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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

5

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:

8

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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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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2013 07 pert

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