project planning and budgeting recall the four stages project definition and conceptualization...
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Recall the four stages• Project Definition and
Conceptualization• Project Planning and Budgeting• Project Execution and Control• Project Termination and
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Ch 17 - 2
Elements Of Project Management
• Project team– individuals from different departments within
company• Matrix organization
– team structure with members from different functional areas depending on skills needed
• Project manager– leader of project team
Ch 17 - 3
Project Planning
• Statement of work– written description of goals, work & time
frame of project• Activities require labor, resources & time• Precedence relationship shows sequential
relationship of project activities
Ch 17 - 4© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Simplified Project Network
1 32Construct forms Pour concrete
Ch 17 - 5
Elements Of Project Planning• Define project objective(s)• Identify activities• Establish precedence relationships• Make time estimates• Determine project completion time• Compare project schedule objectives• Determine resource requirements to meet
objective
Ch 17 - 6© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Work breakdown structure (WBS)
– determine subcomponents, activities & tasks
Ch 17 - 7© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Gantt Chart
• Popular tool for project scheduling• Graph with bar for representing the time for
each task• Provides visual display of project schedule• Also shows slack for activities
– (amount of time activity can be delayed without delaying project)
Ch 17 - 8
20 4 106 8
31 5 7 9Month
Month
Activity
Design house andobtain financing
Lay foundation
Order and receivematerials
Build house
Select paint
Select carpet
Finish work
A Gantt Chart
Ch 17 - 9
CPM/PERT• Critical Path Method (CPM)
– DuPont & Remington-Rand (1956)– deterministic task times– activity-on-node network construction
• Project Eval. & Review Technique (PERT)– US Navy, Booz, Allen & Hamilton– multiple task time estimates– activity-on-arrow network construction
Ch 17 - 11
Network Construction
• In AON, nodes represent activities & arrows show precedence relationships
• In AOA, arrows represent activities & nodes are events for points in time
• An event is the completion or beginning of an activity
• A dummy shows precedence for two activities with same start & end nodes
Ch 17 - 12© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Project Network For A House
1 2 4 6 7
3
5
32
0
1
31
1
1
Lay foundation
Design house and obtain financing
Order and receive materials
Dummy
Finish work
Select carpet
Select paint
Build house
Ch 17 - 13
Critical Path
• A path is a sequence of connected activities running from start to end node in network
• The critical path is the path with the longest duration in the network
• Project cannot be completed in less than the time of the critical path
Ch 17 - 14
All Possible Paths
A: 1-2-3-4-6-73 + 2 + 0 + 3 + 1 = 9 months; the critical path
B: 1-2-3-4-5-6-73 + 2 + 0 + 1 + 1 + 1 = 8 months
C: 1-2-4-6-7
3 + 1 + 3 + 1 = 8 monthsD: 1-2-4-5-6-7
3 + 1 + 1 + 1 + 1 = 7 months
Ch 17 - 15© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Concurrent Activities
4
3
2
DummyLay foundation
2 3
Lay foundation
Order materialOrder material
Incorrect precedence relationship
Correct precedence relationship
Ch 17 - 16© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Early Times(House-building example)
• ES - earliest time activity can start• Forward pass starts at beginning of
CPM/PERT network to determine ES times• EF = ES + activity time
– ESij = maximum (EFi)– EFij = ESij + tij
– ES12 = 0– EF12 = ES12 + t12 = 0 + 3 = 3 months
