project scheduling professor stephen lawrence leeds school of business university of colorado...
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Project Scheduling
Professor Stephen LawrenceLeeds School of Business
University of Colorado
Boulder, CO 80309-0419
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Project Management
Management complex projects
Many parallel tasks
Deadlines and milestones must be met
Difficult to know “what to do first”
Difficult to know when project is in trouble
Often have competition for limited resources
When to use:
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Examples
Building a new airport
Designing a new computer product
Launching an advertising campaign
Construction projects of all types
Maintenance projects
Curriculum reviews
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Project Mgmt Techniques
Critical Path Method (CPM) Developed by DuPont (1950’s) Plan and control maintenance of chemical plants Credited with reducing length of maintenance
shutdown by 40%
Project Evaluation and Review Technique (PERT) Developed by Navy (early 1960’s) Plan and control the Polaris missile project Credited with speeding up project by 2 years
Critical Path Method(CPM)
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Critical Path Method (CPM)
Graphical method of portraying relationship of project activitiesAn activity is any discrete part or task of a project which takes resources and time to completeActivities exhibit precedence relations (some must be completed before others can start)Activities with their precedence relations form a project networkCritical Path Method finds the longest path through the resulting project network
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Precedence Relations
Activity Immediate Predecessor Duration (days)
A (Start) 4B A 3C A 5D B, C 2
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Simple Project Network
AA
BB
CC
DD
Project Network
Activity “A”proceeds “B”
“Activity on Node” representation
Represent precedence relations as “arcs”
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Activity Start/Finish Times
ES
LS
EF
LF
ActivityName
ActivityDuration
EarlyFinishTime
LateFinishTime
EarlyStartTime
LateStartTime
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Finding the Critical Path
A D
C
B
4
3
5
2
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Finding the Critical Path
A D
C
B
4
3
5
20
Start attime t=0
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Finding the Critical Path
A D
C
B
4
3
5
24
0+4=4
0
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Finding the Critical Path
A D
C
B
4
3
5
20
4
4
4
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Finding the Critical Path
A D
C
B
4
3
5
20 4
7
9
4
4
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Finding the Critical Path
A D
C
B
4
3
5
20 4
4
4
7
9
?
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Finding the Critical Path
A D
C
B
4
3
5
20 4
4
4
7
9
9
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Finding the Critical Path
A D
C
B
4
3
5
20 4
4
4
7
9
9 11
The earliest the project can complete is t =11
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Finding the Critical Path
A D
C
B
4
3
5
20 4
4
4
7
9
9 11
11
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Finding the Critical Path
A D
C
B
4
3
5
20 4
4
4
7
9
9 11
119
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9
6
4
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Finding the Critical Path
A D
C
B
4
3
5
20 4
4
4
7
9
9 11
119
9
9
6
4
?
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Finding the Critical Path
A D
C
B
4
3
5
20 4
4
4
7
9
9 11
119
9
9
6
4
40
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Finding the Critical Path
A D
C
B
4
3
5
20 4
4
4
7
9
9 11
119
9
9
6
4
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Define Activity Slack:S = LST-EST = LFT-EFT
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Finding the Critical Path
A D
C
B
4
3
5
20 4
4
4
7
9
9 11
119
9
9
6
4
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S=0-0=4-4=0
S=9-7=2
S=11-11=0
S=9-9=0
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A
Finding the Critical Path
D
C
B
4
3
5
20 4
4
4
7
9
9 11
119
9
9
6
4
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S=0 S=0
S=0
S=2Critical Path: Path with
zero activity slacks
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CPM TerminologyCritical Path: the chain of activities along which the delay of any activity will delay the projectEarly Start Time (ES): the earliest that an activity could possibly start, given precedence relationsLate Start Time (LS): the latest that an activity could possibly start without delaying the projectEarly Finish Time (EF): the earliest that an activity could possibly finishLate Finish Time (LF): the latest that an activity could possibly finish without delaying the projectActivity Slack: the amount of “play” in the timing of the activity; slack = LST-EST = LFT-EFT
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ExampleSuppose you are an advertising manager responsible forthe launch of a new media advertising campaign. Thecampaign (project) has the following activities:
Activity Predecessors TimeA. Media bids none 2 wksB. Ad concept none 6C. Pilot layouts B 3D. Select media A 8E. Client check-off A,C 6F. Pre-production B 8G. Final production E,F 5H. Launch campaign D,G 0
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Example Project Network
A2
A2
B6
B6
F8
F8
D8D8
C3
C3
E6
E6
G5
G5
H0
H0StartStart
Program Evaluation and Review Technique (PERT)
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PERT
Similar to Critical Path Method (CPM)Accounts for uncertainty in activity duration estimatesProvides estimates of project duration probabilitiesBest used for highly uncertain projects new product development unique or first-time projects research and development
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Simple Project Network
AA
BB
CC
DD
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A Simple Example
MostOptimistic
MostLikely
MostPessimistic
Activity
2 10A1 7B4 6C
0.5 5.5D
3
2.55
1.5
ma b
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Distribution AssumptionAssume a “Beta” distribution
activity duration
dens
ity
ma b
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Expected Duration & Variance
Expected Time =
Variance =
a + 4m + b6
(b - a)2
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For the Beta Distribution:
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Distribution Assumption
activity duration
dens
ity
ma b
expectedduration
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Expected Duration & Variance
ET =
Var =
a + 4m + b6
(b - a)2
36
=2+4(3)+10
6= 4.0
=(10-2)2
36 = 1.778
Activity A
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Expected Duration & Variance
ExpectedTime
VarianceCriticalPath?
