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Project Management - CPM/PERT
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Project Network
2
` Use of nodes and arrows
Arrows An arrow leads from tail to head directionally
` Indicate ACTIVITY, a time consuming effort that is required to perform apart of the work.
Nodes A node is represented by a circle- Indicate EVENT, a point in time where one or more activities start and/or
finish.
Network analysis is the general name given to certain specific techniques which can beused for the planning, management and control of projects
Activity
A task or a certain amount of work required in the project Requires time to complete
Represented by an arrow
Dummy Activity
Indicates only precedence relationships
Does not require any time of effort
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3
` Event`
Signals the beginning or ending of an activity` Designates a point in time` Represented by a circle (node)
` Network` Shows the sequential relationships among activities using nodes
and arrows
Activity-on-node (AON)
nodes represent activities, and arrows show precedence relationships
Activity-on-arrow (AOA)arrows represent activities and nodes are events for points in time
Project Network
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A A Pro ect Networ or House
4
3
2 0
1
3
1 1
11 2 4 6 7
3
5
Lay
foundation
Design house
and obtain
financing
Order and
receive
materials
Dummy
Finishwork
Select
carpet
Select
paint
Buildhouse
AON Project Network for House
13
2
2
4
3
31 5
1
61
71Start
Design house
and obtain
financing
Order and receivematerials
Select paint
Select carpet
Lay foundations Build house
Finish work
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Situations in network diagram
5
AB
C
A must finish before either B or C can start
A
B
C both A and B must finish before C can start
D
C
B
Aboth A and C must finish before either of B or D can
start
A
C
B
D
Dummy
A must finish before B can start
both A and C must finish before D can start
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Concurrent Activities
6
2 3
Lay foundationLay foundation
Order materialOrder material
(a)(a) Incorrect precedenceIncorrect precedence
relationshiprelationship
(b)(b) Correct precedenceCorrect precedence
relationshiprelationship
3
42
DummyDummyLayLay
foundationfoundation
Order materialOrder material
11
22 00
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Network example
7
Illustration of network analysis of a minor redesign of a product and its associated packaging.
The key question is: How long will it take to complete this project ?
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For clarity, this list is kept to a minimum by specifying only immediate relationships, that is
relationships involving activities that "occur near to each other in time".
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uest ons to prepare act v ty networ
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` Is this a Start Activity?
` Is this a Finish Activity?
` What Activity Precedes this?` What Activity Follows this?
` What Activity is Concurrent with this?
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CPM calculation
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`
Path` A connected sequence of activities leading from the starting
event to the ending event
` Critical Path
` The longest path (time); determines the project duration
` Critical Activities
` All of the activities that make up the critical path
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Forwar Pass
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` Earliest Start Time (ES)` earliest time an activity can start
` ES = maximum EF of immediate predecessors` Earliest finish time (EF)
