Download - Network Planning Methods Example PERT & CPM
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Network Planning Methods Network Planning Methods Example PERT & CPMExample PERT & CPM
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Terms Used in Project Management Activity : A certain amount of work or task required in the
project Activity duration: In CPM the best estimate of time to
complete an activity . In PERT the expected time or average time to complete an activity
Critical activity : An activity that has no room for schedule slippages : if it slips the entire the entire project completion will slip. An activity with zero slack
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Critical path: The chain of critical activities for the project .The longest path through the network
Dummy activity :An activity that consumes no time but shows precedence among activities
Earliest finish (EF): The earliest that an activity can finish from the beginning of the project
Earliest start ( ES): The earliest that an activity can start from the beginning of the project
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Event :A beginning , a completion point ,or a milestone accomplishment within the project . An activity begins and ends with events
Latest finish (LF) : The latest that an activity can finish from the beginning of the project
Latest start (LS) :The latest that an activity can start from the beginning of the project
Most likely time ( t m) : The time for completing the activity that is is the consensus best estimate, used in PERT
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Optimistic Time (to): The time for completing an activity if all goes well : used in PERT
Pessimistic Time (tp): The time for completing an activity if bad luck is encountered : used in PERT
Predecessor activity : An activity that must occur before another activity .
Slack : The amount of time that an activity or group of activities can slip without causing a delay in the completion of the project
Successor activity : An activity that must occur after another activity
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Conventions used in drawing network diagrams (Arrows & Circles )
Activity on Arrow (AOA) : The activities are denoted by Arrows and events are denoted by circles
Activity on Node(AON) : Activities are denoted by circles(or nodes) and the precedence relation ships between activities are indicated by arrows
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AOA Project Network for HouseAOA Project Network for House
32 0
1
31 1
11 2 4 6 7
3
5
Lay foundation
Design house and obtain financing
Order and receive materials
Dummy
Finish work
Select carpet
Select paint
Build house
AON Project Network for House
13
22
43
31 5
1
61
71Start
Design house and obtain financing
Order and receive materials
Select paintSelect carpet
Lay foundations Build house
Finish work
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Situations in network diagramSituations in network diagram
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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Forward PassForward Pass 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 analysisCPM analysis
Draw the CPM network Analyze the paths through the network Determine the float for each activity
Compute the activity’s 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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Relationship between activities Project duration Critical path Slack for non – critical activities Crashing (cost / time trade-offs) Resource usage
PERT / CPMPERT / CPMNetwork planning methods that generate:Network planning methods that generate:
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St. Paul’s HospitalSt. Paul’s Hospital
ImmediateActivity Description Predecessor(s)
A Select administrative and medical staff.B Select site and do site survey.C Select equipment.D Prepare final construction plans and layout.E Bring utilities to the site.F Interview applicants and fill positions in nursing,
support staff, maintenance, and security.G Purchase and take delivery of equipment.H Construct the hospital.I Develop an information system.J Install the equipment.K Train nurses and support staff.
——ABB
ACDAE,G,HF,I,J
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St. Paul’s HospitalSt. Paul’s Hospital
ImmediateActivity Description Predecessor(s)
A Select administrative and medical staff.B Select site and do site survey.C Select equipment.D Prepare final construction plans and layout.E Bring utilities to the site.F Interview applicants and fill positions in nursing,
support staff, maintenance, and security.G Purchase and take delivery of equipment.H Construct the hospital.I Develop an information system.J Install the equipment.K Train nurses and support staff.
——ABB
ACDAE,G,HF,I,J
AON Network
FinishStart
A
B
C
D
E
F
G
H
I
J
K
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St. Paul’s HospitalSt. Paul’s Hospital
ImmediateActivity Description Predecessor(s)
A Select administrative and medical staff.B Select site and do site survey.C Select equipment.D Prepare final construction plans and layout.E Bring utilities to the site.F Interview applicants and fill positions in nursing,
support staff, maintenance, and security.G Purchase and take delivery of equipment.H Construct the hospital.I Develop an information system.J Install the equipment.K Train nurses and support staff.
——ABB
ACDAE,G,HF,I,J
Completion Time
FinishStart
K9
I15
F10
C10
D10
E24
G35
H40
J4
A12
B9
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St. Paul’s HospitalSt. Paul’s Hospital
ImmediateActivity Description Predecessor(s)
A Select administrative and medical staff.B Select site and do site survey.C Select equipment.D Prepare final construction plans and layout.E Bring utilities to the site.F Interview applicants and fill positions in nursing,
support staff, maintenance, and security.G Purchase and take delivery of equipment.H Construct the hospital.I Develop an information system.J Install the equipment.K Train nurses and support staff.
