Appendix 7.1: PERT and PERT Simulation

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Chapter 7 Managing Risk 239



Carlos: Bill, I am aware of the problem. The PMI Roundtables I attend also talk to the

difficulty of keeping teams and other stakeholders willing to revisit risk once the project is on its way. [PMI Roundtables are monthly meetings of practicing PMs across

industries designed to address project management problems.] I also heard war stories

at a recent project management roundtable meeting. I have some notes from the meeting right here.

It all started with the leader’s question: “How many project managers actually manage risk over the complete project life cycle?”

PM 1: We all work through the risk management process well before the project

begins. We have the process template of risk identification, assessment, response,

control, risk register, and contingency down pat. We just don’t follow through after

the project begins. I think interest dies. Have you ever tried to get project stakeholders to come to a risk meeting when the project is moving relatively well?

PM 2: A recent e-mail from one of our stakeholders said, “We’ll deal with it [risk]

when it happens.”

PM 3: I agree. Interest seems to move from future oriented to reactionary. Also,

risk management seems to degenerate into issue (concerns and problems) management versus real risk management.

PM 4: I ask team members, “What is the risk of not managing risk over the life of

the project?” Sometimes this question nudges a few to respond positively, especially if risks have changed or new ones are perceived. I use a failed project where

a solid risk management process would have avoided the project failure. I explain

all of the risk management processes that would have helped to improve the risk

elements—risk identification, triggers, responsibility, transfer, accept, etc.

PM 5: Risk is not a line item in the budget or schedule. Maybe it is in the contingency budget to cover “unknowns of unknowns.” I have to watch that management

doesn’t try to squeeze out the contingency budget for something else.

Carlos continued to share with his boss that there were many more comments, but very

few gave much guidance. Carlos then shared his idea:

Carlos: Colette is our best trainer, especially in transition management, and she would

be a great choice for following through on this problem. Her training classes on upfront

risk management are excellent. Should we ask her to present a session?

Bill: You are right, Carlos, Colette is ideal. She is smart and a great team motivator.

Ask her, but give her some kind of direction for focus.

A few days later, Carlos sent out a memo:

Colette, this is to follow up on our lunch conversation yesterday discussing sustaining

risk management after the project is on its way. Given the nature of our futuristic company, we should stress the point that our product development projects carry many

more inherent risks than do traditional projects. I suggest the training classes should

drill down on concrete actions and policies that will encourage interest of team members and other project stakeholders in sustaining risk management practices during

project execution.

Colette, we appreciate your taking on this project. When you have developed your

training session, please give me a copy so I can schedule and support your efforts.

Regards, Carlos



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240 Chapter 7 Managing Risk



CHALLENGE

Divide the class into teams of three or more participants.

Colette needs your help to develop her training program. You may wish to consider

the questions listed below to initiate ideas.

∙ Why do project stakeholders lose interest in project risk after the project is under

way?

∙ What are the dangers of not keeping on top of risk management during

implementation?

∙ What kind of business is Futuronics in?

Brainstorm specific actions that will encourage project stakeholders to continue to

scan and track the project environment for risk events. Suggest three concrete actions

or scenarios that will encourage project stakeholders to change their behavior and truly

support risk management while projects are being implemented. The following outline

headings may be helpful in developing possible actions that would improve/enhance

stakeholder support.

∙ Improving the risk management process

∙ Organization actions

∙ Motivating participation



Appendix 7.1

PERT and PERT Simulation

LEARNING OBJECTIVES

After reading this appendix you should be able to:

A7-1 Calculate basic Pert Simulation projections.



PERT—PROGRAM EVALUATION AND REVIEW TECHNIQUE

LO A7-1

Calculate basic Pert

Simulation projections.



In 1958 the Special Office of the Navy and the Booze, Allen, and Hamilton consulting

firm developed PERT (program evaluation and review technique) to schedule the more

than 3,300 contractors of the Polaris submarine project and to cover uncertainty of

activity time estimates.