` earliest time an activity can finish` earliest start time plus activity time
EF= ES + t
Latest Start Time (LS)
Latest time an activity can start without delaying critical path time
LS= LF - t
Latest finish time (LF)latest time an activity can be completed without delaying critical path time
LS = minimum LS of immediate predecessors
Backward Pass
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CPM analysis
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` Draw the CPM network
` Analyze the paths through the network
` Determine the float for each activity
` Compute the activitys float
float = LS - ES = LF - EF
` Float is the maximum amount of time that this activity can be
delay in its completion before it becomes a critical activity, i.e.,
delays completion of the project
` Find the critical path is that the sequence of activities and events
where there is no slack i.e.. Zero slack` Longest path through a network
` Find the project duration is minimum project completion time
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CPM Example:
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` CPMNetwork
a, 6a, 6a, 6a, 6
f, 15f, 15f, 15f, 15
b, 8b, 8b, 8b, 8
c, 5c, 5c, 5c, 5
e, 9e, 9e, 9e, 9
d, 13d, 13d, 13d, 13
g, 17g, 17g, 17g, 17 h, 9h, 9h, 9h, 9
i, 6i, 6i, 6i, 6
j, 12j, 12j, 12j, 12
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CPM Example
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` ES and EF Times
a, 6a, 6a, 6a, 6
f, 15f, 15f, 15f, 15
b, 8b, 8b, 8b, 8
c, 5c, 5c, 5c, 5
e, 9e, 9e, 9e, 9
d, 13d, 13d, 13d, 13
g, 17g, 17g, 17g, 17 h, 9h, 9h, 9h, 9
i, 6i, 6i, 6i, 6
j, 12j, 12j, 12j, 12
0 6
0 8
0 5
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CPM Example
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` ES and EF Times
a, 6a, 6a, 6a, 6
f, 15f, 15f, 15f, 15
b, 8b, 8b, 8b, 8
c, 5c, 5c, 5c, 5
e, 9e, 9e, 9e, 9
d, 13d, 13d, 13d, 13
g, 17g, 17g, 17g, 17 h, 9h, 9h, 9h, 9
i, 6i, 6i, 6i, 6
j, 12j, 12j, 12j, 12
0 6
0 8
0 5
5 14
8 21
6 23
6 21
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CPM Example
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` ES and EF Times
a, 6a, 6a, 6a, 6
f, 15f, 15f, 15f, 15
b, 8b, 8b, 8b, 8
c, 5c, 5c, 5c, 5
e, 9e, 9e, 9e, 9
d, 13d, 13d, 13d, 13
g, 17g, 17g, 17g, 17 h, 9h, 9h, 9h, 9
i, 6i, 6i, 6i, 6
j, 12j, 12j, 12j, 12
0 6
0 8
0 5
5 14
8 21 21 33
6 2321 30
23 29
6 21
Projects EF = 33Projects EF = 33
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CPM Example
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` LS and LF Times
a, 6a, 6a, 6a, 6
f, 15f, 15f, 15f, 15
b, 8b, 8b, 8b, 8
c, 5c, 5c, 5c, 5
e, 9e, 9e, 9e, 9
d, 13d, 13d, 13d, 13
g, 17g, 17g, 17g, 17
h, 9h, 9h, 9h, 9
i, 6i, 6i, 6i, 6
j, 12j, 12j, 12j, 12
0 6
0 8
0 5
5 14
8 21
21 33
6 23
21 30
23 29
6 21
21 33
27 33
24 33
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CPM ExampleCPM Example
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`
LS and LF Times
a, 6a, 6a, 6a, 6
f, 15f, 15f, 15f, 15
b, 8b, 8b, 8b, 8
c, 5c, 5c, 5c, 5
e, 9e, 9e, 9e, 9
d, 13d, 13d, 13d, 13
g, 17g, 17g, 17g, 17
h, 9h, 9h, 9h, 9
i, 6i, 6i, 6i, 6
j, 12j, 12j, 12j, 12
0 6
0 8
0 5
5 14
8 21
21 33
6 23
21 30
23 29
6 21
4 10
0 8
7 12
12 21
21 33
27 33
8 21
10 27
24 33
18 24
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CPM Example
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`
Critical Path
a, 6a, 6a, 6a, 6
f, 15f, 15f, 15f, 15
b, 8b, 8b, 8b, 8
c, 5c, 5c, 5c, 5
e, 9e, 9e, 9e, 9
d, 13d, 13d, 13d, 13
g, 17g, 17g, 17g, 17 h, 9h, 9h, 9h, 9
i, 6i, 6i, 6i, 6
j, 12j, 12j, 12j, 12
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PERT Example
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Immed. Optimistic Most Likely Pessimistic
Activity Predec. Time (Hr.) Time (Hr.) Time (Hr.)