——ABB
ACDAE,G,HF,I,J
Completion Time
FinishStart
K9
I15
F10
C10
D10
E24
G35
H40
J4
A12
B9
Path Expected Time (wks)
A-I-K 36A-F-K 31A-C-G-J-K 70B-D-H-J-K 72B-E-J-K 46
CriticalPath
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Critical PathCritical Path The longest path in the network Defines the shortest time project can be completed Critical path activity delay project delay
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Begin at starting event and work forward ES is earliest start
ES = 0 for starting activities ES = Maximum EF of all
predecessors for non-starting activities
EF is earliest finish EF = ES + Activity time
Earliest Start and Earliest FinishEarliest Start and Earliest Finish
ESES
LS
EFEF
LF
Activity Name
Activity Duration
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A
12
K
9
C
10
G
35
J
4
H
40
B
9
D
10
E
24
I
15
F
10
FinishStart
Earliest Start / Earliest FinishEarliest Start / Earliest Finish
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Earliest Start / Earliest FinishEarliest Start / Earliest Finish
Finish
Earliest start time Earliest finish time
A
12
K
9
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22 63 72
22 57
59 6319 59
9 33
0 9 9 19
12 22
Critical path
Start
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Begin at ending event and work backward LF is latest finish
LF = Maximum EF for ending activities
LF = Minimum LS of all successors for non-ending activities
LS is latest start LS = LF – Activity time
Latest Start and Latest FinishLatest Start and Latest Finish
ES
LS
EF
LF
Activity Name
Activity Duration
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Latest Start / Latest FinishLatest Start / Latest Finish
A
12
K
9
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22 63 72
22 57
59 6319 59
9 33
0 9 9 19
12 22
48 63
2 14 53 63 63 72
14 24 24 59
0 9 9 19 19 59
35 59
59 63
Latest start time Latest finish time
Critical path
FinishStart
What do you notice about ES/LS & EF/LF?
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What do you notice about ES/LS & EF/LF?
For Activity A ES = 0 LS = 2 Meaning: Due to some reason of if activity A is not started
at 0 weeks but 1, 2 or 3 weeks, even then completion of project is not delayed
For Activity B ES = 0 LS = 0 Meaning Any delay in start would delay project completion.
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Activity Slack AnalysisActivity Slack Analysis
A
12
K
9
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22 63 72
22 57
59 6319 59
9 33
0 9 9 19
12 22
48 63
2 14 53 63 63 72
14 24 24 59
0 9 9 19 19 59
35 59
59 63
Latest start time Latest finish time
Critical path
FinishStartSlackK = 63 – 63 = 0
or
SlackK = 72 – 72 = 0
Slack = LS – ES
or
Slack = LF – EF
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Activity Slack AnalysisActivity Slack Analysis
A
12
K
9
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22 63 72
22 57
59 6319 59
9 33
0 9 9 19
12 22
48 63
2 14 53 63 63 72
14 24 24 59
0 9 9 19 19 59
35 59
59 63
Latest start time Latest finish time
Critical path
FinishStart
Node Duration ES LS Slack
A 12 0 2 2BB 99 00 00 00C 10 12 14 2DD 1010 99 99 00E 24 9 35 26F 10 12 53 41G 35 22 24 2HH 4040 1919 1919 00I 15 12 48 36JJ 44 5959 5959 00KK 66 6363 6363 00
Activity slack = maximum delay time
Critical path activities have zero slack
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Activity SlackActivity Slack
How much would we like to reduce the time for activity B?
C
15
5 20
10 25
A
5
0 50 5
FinishStart
B
20
5 25
5 25D
10
25 35
25 35
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PERT PERT PERT is based on the assumption that an activity’s duration follows a
probability distribution instead of being a single value Three time estimates are required to compute the parameters of an
activity’s duration distribution: pessimistic time (tp ) - the time the activity would take if things did
not go well most likely time (tm ) - the consensus best estimate of the activity’s
duration optimistic time (to ) - the time the activity would take if things did go
well
Mean (expected time): te =tp + 4 tm + to
6
Variance: Vt =2 =tp - to
6
2
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PERT analysisPERT analysis Draw the network. Analyze the paths through the network and find the critical path. The length of the critical path is the mean of the project duration
probability distribution which is assumed to be normal The standard deviation of the project duration probability distribution is
computed by adding the variances of the critical activities (all of the activities that make up the critical path) and taking the square root of that sum
Probability computations can now be made using the normal distribution table.
