G

2 5

MAX TIME = 120 MIN

.
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NODE DIAGRAM

1 3 4 6 7 8 9 10

2 5

CRITICAL PATH 1-3-

4-5-6-7-8-9-10
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CPM

EXAMPLE CONSTRUCTION
OF A ROOM
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ACIVITIES TIME IN DAYS
A 1-3 FOUNDATION 2
B 1-2 BRICKS COLLECTION 1
C 2-3 CEMENT COLLECTION 1
D 3-4 FIRST DPC 3
E 4-6 CURING 2
F 4-5 BRICKS COLLECTION 1
G 5-6 CEMENT COLLECTION 1
H 6-7 2ND DPC 2
I 7-9 CURING 2
J 7-8 BRICKS COLLECTION 1
K 8-9 CEMENT COLLECTION 1
L 9-11 WALLS 5
M 10-11 EARTH FILLING 1
N 11-13 ROOF 21
O 11-12 DOOR AND WINDOW 5
P 12-16 SERVICES 15
Q 13-14 PLASTERS 2
R 14-16 FLOORS 15
S 14-15 WHITE WASH 2
17-25maintenance
Project Management
Optimization MSc

NODE DIAGRAM

15
8 10
2 5

1 3 4 6 7 9 11 13 14 16

12
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FIND OUT THE CRITICAL PATH

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PERT

Program
Evaluation and
Review
Technique
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Probabilistic Time Estimates

Optimistic time
Time required under optimal conditions
Pessimistic time
Time required under worst conditions
Most likely time
Most probable length of time that will be required
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Probabilistic Estimates

to tm te tp

Activity Optimistic Most likely Pessimistic

start time time (mode) time
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Expected Time

te = t o + 4t m +t p
6
te = expected time
to = optimistic time
tm = most likely time
tp = pessimistic time
17-35 Project Management

Variance

2 (t
= p o t ) 2

36

2 = variance
to = optimistic time
tp = pessimistic time
17-36 Project Management

Example

Optimistic Most likely Pessimistic

time time time

2-4-6
b

3-4-5 3-5-7 5-7-9

d e f

4-6-8
h
17-37 Project Management

Path Probabilities

Specified time Path mean

Z =
Path standard deviation

Z indicates how many standard deviations

of the path distribution the specified time
is beyond the expected path duration.
17-38 Project Management

17
Weeks
1.00
a-b-c
Weeks
10.0

d-e-f
Weeks
16.0

1.00
g-h-i
13.5 Weeks
17-39 Project Management

Time-cost Trade-offs: Crashing

Crash shortening activity duration
Procedure for crashing
Crash the project one period at a time
Only an activity on the critical path
Crash the least expensive activity
Multiple critical paths: find the sum of crashing
the least expensive activity on each critical
path
17-40 Project Management

Advantages of PERT

Forces managers to organize

Provides graphic display of activities
Identifies 4
2
Critical activities
Slack activities 1 5 6

3
17-41 Project Management

Limitations of PERT

Important activities may be omitted

Precedence relationships may not
4 be
correct 2
Estimates may include
a fudge factor 1 5 6

May focus solely

on critical path 142 weeks