PERT is almost identical to the critical path method (CPM) technique except it

assumes each activity duration has a range that follows a statistical distribution. PERT

uses three time estimates for each activity. Basically, this means each activity duration

can range from an optimistic time to a pessimistic time, and a weighted average can be

computed for each activity. Because project activities usually represent work, and

because work tends to stay behind once it gets behind, the PERT developers chose an

approximation of the beta distribution to represent activity durations. This distribution

is known to be flexible and can accommodate empirical data that do not follow a normal distribution. The activity durations can be skewed more toward the high or low

end of the data range. Figure A7.1A depicts a beta distribution for activity durations

that is skewed toward the right and is representative of work that tends to stay late once

it is behind. The distribution for the project duration is represented by a normal



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Chapter 7 Managing Risk 241



FIGURE A7.1 Activity and Project Frequency Distributions

PROJECT



ACTIVITY



a



m



b



TE



(A)



(B)



(symmetrical) distribution shown in Figure A7.1B. The project distribution represents

the sum of the weighted averages of the activities on the critical path(s).

Knowing the weighted average and variances for each activity allows the project

planner to compute the probability of meeting different project durations. Follow the

steps described in the hypothetical example given next. (The jargon is difficult for

those not familiar with statistics, but the process is relatively simple after working

through a couple of examples.)

The weighted average activity time is computed by the following formula:

te =



a + 4m + b

6



(7.1)



where

te = weighted average activity time

a = optimistic activity time (1 chance in 100 of completing the activity

earlier under normal conditions)

b = pessimistic activity time (1 chance in 100 of completing the activity

later under normal conditions)

m = most likely activity time

When the three time estimates have been specified, this equation is used to compute

the weighted average duration for each activity. The average (deterministic) value is

placed on the project network as in the CPM method and the early, late, slack, and

project completion times are computed as they are in the CPM method.

The variability in the activity time estimates is approximated by the following equations: Equation 7.2 represents the standard deviation for the activity. Equation 7.3 represents the standard deviation for the project. 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.

b−a

σt = (

e

6 )



(7.2)



σT = √ Σσ2t



(7.3)



E



e



Finally, the average project duration (TE) is the sum of all the average activity times

along the critical path (sum of te), and it follows a normal distribution.



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242 Chapter 7 Managing Risk



Knowing the average project duration and the variances of activities allows the

probability of completing the project (or segment of the project) by a specific time to

be computed using standard statistical tables. The equation below (Equation 7.4) 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.

Z=



TS − TE



(7.4)



√ Σσ2



te



where

TE = critical path duration

TS = scheduled project duration

Z = probability (of meeting scheduled duration) found in statistical Table A7.2



A HYPOTHETICAL EXAMPLE USING THE PERT TECHNIQUE

The activity times and variances are given in Table A7.1. The project network is presented

in Figure A7.2. This figure shows the project network as AOA and AON. The AON network is presented as a reminder that PERT can use AON networks as well as AOA.

The expected project duration (TE) is 64 time units; the critical path is 1-2-3-5-6.

With this information, the probability of completing the project by a specific date can

easily be computed using standard statistical methods. For example, what is the probability the project will be completed before a scheduled time (TS) of 67? The normal

curve for the project would appear as shown in Figure A7.3.

Using the formula for the Z value, the probability can be computed as follows:

Z=



TS − TE

√ Σσ2



te



=



67 − 64

√25 + 9 + 1 + 1



=



+3



√36

= +0.50

P = 0.69



Reading from Table A7.2, a Z value of +0.5 gives a probability of 0.69, which is interpreted to mean there is a 69 percent chance of completing the project on or before 67

time units.