A -- 4 6 8B -- 1 4.5 5
C A 3 3 3D A 4 5 6E A 0.5 1 1.5F B,C 3 4 5
G B,C1
1
.5 5H E,F 5 6 7I E,F 2 5 8J D,H 2.5 2.75 4.5K G,I 3 5 7
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PERT Example
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AA
DD
CC
BB
FF
EE
GG
II
HH
KK
JJ
PERT Network
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PROJECT COST
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Cost consideration in project
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` Project managers may have the option or requirement to crash
the project, or accelerate the completion of the project.` This is accomplished by reducing the length of the critical path(s).
` The length of the critical path is reduced by reducing the durationof the activities on the critical path.
` If each activity requires the expenditure of an amount of money
to reduce its duration by one unit of time, then the projectmanager selects the least cost critical activity, reduces it by onetime unit, and traces that change through the remainder of thenetwork.
` As a result of a reduction in an activitys time, a new critical pathmay be created.
` When there is more than one critical path, each of the criticalpaths must be reduced.
` If the length of the project needs to be reduced further, theprocess is repeated.
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Project Crashing
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`
Crashing` reducing project time by expending additional resources
` Crash time
` an amount of time an activity is reduced
` Crash cost` cost of reducing activity time
` Goal
` reduce project duration at minimum cost
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Activity crashing
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Activity time
Crashing activity
Crash time
Crash cost
Normal Activity
Normaltime
Normal
cost
Slope = crash cost per unit time
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Time-Cost Relationship
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Crashing costs increase as project duration decreases
Indirect costs increase as project duration increases
Reduce project length as long as crashing costs are less than indirect costs
Time-Cost Tradeoff
time
Direct cost
Indirect cost
Total project costMin total cost =
optimal project time
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Project Crashing example
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11
1212
22
88
441212
33
44 55
44
66
44
77
44
Project duration = 36
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Time Cost data
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Activity Normal
time
Normal
cost Rs
Crash
time
Crash
cost Rs
Allowable
crash time
slope
1
2
3
4
5
6
7
12
8
4
12
4
4
4
3000
2000
4000
50000
500
500
1500
7
5
3
9
1
1
3
5000
3500
7000
71000
1100
1100
22000
5
3
1
3
3
3
1
400
500
3000
7000
200
200
7000
75000 110700
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30
1
12
2
8
3
4 5
4
6
4
7
4
R400
R500
R3000
R7000
R200
R200
R70012
4
Project duration = 36
From..
To..
1
7
2
8
3
4 5
4
6
4
7
4
R400
R500
R3000
R7000
R200
R200
R70012
4
Project
duration = 31
Additional cost =
R2000
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Benefits of CPM/PERT
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Useful at many stages of project management
Mathematically simple
Give critical path and slack time
Provide project documentation
Useful in monitoring costs
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Limitations to CPM/PERT
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Clearly defined, independent and stable activities
Specified precedence relationships
Over emphasis on critical paths
Deterministic CPM model
Activity time estimates are subjective and depend on judgment
PERT assumes a beta distribution for these time estimates, but
the actual distribution may be different
PERT consistently underestimates the expected project
completion time due to alternate paths becoming critical
To overcome the limitation, Monte Carlo simulations can be performed on the network
to eliminate the optimistic bias
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Computer Software
for Project Management
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` Microsoft Project (Microsoft Corp.)
` MacProject (Claris Corp.)
` PowerProject (ASTA Development Inc.)
` Primavera Project Planner (Primavera)
` Project Scheduler (Scitor Corp.)
` Project Workbench (ABT Corp.)
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Practice Example
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A social project manager is faced with a project with the following activities:
Activity Description Duration
Social work team to live in village 5w
Social research team to do survey 12w
Analyse results of survey 5w
Establish mother & child health program 14w
Establish rural credit programme 15w
Carry out immunization of under fives 4w
Draw network diagram and show the critical path. Calculate project duration.
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Practice problem
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Activity Description Duration
1-2 Social work team to live in village 5w
1-3 Social research team to do survey 12w
3-4 Analyse results of survey 5w
2-4 Establish mother & child health program 14w
3-5 Establish rural credit programme 15w4-5 Carry out immunization of under fives 4w
3
1
2
4
5
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