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case_16_2__1_.docx

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Case 16-2 “School’s Out Forever . . .”

Alice Cooper

Brent Bonnin begins his senior year of college filled with excitement and a twinge of fear. The

excitement stems from his anticipation of being done with it all—professors, exams, problem

sets, grades, group meetings, all-nighters . . . The list could go on and on. The fear stems from the fact

that he is graduating in December and has only four months to find a job.

Brent is a little unsure about how he should approach the job search. During his

sophomore and junior years, he had certainly heard seniors talking about their strategies for

finding the perfect job, and he knows that he should first visit the Campus Career Planning Center to

devise a search plan.

On September 1, the first day of school, he walks through the doors of the Campus

Career PlanningCenter and meets Elizabeth Merryweather, a recent graduate overflowing with

energy and comforting smiles. Brent explains to Elizabeth that since he is graduating in

December and plans to begin work in January, he wants to leave all of November and December open for

interviews. Such a plan means that by October 31 he has to have all his preliminary materials, such as

cover letters and résumés, submitted to the companies where he wants to work.

Elizabeth recognizes that Brent has to follow a very tight schedule, if he wants to meet

his goal within the next 60 days. She suggests that the two of them sit down together and decide the major

milestones that need to be completed in the job search process. Elizabeth and Brent list the 19 major

milestones. For each of the 19 milestones, they identify the other milestones that must be accomplished

directly before Brent can begin this next milestone. They also estimate the time needed to complete each

milestone. The list is shown below.

In the evening after his meeting with Elizabeth, Brent meets with his buddies at the

college coffee house to chat about their summer endeavors. Brent also tells his friends about the meeting

he had earlier with Elizabeth. He describes the long to-do list he and Elizabeth developed and says that he

is really worried about keeping track of all the major milestones and getting his job search organized. One

of his friends reminds him of the cool management science class they all took together in the first

semester of Brent’s junior year and how they had learned about some techniques to organize large

projects. Brent remembers this class fondly since he was able to use a number of the methods he studied

in that class in his last summer job.

a. Draw the project network for completing all milestones before the interview process. If

everything stays on schedule, how long will it take Brent until he can start with the interviews? What are

the critical steps in the process?

b. Brent realizes that there is a lot of uncertainty in the times it will take him to complete

some of the milestones. He expects to get really busy during his senior year, in particular

since he is taking a demanding course load. Also, students sometimes have to wait quite a

while before they get appointments with the counselors at the career center. In addition to

the list estimating the most likely times that he and Elizabeth wrote down, he makes a list

of optimistic and pessimistic estimates of how long the various milestones might take.

How long will it take Brent to get everything done under the worst-case scenario? How

long will it take if all his optimistic estimates are correct?

c. Determine the mean critical path for Brent’s job search process. What is the variance of

the project duration?

d. Give a rough estimate of the probability that Brent will be done within 60 days.

e. Brent realizes that he has made a serious mistake in his calculations so far. He cannot

schedule the career fair to fit his schedule. Brent read in the campus newspaper that the

fair has been set 24 days from today on September 25th. Draw a revised project network

that takes into account this complicating fact.

f. What is the mean critical path for the new network? What is the probability that Brent

will complete his project within 60 days?

0

S TART

A

Register

onlin e

2

G

Atten d mock

inter view

B

C

Attend

5

orientation

W rite initial

7

r esu me

D

F

4

E

Search

Intern et

10

Attend company

25

sessions

H

Review

industry

Sub mit

initial resu me 2

7

I

Meet resume

expert

1

J

Revise

resume

4

L

K

S earch

jobs

Attend

caree r fair

5

M

Decide

jobs

N

3

O

Bid

1

3

W rite cover

10

le tters

P

Submit cover

4

letters

Q

Re vise cover

letters

4

S

R

Drop

FINIS H

0

2

Mail

6

START

A

Regist er

online

2

B

C

A ttend

orientation

W rite initial

resume

G

Attend moc k

int erview

5

0

T

D

Dum my

7

F

10

H

Review

industry

4

24

E

Search

Inte rnet

Submit

initial re sume

7

2

I

Mee t resume

expert

1

J

L

Revise

resum e

4

Attend

care er fair

1

K

Search

jobs

5

M

Decide

jobs

N

3

O

Bid

3

W rite cove r

letters

10

Submit cover

letters

4

Revise cover

letters

4

P

Q

S

R

Drop

FINISH

0

2

Mail

6

Attend

company

sessions

25

Reliable Construction Company Project

•

The Reliable Construction Company has just made the winning bid of $5.4

million to construct a new plant for a major manufacturer.

