2013 07 PERT
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Transcript of 2013 07 PERT
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MANAJEMEN PROYEK
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PERT AND CRASH PROGRAM
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PERT: PROGRAM EVALUATION
REVIEW TECHNIQUE
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One way of incorporating Risk Planning:
Program Evaluation Review Technique
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Assumes each activity duration has a range that statistically
follows a beta distribution
PERT incorporates three time estimates for each activity: an
optimistic time, a pessimistic time, and a most likely time torepresent activity durations
These estimates usually gathered from polling individuals or from lookingat history for similar tasks
A weighted average and variance for each activity is computed
Knowing the weighted average and variances for each activity allows the
project planner to compute the probability of meeting different project
durations
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Activity and Project Frequency
Distributions
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Why might activity distributions look so skewed?
Even with such skewed activity distributions, why
is the overall
Project distribution symmetric?
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Activity Time Calculations
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The weighted average activity time is computed by thefollowing formula:
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Activity Time Calculations
(contd)
The variability in the activity time estimates is approximated bythe following equations:
The standard
deviation for theactivity:
The standard
deviation for theproject:
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Note the standard deviation of the activity is squared in this
equation; this is also called variance. This sum includes only
activities on the critical path(s) or path being reviewed.
2eE
tT
6
ab
et
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Example
Given the following activities, expected durations and
predecessor information, construct the AoA project
network and use the CPM.
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Activity duration predecessors
a1 30 ---
a2 13 a1
a3 20 a1
a4 16 a2
a5 6 a3
a6 5 a5,a4
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Activity Times and Variances
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TABLE A7.1
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Probability of Completing the
Project
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The equation below is used to compute the Z value found in
statistical tables (Z = number of standard deviations from the
mean), which, in turn, tells the probability of completing the
project in the time specified.
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Hypothetical Network
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Text Example
Consider the following 6-activity project
Draw the AoN and use the CPM to compute the CP, slack
Use PERT to analyze the chance the delays on CP activities does not
push the project duration beyond 67 days.
Anything else we should consider? (even though your text doesnt?)
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Activity a m b te=(a+b+4m)/6 var=((b-a)/6) 2
a1 17 29 47 30 25
a2 6 12 24 13 9a3 16 19 28 20 4
a4 13 16 19 16 1
a5 2 5 14 6 4
a6 2 5 8 5 1
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Example: Network,CP,Slack
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Fill in the rest if you want practice finding slack
a1
a3 a5
a6
a4a2
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PERT, Considering the CP
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Activity a m b te=(a+b+4m)/6 var=((b-a)/6) 2a1 17 29 47 30 25
a2 6 12 24 13 9
a3 16 19 28 20 4
a4 13 16 19 16 1
a5 2 5 14 6 4
a6 2 5 8 5 1nice they div ide by 6! even nicer the sqrts a
CPM
paths a1->a2->a4->a6 64 thus this is the critical path
a1->a3->a5->a6 61 total slack = 3
Given a scheduled time: Ts 67
Chance project (considering CP) is less:
stdev(path) =sqrt( sum var(path) 6.00 still integer-wheee!
z = (Ts-Te)/stdev(Cpath) 0.5
so prob = 69% is the chance w e are not later than the scheduled time, considering the CP.
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Example: Possible Project Duration
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Some Sample Z Values
A Z-table listing such values will be provided to you on exams
Excel has these calculations built in =normsdist(z), =normsinv(%)
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Possible Project Duration
Probability project is completed before
scheduled time (TS
) of 67 units
Probability project is completed
by the 60th unit time period (TS
)
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ZValues and Probabilities
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What Might We Have Forgotten?
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In the CPM, it is clear what the
critical path is!
With PERT we can now consider
network sensitivity in more detail.
Extension of the textbook example- what
additional analysis might you do?
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PERT: Caveats Abound
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For checking project duration considering multiple
paths, its not as simple as adding up the
probabilities.
Different paths usually have some activities in common.
Once again, the whole assumption of independence of
activity durations must be considered.
For complex or high-value projects, Monte Carlo
simulation is often a more appropriate approach.
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REDUCING PROJECT DURATION
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Rationale for Reducing Project DurationTime Is Money: Cost-Time Tradeoffs
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Reducing the time of a critical activity usually incurs additional direct costs.
Cost-time solutions focus on reducing (crashing) activities onthe critical path to shorten overall duration of the project.
Reasons for imposed project duration dates:
Customer requirements and contract commitments
Time-to-market pressures
Incentive contracts (bonuses for early completion)
Unforeseen delays
Overhead and goodwill costs
Pressure to move resources to other projects
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Options for Accelerating Project
Completion
Adding Resources
Outsourcing Project Work
Scheduling Overtime
Establishing a Core Project
Team
Do It TwiceFast and
Correctly
Fast-Tracking
Critical-Chain
Reducing Project Scope
Compromise Quality
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When Resources are NOTconstrained
When Resources areconstrained
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Explanation of Project Costs
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Project Indirect Costs
Costs that cannot be associated with any particular work package or
project activity.
Supervision, administration, consultants, and interest
Costs that vary (increase) with time.
Reducing project time directly reduces indirect costs.
Direct Costs
Normal costs that can be assigned directly to a specific work packageor project activity.
Labor, materials, equipment, and subcontractors
Crashing activities increases direct costs.
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Reducing Project Duration to
Reduce Project Cost
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Project CostDuration Graph
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Constructing a Project Cost
Duration Graph
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Find total direct costs for selected project durations.
Find total indirect costs for selected project durations.
Sum direct and indirect costs for these selected project durations.
Compare additional cost alternatives for benefits.
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Constructing a Project Cost
Duration Graph
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Determining Activities to Shorten
Shorten the activities with the smallest increase in cost per unit of
time.
Assumptions: The cost relationship is linear.
Normal time assumes low-cost, efficient methods to complete
the activity.
Crash time represents a limitthe greatest time reductionpossible under realistic conditions.
Slope represents a constant cost per unit of time.
All accelerations must occur within the normal and crash times.
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Activity Graph
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CostDuration Trade-off Example
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CostDuration Trade-off Example
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CostDuration Trade-off Example
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CostDuration Trade-off Example
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CostDuration Trade-off Example
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Summary Costs by Duration
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Project CostDuration Graph
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Practical Considerations
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Using the Project CostDuration Graph
Crash Times
Linearity Assumption
Choice of Activities to Crash Revisited
Time Reduction Decisions and Sensitivity
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What if Cost, Not Time is the Issue?
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Commonly
Used
Options
for Cutting
Costs
Reduce project scope
Have owner take on more
responsibility
Outsourcing project activities or
even the entire project
Brainstorming cost savingsoptions
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END OF THIS CHAPTER
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