Activity
4 1.778A3 1.0B5 0.111C2 0.694D
????
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Critical Path of the Example
A D
C
B
4
3
5
2
Critical Path Duration = 11 days
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Time and Variance Example
ExpectedTime
VarianceCriticalPath?
Activity
4 1.778 A3 1.0 noB5 0.111 C2 0.694 D
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Probability of CompletionWhat is the probability that a project will be completed by a specified due date?
Due Date - Expected Completion Date
Sum of the Variances on the Critical Pathz =
NormalDistribution
z
Due Date
Expected Completion
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Completion Probability Example
What is the probability of completing the project within 12 days?
z = 12 - 111.778 + 0.111 + 0.694
= 0.622
From a Z-table for standard Normal distributions:
Probability of completion = 0.7324 = 73.2%
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Larger Example
(a) (m) (b)Activity Preds Optimistic Likely Pessimistic
A. none 1 2 3 wks B. none 4 6 8 C. B 3 3 3 D. A 2 8 10 E. A,C 3 6 9 F. B 1 8 15 G. E,F 4 5 6 H. D,G 0 0 0
Suppose the duration of the activities of the adcampaign are, in fact, uncertain:
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Activity DSuppose the duration of the activities of the adcampaign are, in fact, uncertain:
(a) (m) (b)Activity Preds Optimistic Likely Pessimistic
A. none 1 2 3 wks B. none 4 6 8 C. B 3 3 3
D. A 2 8 10 E. A,C 3 6 9 F. B 1 8 15 G. E,F 4 5 6 H. D,G 0 0 0
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Activity D
Variance of Activity Duration for “D”:
Var = (b - a)2
36 =
(10-2)2
36 = 1.78
Expected Activity Duration for “D”:
ET =a + 4m + b
6=
2+4(8)+106
= 7.33
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Project Duration Statistics
A. 2 0.11 B. 6 0.44 C. 3 0.00 E. 6 1.00 F. 8 5.44 G. 5 0.11 H. 0 0.00
Activity Critical? Mean Var C.P. Var
D. 7.33 1.78
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Example Project Network
A2
A2
B6
B6
F8
F8
DD
C3
C3
E6
E6
G5
G5
H0
H0StartStart
Critical Path Duration = 20 days
7.33
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Project Duration Statistics
Activity Critical? Mean Var C.P. Var A. 2 0.11 B. 6 0.44 C. 3 0.00 D. 7.33 1.78 E. 6 1.00 F. 8 5.44 G. 5 0.11 H. 0 0.00
Critical Path Variance = 2 = 1.55
YesYes
Yes
YesYes
0.440.00
1.00
0.110.00
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Using Project Statistics
What is the probability that the ad campaign can be completed in 18 weeks? 20? 24?
18 weeks: Z = x -
18 - 20sqrt(1.55)= = -1.61
Prob(x<18) = 1 - 0.9463 = 0.054 or 5.4%
Corresponding probability from standard normal Z-Table is 0.9463:
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Using Project Statistics
What is the probability that the ad campaign can be completed in 18 weeks? 20? 24?
18 weeks: Z = -1.61 Prob(x<18) = 5.4%
20 weeks: Z = 0.00 Prob(x<20) = 50%
24 weeks: Z = 3.21 Prob(x<24) = 99.93%
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Other Project Mgmt TechniquesProject crashing where to devote extra resources to reduce
activity/project durations while minimizing costs
Resource leveling how to schedule resources (equipment, people) to
minimizes peaks and valleys
Multiple resource scheduling how to schedule resources when activities can require
more than one resource type
Cash flow and budgeting combine cash and budget information with project
scheduling to track expenditures, project cash flows
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Further Information
Project Management Institute (PMI)www.PMI.org
Professional organization of project managers
Offers a certification in project management