•

The contract includes the following provisions:

–

–

A penalty of $300,000 if Reliable has not completed construction within 47 weeks.

A bonus of $150,000 if Reliable has completed the plant within 40 weeks.

Questions:

1.

2.

3.

4.

5.

6.

7.

8.

How can the project be displayed graphically to better visualize the activities?

What is the total time required to complete the project if no delays occur?

When do the individual activities need to start and finish?

What are the critical bottleneck activities?

For other activities, how much delay can be tolerated?

What is the probability the project can be completed in 47 weeks?

What is the least expensive way to complete the project within 40 weeks?

How should ongoing costs be monitored to try to keep the project within budget?

McGraw-Hill/Irwin

16.1

© The McGraw-Hill Companies, Inc., 2013

Activity List for Reliable Construction

Activity

Activity Description

Immediate

Predecessors

Estimated

Duration (Weeks)

A

Excavate

—

2

B

Lay the foundation

A

4

C

Put up the rough wall

B

10

D

Put up the roof

C

6

E

Install the exterior plumbing

C

4

F

Install the interior plumbing

E

5

G

Put up the exterior siding

D

7

H

Do the exterior painting

E, G

9

I

Do the electrical work

C

7

J

Put up the wallboard

F, I

8

K

Install the flooring

J

4

L

Do the interior painting

J

5

M

Install the exterior fixtures

H

2

N

Install the interior fixtures

K, L

6

McGraw-Hill/Irwin

16.2

© The McGraw-Hill Companies, Inc., 2013

Reliable Construction Project Network

START

A

Activity C ode

0

A. Excavate

2

B. Foundation

C. Rough wall

B

D. Roof

4

E. Exterior plumbing

C

F. Interior plumbing

10

G. Exterior siding

H. Exterior painting

D

E

6

4

I

I. Electrical work

7

J. Wallboard

K. Flooring

L. Interior painting

G

F

7

5

M. Exterior fixtures

N. Interior fixtures

J

H

9

K

M

4

L

5

2

N

McGraw-Hill/Irwin

8

FINISH

0

16.3

6

© The McGraw-Hill Companies, Inc., 2013

The Critical Path

•

A path through a network is one of the routes following the arrows (arcs) from

the start node to the finish node.

•

The length of a path is the sum of the (estimated) durations of the activities

on the path.

•

The (estimated) project duration equals the length of the longest path through

the project network.

•

This longest path is called the critical path. (If more than one path tie for the

longest, they all are critical paths.)

McGraw-Hill/Irwin

16.4

© The McGraw-Hill Companies, Inc., 2013

The Paths for Reliable’s Project Network

Path

Length (Weeks)

Start A B C D G H M Finish

2 + 4 + 10 + 6 + 7 + 9 + 2 = 40

Start A B C E H M Finish

2 + 4 + 10 + 4 + 9 + 2 = 31

Start A B C E F J K N Finish

2 + 4 + 10 + 4 + 5 + 8 + 4 + 6 = 43

Start A B C E F J L N Finish

2 + 4 + 10 + 4 + 5 + 8 + 5 + 6 = 44

Start A B C I J K N Finish

2 + 4 + 10 + 7 + 8 + 4 + 6 = 41

Start A B C I J L N Finish

2 + 4 + 10 + 7 + 8 + 5 + 6 = 42

McGraw-Hill/Irwin

16.5

© The McGraw-Hill Companies, Inc., 2013

Earliest Start and Earliest Finish Times

•

The starting and finishing times of each activity if no delays occur anywhere in

the project are called the earliest start time and the earliest finish time.

–

–

ES = Earliest start time for a particular activity

EF = Earliest finish time for a particular activity

•

Earliest Start Time Rule: ES = Largest EF of the immediate predecessors.

•

Procedure for obtaining earliest times for all activities:

1. For each activity that starts the project (including the start node), set its ES = 0.

2. For each activity whose ES has just been obtained, calculate EF = ES + duration.

3. For each new activity whose immediate predecessors now have EF values, obtain

its ES by applying the earliest start time rule. Apply step 2 to calculate EF.