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Probability computationProbability computation
Determine probability that project is completed within specified time
Z = x -
where = tp = project mean time
= project standard mean time
x = (proposed ) specified time
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Normal Distribution of Project TimeNormal Distribution of Project Time
= tp Timex
Z
Probability
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PERT Example PERT Example
Immed. Optimistic Most Likely Pessimistic
Activity Predec. Time (Hr.) Time (Hr.) Time (Hr.)
A -- 4 6 8B -- 1 4.5 5C A 3 3 3
D A 4 5 6 E A 0.5 1 1.5 F B,C 3 4 5 G B,C 1 1.5 5 H E,F 5 6 7 I E,F 2 5 8 J D,H 2.5 2.75 4.5 K G,I 3 5 7
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PERT ExamplePERT Example
AA
DD
CC
BB
FF
EE
GG
II
HH
KK
JJ
PERT Network
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PERT ExamplePERT Example
Activity Expected Time Variance A 6 4/9
B 4 4/9 C 3 0 D 5 1/9 E 1 1/36 F 4 1/9 G 2 4/9 H 6 1/9 I 5 1 J 3 1/9 K 5 4/9
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PERT ExamplePERT Example
Activity ES EF LS LF Slack A 0 6 0 6 0 *critical
B 0 4 5 9 5 C 6 9 6 9 0 * D 6 11 15 20 9 E 6 7 12 13 6 F 9 13 9 13 0 * G 9 11 16 18 7 H 13 19 14 20 1 I 13 18 13 18 0 * J 19 22 20 23 1 K 18 23 18 23 0 *
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PERT ExamplePERT Example
Vpath = VA + VC + VF + VI + VK
= 4/9 + 0 + 1/9 + 1 + 4/9
= 2
path = 1.414
z = (24 - 23)/(24-23)/1.414 = .71
From the Standard Normal Distribution table:
P(z < .71) = .5 + .2612 = .7612
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PROJECT COSTPROJECT COST
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Cost consideration in projectCost consideration in project
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 duration of 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 project manager selects the least cost critical activity, reduces it by one time unit, and traces that change through the remainder of the network.
When there is more than one critical path, each of the critical paths must be reduced.
If the length of the project needs to be reduced further, the process is repeated.
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Project CrashingProject Crashing Crashing
reducing project time by expending additional resources
Reduction in activity duration by any change in its resources, resource use, method or material is referred to as crashing of the activity
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 crashingActivity crashingA
ctiv
ity
cost
Activity time
Crashing activity
Crash time
Crash cost
Normal Activity
Normal time
Normal cost
Slope = crash cost per unit time
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Time-Cost RelationshipTime-Cost Relationship 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 costsTime-Cost Tradeoff
cost
time
Direct cost
Indirect cost
Total project costMin total cost = optimal project time
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Project Crashing exampleProject Crashing example
111122
2288
441122
3344 55
44
6644
7744
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Time Cost dataTime Cost data
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
2800
3500
6000
71000
1100
1100
21000
5
3
1
3
3
3
1
400
700
2000
8000
1100
1100
7000
75000
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112
28
34 5
4
64
74
12
4Project duration = 36
From…..
To…..17
28
34 5
4
64
74
R400
12
4
Project
duration = 31
Additional cost = R2000
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GANTT CHARTGANTT CHART
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Gantt ChartGantt ChartGantt Chart was developed by…
Henry Laurence Gantt (1861-1919) was a mechanical engineer and management consultant who is most famous for developing the ‘Gantt chart’ in the 1910s. These Gantt charts were employed on major infrastructure projects including the Hoover Dam and Interstate highway system. He refined production control and cost control techniques.
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Example of Gantt ChartExample of Gantt Chart
| | | | |Activity
Design house and obtain financing
Lay foundation
Order and receive materials
Build house
Select paint
Select carpet
Finish work
00 22 44 66 88 1010MonthMonth
MonthMonth11 33 55 77 99
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Gantt ChartGantt ChartActivities in Buy a HouseActivities in Buy a House
` BUY A HOUSE
LOCATION FINANCINGFIND HOUSE
1 - Criteria 3- Determine affordability
6- Type of House
2- Visit Locations
4- Determine mortgage provider
7- Find Real Estate Agent
5- Lockup mortgage commitment
8- Look for House
9- Make Offer, P&S Agreem't
10 - Closing
TASK PREDECESSOR1-criteria 32-visit loc. 13-affordability4-mortgage co 35-mortg lock 46-type of hse 17-real est agent 2, 68-look for hse 79-offer, P&S 5, 810-closing 9