TABLE A7.1



Activity Times and

Variances



Activity



a



m



b



te



[(b – a)/6]2



1–2

2–3

2–4

3–5

4–5

5–6



17

6

16

13

2

2



29

12

19

16

5

5



47

24

28

19

14

8



30

13

20

16

6

5



25

9

4

1

4

1



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Chapter 7 Managing Risk 243



FIGURE A7.2



3



Hypothetical

Network



AOA Network



13

30



1



16

59

56



2

20



5



5



6



6

TE = 64



4

AON Network



0



30 B 43



43 D 59



13



16

59 F 64



A 30

59

56



30

30 C 50



50 E 56



20



6



5 64

TE = 64



Conversely, the probability of completing the project by time period 60 is computed

as follows:

Z=

=



60 − 64

√25 + 9 + 1 + 1



−4



√36

= −0.67

P ≈ 0.26



FIGURE A7.3



Possible Project

Durations



TS = 67

TE = 64



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244 Chapter 7 Managing Risk



TABLE A7.2



Z Values and

Probabilities



Z Value



Probability



Z Value



Probability



.001

.003

.005

.008

.014

.023

.036

.055

.081

.115

.159

.212

.274

.345

.421



+0.0

+0.2

+0.4

+0.6

+0.8

+1.0

+1.2

+1.4

+1.6

+1.8

+2.0

+2.2

+2.4

+2.6

+2.8



.500

.579

.655

.726

.788

.841

.885

.919

.945

.964

.977

.986

.992

.995

.997



−3.0

−2.8

−2.6

−2.4

−2.2

−2.0

−1.8

−1.6

−1.4

−1.2

−1.0

−0.8

−0.6

−0.4

−0.2



From Table A7.2, a Z value of −0.67 gives an approximate probability of 0.26, which

is interpreted to mean there is about a 26 percent chance of completing the project on

or before 60 time units. Note that this same type of calculation can be made for any

path or segment of a path in the network.

When such probabilities are available to management, trade-off decisions can be

made to accept or reduce the risk associated with a particular project duration. For

example, if the project manager wishes to improve the chances of completing the project by 64 time units, at least two choices are available. First, management can spend

money up front to change conditions that will reduce the duration of one or more

activities on the critical path. A more prudent, second alternative would be to allocate

money to a contingency fund and wait to see how the project is progressing as it is

implemented.



EXERCISES

1. Given the project information below, what is the probability of completing the

National Holiday Toy project in 93 time units?

Act. ID

1

2

3

4

5

6

7



Description



Predecessor



Optm. (a)



Most likely (m)



Pess. (b)



Design package

Design product

Build package

Secure patent

Build product

Paint

Test market



None

1

1

2

2

3, 4, 5

6



6

16

4

 24

17

4

13



12

19

7

27

29

7

16



24

28

10

36

47

10

19



Act time te



Variance [(b − a)/6]2



Critical



2. The Global Tea and Organic Juice companies have merged.

The following information has been collected for the “Consolidation Project.”



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Chapter 7 Managing Risk 245



Activity

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15



1.

2.

3.

4.

5.



Description



Predecessor



a opt



m ml



b pess



Codify accounts

File articles of unification

Unify price and credit policy

Unify personnel policies

Unify data processing

Train accounting staff

Pilot run data processing

Calculate P & L and balance sheet

Transfer real property

Train salesforce

Negotiate with unions

Determine capital needs

Explain personnel policies

Secure line of credit

End



None

None

None

None

1

1

5

6, 7

2

3

4

8

11

9, 12

10, 13, 14



16

30

60

18

17

4

12

6

18

20

40

11

14

13

0



19

30

72

27

29

7

15

12

27

35

55

20

23

16

0



28

30

90

30

47

10

18

24

30

50

100

29

26

19

0



Compute the expected time for each activity.

Compute the variance for each activity.

Compute the expected project duration.

What is the probability of completing the project by day 112? Within 116 days?

What is the probability of completing “Negotiate with Unions” by day 90?



3. The expected times and variances for the project activities are given below. What is

the probability of completing the project in 25 periods?



ID



Description



Predecessor



te



Variance

[(b − a)/6]2



1

2

3

4

5

6

7

8



Pilot production

Select channels of distrib.