4. Repeat step 3 until ES and EF have been obtained for all activities.

McGraw-Hill/Irwin

16.6

© The McGraw-Hill Companies, Inc., 2013

ES and EF Times for Reliable Construction

START

D

6 ES = 16

EF = 22

G

ES = 22

7 EF = 29

H

0

ES = 0

EF = 0

A

2

ES = 0

EF = 2

B

4

ES = 2

EF = 6

C

10

ES = 6

EF = 16

E

4

ES = 16

EF = 20

F

I

ES = 16

7 EF = 23

J

8

ES = 20

EF = 25

5

ES = 29

9 EF = 38

K

M

4 ES = 33

EF = 37

L

2 ES = 38

EF = 40

N

McGraw-Hill/Irwin

ES = 25

EF = 33

FINISH

0 ES = 44

EF = 44

16.7

6

5 ES = 33

EF = 38

ES = 38

EF = 44

© The McGraw-Hill Companies, Inc., 2013

Latest Start and Latest Finish Times

•

The latest start time for an activity is the latest possible time that it can start

without delaying the completion of the project (so the finish node still is

reached at its earliest finish time). The latest finish time has the corresponding

definition with respect to finishing the activity.

–

–

LS = Latest start time for a particular activity

LF = Latest finish time for a particular activity

•

Latest Finish Time Rule: LF = Smallest LS of the immediate successors.

•

Procedure for obtaining latest times for all activities:

1. For each of the activities that together complete the project (including the finish

node), set LF equal to EF of the finish node.

2. For each activity whose LF value has just been obtained, calculate LS = LF –

duration.

3. For each new activity whose immediate successors now have LS values, obtain its

LF by applying the latest finish time rule. Apply step 2 to calculate its LS.

4. Repeat step 3 until LF and LS have been obtained for all activities.

McGraw-Hill/Irwin

16.8

© The McGraw-Hill Companies, Inc., 2013

LS and LF Times for Reliable’s Project

START

D

G

6 LS = 20

LF = 26

LS = 0

LF = 0

0

LS = 0

LF = 2

A

2

B

4

LS = 2

LF = 6

C

10

LS = 6

LF = 16

E

4

LS = 16

LF = 20

LS = 26

7 LF = 33

H

9

F

I

LS = 18

7 LF = 25

J

8

LS = 20

LF = 25

5

LS = 33

LF = 42

K

M

4 LS = 34

LF = 38

L

2 LS = 42

LF = 44

N

McGraw-Hill/Irwin

LS = 25

LF = 33

FINISH

0

LS = 44

LF = 44

16.9

6

5

LS = 33

LF = 38

LS = 38

LF = 44

© The McGraw-Hill Companies, Inc., 2013

The Complete Project Network

START

D

G

6 S = (16, 20)

F = (22, 26)

9

S = (0, 0)

F = (0, 0)

S = (0, 0)

F = (2, 2)

A

2

B

4

S = (2, 2)

F = (6, 6)

C

10

S = (6, 6)

F = (16, 16)

E

4

S = (22, 26)

7 F = (29, 33)

H

0

S = (16, 16)

F = (20, 20)

F

5

I

7

J

8

S = (20, 20)

F = (25, 25)

S = (25, 25)

F = (33, 33)

S = (29, 33)

F = (38, 42)

K

M

4 S = (33, 34)

F = (37, 38)

2 S = (38, 42)

F = (40, 44)

N

FINISH

McGraw-Hill/Irwin

S = (16, 18)

F = (23, 25)

6

0 S = (44, 44)

F = (44, 44)

16.10

L

5 S = (33, 33)

F = (38, 38)

S = (38, 38)

F = (44, 44)

© The McGraw-Hill Companies, Inc., 2013

Slack for Reliable’s Activities

McGraw-Hill/Irwin

Activity

Slack (LF–EF)

On Critical Path?

A

0

Yes

B

0

Yes

C

0

Yes

D

4

No

E

0

Yes

F

0

Yes

G

4

No

H

4

No

I

2

No

J

0

Yes

K

1

No

L

0

Yes

M

4

No

N

0

Yes

16.11

© The McGraw-Hill Companies, Inc., 2013

Spreadsheet to Calculate ES, EF, LS, LF, Slack

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

B

Activity

A

B

C

D

E

F

G

H

I

J

K

L

M

N

C

Description

Excavate

Foundation

Rough Wall

Roof

Exterior Plumbing

Interior Plumbing

Exterior Siding

Exterior Painting

Electrical Work

Wallboard

Flooring

Interior Painting

Exterior Fixtures

Interior Fixtures

McGraw-Hill/Irwin

D

Time

2

4

10

6

4

5

7

9

7

8

4

5

2

6

E

ES

0

2

6

16

16

20

22

29

16

25

33

33

38

38

Project Duration

16.12

F

EF

2

6

16

22

20

25

29

38

23

33

37

38

40

44

G

LS

0

2

6

20

16

20

26

33

18

25

34

33

42

38

H

LF

2

6

16

26

20

25

33

42

25

33

38

38

44

44

I

Slack

0

0

0

4

0

0

4

4

2

0

1

0

4

0

J

Critical?

