Project Scheduling

Professor Stephen LawrenceGraduate School of Business Administration

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)B AC AD B, C

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Simple Project Network

AA

BB

CC

DD

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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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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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Critical Path of the Example

A D

C

B

4

3

5

2

Critical Path Duration =

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Time and Variance Example

ExpectedTime

VarianceCriticalPath?

Activity

4 1.778A3 1.0B5 0.111C2 0.694D

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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

=

From a Z-table for standard Normal distributions:

Probability of completion =

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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

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Expected Activity Duration for “D”:

ET =a + 4m + b

6=

2+4(8)+106

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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

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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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)=

Prob(x<18) = 1 - 0.9463 =

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) =

20 weeks: Z = 0.00 Prob(x<20) =

24 weeks: Z = 3.21 Prob(x<24) =

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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