Develop mktg. program

Test market

Patent

Full production

Ad promotion

Release



None

None

None

1

1

4

3

2, 5, 6, 7



6

7

4

4

10

16

3

2



3

4

2

2

5

10

2

1



Case A7.1



International Capital, Inc.—Part A

International Capital, Inc. (IC), is a small investment banking firm that specializes in securing funds for small- to medium-sized firms. IC is able to use a standardized project format for each engagement. Only activity times and unusual

circumstances change the standard network. Beth Brown has been assigned to this



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246 Chapter 7 Managing Risk



client as project manager partner and has compiled the network information and

activity times for the latest client as follows:

Activity

A

B

C

D

E

F

G

H

I

J

K



Description



Immediate Predecessor



Start story draft using template

Research client firm

Create “due diligence” rough draft

Coordinate needs proposal with client

Estimate future demand and cash flows

Draft future plans for client company

Create and approve legal documents

Integrate all drafts into first-draft proposal

Line up potential sources of capital

Check, approve, and print final legal proposal

Sign contracts and transfer funds



—

—

A, B

C

C

E

C

D, F, G

G, F

H

I, J



Time in Workdays

Activity



Optimistic



Most Likely



Pessimistic



4

2

2

16

6

1

4

2

5

2

17



7

4

5

19

9

7

10

5

8

5

29



10

8

8

28

24

13

28

14

17

8

45



A

B

C

D

E

F

G

H

I

J

K



MANAGERIAL REPORT

Brown and other broker partners have a policy of passing their plan through a project

review committee of colleagues. This committee traditionally checks that all details

are covered, times are realistic, and resources are available. Brown wishes you to

develop a report that presents a planned schedule and expected project completion

time in workdays. Include a project network in your report. The average duration for a

sourcing capital project is 70 workdays. IC partners have agreed it is good business to

set up projects with a 95 percent chance of attaining the plan. How does this project

stack up with the average project? What would the average have to be to ensure a

95 percent chance of completing the project in 70 workdays?



Case A7.2



Advantage Energy Technology Data Center Migration—

Part B

In Chapter 6, Brian Smith, network administrator at Advanced Energy Technology

(AET), was given the responsibility of implementing the migration of a large data

center to a new office location.



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Chapter 7 Managing Risk 247



Time in Workdays

Task Name

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28



AET DATA CENTER MIGRATION

Team meeting

Hire contractors

Network design

Ventilation system

Order ventilation system

Install ventilation system

New racks

Order new racks

Install racks

Power supplies and cables

Order power supplies & cables

Install power supplies

Install cables

Renovation of data center

City inspection

Switchover Meetings

Facilities

Operations/systems

Operations/telecommunications

Systems & applications

Customer service

Power check

Install test servers

Management safety check

Primary systems check

Set date for move

Complete move



Optimistic

Dur.



Most Likely

Dur.



Pessimistic

Dur.



54

0.5

6

12

—

18

5

—

13

17

—

6

5

6

19

1

—

7

5

6

7

5

0.5

5

1

1.5

1

1



68

1

7

14

—

21

7

—

14

21

—

7

5

8

20

2

—

8

7

7

7

6

1

7

2

2

1

2



92

1.5

8

16

—

30

9

—

21

25

—

8

11

10

27

3

—

9

9

8

13

13

1.5

9

3

2.5

1

3



Immediate

Predecessor



Critical Path

✓



2

2

—

2

6

—

2

9

—

2

12, 16

12, 16

3, 4

3, 7, 10

—

14

14

14

14

14

13, 14, 15

18, 19, 20, 21, 22, 23

7, 23, 24

25

26

27



✓

✓



✓

✓



✓

✓

✓

✓

✓

✓

✓



Careful planning was needed because AET operates in the highly competitive

petroleum industry. AET is one of five national software companies that provide an

accounting and business management package for oil jobbers and gasoline distributors. A few years ago, AET jumped into the “application service provider” world.

Their large data center provides clients with remote access to AET’s complete suite of

application software systems. Traditionally, one of AET’s primary competitive advantages has been the company’s trademark IT reliability. Due to the complexity of this

project, the Executive Committee insisted that preliminary analysis of the anticipated

completion date be conducted.