Yes

Yes

Yes

No

Yes

Yes

No

No

No

Yes

No

Yes

No

Yes

44

© The McGraw-Hill Companies, Inc., 2013

The PERT Three Estimate Approach

Most likely estimate (m) = Estimate of most likely value of the duration

Optimistic estimate (o) = Estimate of duration under most favorable conditions.

Pessimistic estimate (p) = Estimate of duration under most unfavorable conditions.

Beta distribution

0

o

m

p

Elapsed time

McGraw-Hill/Irwin

16.13

© The McGraw-Hill Companies, Inc., 2013

Mean and Standard Deviation

An approximate formula for the variance (2) of an activity is

2

p o

6

2

An approximate formula for the mean (m) of an activity is

m

McGraw-Hill/Irwin

o 4m p

6

16.14

© The McGraw-Hill Companies, Inc., 2013

Time Estimates for Reliable’s Project

Activity

o

m

p

Mean

Variance

A

1

2

3

2

1/

B

2

3.5

8

4

1

C

6

9

18

10

4

D

4

5.5

10

6

1

E

1

4.5

5

4

4/

9

F

4

4

10

5

1

G

5

6.5

11

7

1

H

5

8

17

9

4

I

3

7.5

9

7

1

J

3

9

9

8

1

K

4

4

4

4

0

L

1

5.5

7

5

1

M

1

2

3

2

1/

9

N

5

5.5

9

6

4/

9

McGraw-Hill/Irwin

16.15

9

© The McGraw-Hill Companies, Inc., 2013

Pessimistic Path Lengths for Reliable’s Project

Path

Pessimistic Length (Weeks)

Start A B C D G H M Finish

3 + 8 + 18 + 10 + 11 + 17 + 3 = 70

Start A B C E H M Finish

3 + 8 + 18 + 5 + 17 + 3 = 54

Start A B C E F J K N Finish

3 + 8 + 18 + 5 + 10 + 9 + 4 + 9 = 66

Start A B C E F J L N Finish

3 + 8 + 18 + 5 + 10 + 9 + 7 + 9 = 69

Start A B C I J K N Finish

3 + 8 + 18 + 9 + 9 + 4 + 9 = 60

Start A B C I J L N Finish

3 + 8 + 18 + 9 + 9 + 7 + 9 = 63

McGraw-Hill/Irwin

16.16

© The McGraw-Hill Companies, Inc., 2013

Three Simplifying Approximations of PERT/CPM

1. The mean critical path will turn out to be the longest path through the project

network.

2. The durations of the activities on the mean critical path are statistically

independent. Thus, the three estimates of the duration of an activity would

never change after learning the durations of some of the other activities.

3. The form of the probability distribution of project duration is the normal

distribution. By using simplifying approximations 1 and 2, there is some

statistical theory (one version of the central limit theorem) that justifies this as

being a reasonable approximation if the number of activities on the mean

critical path is not too small.

McGraw-Hill/Irwin

16.17

© The McGraw-Hill Companies, Inc., 2013

Calculation of Project Mean and Variance

Activities on Mean Critical Path

Mean

Variance

A

2

1/

B

4

1

C

10

4

E

4

4/

F

5

1

J

8

1

L

5

1

N

6

4/

Project duration

mp = 44

2p = 9

McGraw-Hill/Irwin

16.18

9

9

9

© The McGraw-Hill Companies, Inc., 2013

Probability of Meeting Deadline

2

p=9

d – m p = 47 – 44 = 1

p

3

44

(Mean)

McGraw-Hill/Irwin

47

(Deadline)

16.19

Project duration

(in weeks)

© The McGraw-Hill Companies, Inc., 2013

Spreadsheet for PERT Three-Estimate Approach

B

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

Activity

A

B

C

D

E

F

G

H

I

J

K

L

M

N

McGraw-Hill/Irwin

C

D

E

Time Estimates

o

m

p

1

2

3

2

3.5

8

6

9

18

4

5.5

10

1

4.5

5

4

4

10

5

6.5

11

5

8

17

3

7.5

9

3

9

9

4

4

4

1

5.5

7

1

2

3

5

5.5

9

F

On Mean

Critical Path

*

*

*

*

*

*

*

*

16.20

G

H

m

2

4

10

6

4

5

7

9

7

8

4

5

2

6

0.1111

1

4

1

0.4444

1

1

4

1

1

0

1

0.1111

0.4444

I

J

K

Mean Critical

Path

m

44

9

P(T<=d) =
where
d=
0.8413
47
© The McGraw-Hill Companies, Inc., 2013
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