Ch 17 - 17© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Computing Early Times
– ES23 = max (EF2) = 3 months
– ES46 = max (EF4) = max (5,4) = 5 months
– EF46 = ES46 + t46 = 5 + 3 = 8 months
– EF67 =9 months, the project duration
Ch 17 - 18© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Late Times
• LS - latest time activity can start & not delay project
• Backward pass starts at end of CPM/PERT network to determine LS times
• LF = LS + activity time– LSij = LFij - tij
– LFij = minimum (LSj)
Ch 17 - 19© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Computing Late Times
– LF67 = 9 months
– LS67 = LF67 - t67 = 9 - 1 = 8 months
– LF56 = minimum (LS6) = 8 months
– LS56 = LF56 - t56 = 8 - 1 = 7 months
– LF24 = minimum (LS4) = min(5, 6) = 5 months
– LS24 = LF24 - t24 = 5 - 1 = 4 months
Ch 17 - 20© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Early And Late Times
1 2 4 6 7
3
5
32
0
1
31
1
1
( )ES=0, EF=3
LS=0, LF=3
( )ES=3, EF=5
LS=3, LF=5( )
ES=5, EF=5
LS=5, LF=5
( )ES=5, EF=8
LS=5, LF=8
( )ES=6, EF=7
LS=7, LF=8
( )ES=8, EF=9
LS=8, LF=9
( )ES=3, EF=4
LS=4, LF=5
( )ES=5, EF=6
LS=6, LF=7
Ch 17 - 21© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Activity Slack
• Activities on critical path have ES=LS & EF=LF
• Activities not on critical path have slack– Sij = LSij - ESij
– Sij = LFij - EFij
– S24 = LS24 - ES24 = 4 - 3 = 1 month
Ch 17 - 22© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Activity Slack Data
ActivityLS ES LF EF Slack (S)1-2* 0 0 3 3 02-3 3 3 5 5 02-4 4 3 5 4 13-4* 5 5 5 5 04-5 6 5 7 6 14-6* 5 5 8 8 05-6 7 6 8 7 16-7* 8 8 9 9 0
* Critical path
Ch 17 - 23© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Probabilistic Time Estimates
• Reflect uncertainty of activity times• Beta distribution is used in PERT
b - a6
( )Variance: 2 =
a = optimistic estimatem = most likely time estimateb = pessimistic time estimate
Where,
2
Mean (expected time): a + 4m + b6
t =
Ch 17 - 24© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Example Beta Distributions
m = t ba
P (
time)
ba
P (
time)
tm
b
mta
P (
time)
Ch 17 - 25© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
PERT Example
1
2
4
6
73 5 9
8
Manual Testing
Dummy
System Training
Dummy
System Testing
Orientation
Position recruiting
System development
Equipment installation
Equipment testing and modification
Final debugging
System changeover
Job training
Ch 17 - 26© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Activity Information
1 - 2 6 8 10 8 .441 - 3 3 6 9 6 1.001 - 4 1 3 5 3 .442 - 5 0 0 0 0 .002 - 6 2 4 12 5 2.783 - 5 2 3 4 3 .114 - 5 3 4 5 4 .114 - 8 2 2 2 2 .005 - 7 3 7 11 7 1.785 - 8 2 4 6 4 .447 - 8 0 0 0 0 .006 - 9 1 4 7 4 1.007 - 9 1 10 13 9 4.00
Time estimates (wks) Mean Time VarianceActivity a b c t 2
Ch 17 - 27© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Early And Late Times1 - 2 8 0.44 0 8 1 9 11 - 3 6 1.00 0 6 0 6 01 - 4 3 0.44 0 3 2 5 22 - 5 0 0.00 8 8 9 9 12 - 6 5 2.78 8 13 16 21 83 - 5 3 0.11 6 9 6 9 04 - 5 4 0.11 3 7 5 9 2
4 - 8 2 0.00 3 5 14 16 115 - 7 7 1.78 9 16 9 16 05 - 8 4 0.44 9 13 12 16 37 - 8 0 0.00 13 13 16 16 36 - 9 4 1.00 13 17 21 25 87 - 9 9 4.00 16 25 16 25 0
Activity t 2 ES EF LS LF S
Ch 17 - 28© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Network With Times
1
2
4
6
73 5 9
8
( )ES=8, EF=8
LS=9, LF=9
( )ES=6, EF=9
LS=6, LF=9
( )ES=3, EF=5
LS=14, LF=16
( )ES=0, EF=3
LS=2, LF=5
( )ES=0, EF=6
LS=0, LF=6
( )ES=0, EF=8
LS=1, LF=9
3
80
5
4
4
7
0
2
93
6
( )ES=3, EF=7
LS=5, LF=9
4 ( )ES=9, EF=13
LS=12, LF=16
( )ES=9, EF=13
LS=9, LF=16
( )ES=13, EF=13
LS=16 LF=16
( )ES=13, EF=25
LS=16 LF=25
( )ES=13, EF=25
LS=16 LF=25
( )ES=8, EF=13
LS=16 LF=21
Ch 17 - 29© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Project Variance
• Project variance is the sum of variances on the critical path
2132
352
572
792
100 011 178 4 00
6 89
. . . .