Brian compiled the following information, in preparation for some PERT analysis:

1. Based on these estimates and the resultant expected project duration of 69 days, the

executive committee wants to know what the probability is of completing the project before a scheduled time (TS) of 68 days.

2. The significance of this project has the executive committee very concerned. The committee has decided that more analysis of the duration of each activity is needed. Prior

to conducting that effort, they asked Brian to calculate what the expected project duration would have to be to ensure a 93 percent chance of completion within 68 days.



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248 Chapter 7 Managing Risk



ADVANTAGE ENERGY TECHNOLOGY (AET)—ACCOUNTS

PAYABLE SYSTEM

The AET sales department has been concerned about a new start-up company that is

about to release an accounts payable system. Their investigation indicates that this new

package will provide features which will seriously compete with AET’s current

Accounts Payable system and in some cases exceed what AET offers.

Tom Wright, senior applications developer at AET, has been given the responsibility of analyzing, designing, developing, and delivering a new accounts payable system

(A/P) for AET customers.

Complicating the issue is the concern of the sales department about AET’s recent

inability to meet promised delivery dates. They have convinced CEO (Larry Martain)

that a significant marketing effort will have to be expended to convince the clients they

should wait for the AET product rather than jump to a package provided by a new

entry to the petroleum software business. Companion to this effort is the importance of

the performance of the software development group.

Consequently, Tom has decided to take the following action: tighten up the estimating effort by his developers; incorporate some new estimating procedures; and use

some PERT techniques to generate probabilities associated with his delivery dates.

Tom’s planning team made a first-cut at the set of activities and associated durations:

Time in Workdays

Task Name

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25



ACCOUNTS PAYABLE SYSTEM

Planning meeting

Team assignments

Program specification

Customer requirements

Feasibility study

Systems analysis

Prelim budget & schedule

Functional specification

Prelim design

Configuration & perf needs

Hardware requirements

System specification

Detailed design

Program specification

Programming—first phase

Documentation

Prototype

Development

User testing & feedback

Programming—second phase

Beta testing

Final documentation pkg

Training pkg

Product release



SS = Start to Start lag



Optimistic

Dur.



Most Likely

Dur.



Pessimistic

Dur.



Immediate

Predecessor



1

3



1

4



2

5



8

3

6

1

3

10

3

4

5

12

8

27

14



10

5

8

2

5

12

4

6

7

14

10

32

16



12

7

10

3

7

14

5

8

9

16

12

37

18



3

5

5

7

7

9

10

11

10

12, 13

14

15

10



✓



5

12

10

18

9

4

3



7

14

12

20

10

5

5



9

16

14

22

11

6

7



16

19

16

21

17, 20

21SS, 23

22, 23, 24



✓

✓



2



Critical Path

✓

✓



✓

✓

✓

✓

✓

✓

✓

✓

✓



✓

✓

✓



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Chapter 7 Managing Risk 249



3. Based on these estimates and the critical path, the project duration is estimated at

149 days. But an AET salesperson in the Southeast Region has discovered that the

competing A/P package (with significant improvements) is scheduled for delivery

in approximately 145 days. The sales force is very anxious to beat that delivery

time. The executive committee asks Tom for an estimated probability of reducing

his expected project duration by two days.

4. The executive committee is advised by Tom that after all the estimating was completed, he determined that one of his two critical systems analysts might have to

move out of the area for critical family reasons. Tom is still very confident that with

some staff rearrangements, assistance from a subcontractor, and some “hands on”

activities on his part he can still meet the original delivery date, based on 149 days.

This news is very disconcerting to the committee and the sales staff. At this

point, the committee decides that based on the most recent delivery performance of

AET, a modified, comfortable delivery date should be communicated to AET clients—one that Tom and his staff are very likely to meet. Consequently, Tom is

asked to calculate what the expected project duration would have to be to ensure a

98 percent chance of completion within 160 days—that is a “published, drop dead

date” that can be communicated to the clients.