. weeks
Ch 17 - 30© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Probabilistic Network AnalysisDetermine probability that project is completed within
specified time
where = tp = project mean time
= project standard deviationx = proposed project timeZ = number of standard deviations x is from mean
Z = x -
Ch 17 - 31© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Normal Distribution Of Project Time
= tp Timex
Z
Probability
Ch 17 - 32© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Probabilistic Analysis Example
What is the probability that the project is completed within 30 weeks?
2 6 89
6 89 2 62
30 252 62
191
191 0 9719
.
. .
..
( . ) .
weeks
weeks
Zx
P Z
Ch 17 - 33© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Determining Probability From Z Value
Z 0.00 0.01 ...0.09
1.9 0.4713 0.4719 …0.4767
......
......
= 25 Time (weeks)
x = 30
P( x<= 30 weeks) = 0.9719
Ch 17 - 34© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
What is the probability that the project is completed within 22 weeks?
= 25 Time (weeks)
x = 22
P( x<= 22 weeks) =0.1271
Z
P Z
22 252 62
32 62
114
114 01271. .
.
( . ) .
Ch 17 - 35© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Project Crashing• Crashing is reducing project time by
expending additional resources• Crash time is an amount of time an activity
is reduced• Crash cost is the cost of reducing the activity
time• Goal is to reduce project duration at
minimum cost
Ch 17 - 36© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
House-building Network
Activity times in weeks
1 2 4 6 7
3
5
12
80
4
124
4
4
Ch 17 - 37© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Normal Activity And Crash Data
1-2 12 7 $3,000 $5,000 5 $4002-3 8 5 2,000 3,500 3 5002-4 4 3 4,000 7,000 1 3,0003-4 0 0 0 0 0 04-5 4 1 500 1,100 3 2004-6 12 9 50,000 71,000 3 7,0005-6 4 1 500 1,100 3 2006-7 4 3 15,000 22,000 1 7,000
$75,000 $110,700
TotalNormal Crash Allowable CrashTime Time Normal Crash Crash Time Cost per
Activity (wks) (wks) Cost Cost (wks) Week
Ch 17 - 38© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Network With Crashing Costs
1 2 4 6 7
3
5
128
0
4
124
4
4
$7,000$7,000
$500
$3,000$400
$200 $200
Activity 1-2 can be crashed a total of 5 weeks for $2000Crash cost per week = Total crash cost/Total crash time
= $2,000/5 = $400 per week
Ch 17 - 39© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Normal And Crash Relationships
1242 6 8 10 140
1,000
3,000
4,000
5,000
7,000
2,000
6,000
$
Weeks
Crashed activity
Normal activity
Crash cost
Normal cost
Crash time Normal time
Slope = crash cost per week
Ch 17 - 40© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Crashing Solution
1-2 12 7 5 $400 $2,0002-3 8 5 3 500 1,5002-4 4 3 0 3,000 03-4 0 0 0 0 04-5 4 1 0 200 04-6 12 9 3 7,000 21,0005-6 4 1 0 200 06-7 4 3 1 7,000 7,000
12 $31,500
Normal Crash Crash Crash CrashingTime Time Time Cost per Cost
Activity (wks) (wks) Used Week Incurred
Ch 17 - 41© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Crashed Project
1 2 4 6 7
3
5
12 7
8 5
0
4 3
12 9
44
4 3
Original time Crashed times
Ch 17 - 42© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e
Time-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 costs
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