To Accompany Krajewski Ritzman Operations Management: Strategy and Analysis, Seventh Edition 2004 Prentice Hall, Inc. All rights reserved. Planning

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Planning and Planning and Managing ProjectsManaging Projects

Chapter 8Chapter 8


Implementchanges

6Redesignprocess

5

Implementing ChangesImplementing Changes

Documentprocess

3

Definescope

2

Evaluateperformance

4

Figure 8.1Figure 8.1

Identify opportunity

1


Develop Marketing

Plan

Install Operating

Control Base

Select Bank Select Name Find Location

Provide Staffing Provide Physical Facilities

Establish Business Structure

Work Breakdown StructureWork Breakdown Structure


Strategic Plan Define Business Opportunity

Plan for Action

Proceed With Startup Plan

Start a New Business


Activity RelationshipsActivity RelationshipsActivity RelationshipActivity Relationship

AOA AON




S precedes T, which precedes U.S precedes T, which precedes U.

AOA AON

1 2S

3T

4U

S T U




S and T must be completed before U can be started.S and T must be completed before U can be started.

AOA AON

S

T

U

1

2

3T

S

4U




T and U cannot begin until S has been completed.T and U cannot begin until S has been completed.

AOA AON

T

U

S

3

4

1

T

U2S




U and V cannot begin until both S and T have been U and V cannot begin until both S and T have been completed. completed.

AOA AON

1

2

4

5

U

V

S

T 3

S

T

U

V




U cannot begin until both S and T have been completed; U cannot begin until both S and T have been completed; V cannot begin until T has been completed.V cannot begin until T has been completed.

AOA AON

S

T

U

V

1 3

DummyDummy

5

2 4 6

S U

T V




T and U cannot begin until S has been completed; V T and U cannot begin until S has been completed; V cannot begin until both T and U have been completed.cannot begin until both T and U have been completed.

AOA AON

1 2 4

3

S T5

V

UDummyDummy

S T V

U



St. Adolf’s HospitalSt. Adolf’s Hospital



Example 8.1Example 8.1

ImmediateImmediateActivityActivity DescriptionDescription Predecessor(s)Predecessor(s) ResponsibilityResponsibility

AASelect administrative and medical staff.Select administrative and medical staff.BBSelect site and do site survey.Select site and do site survey.CCSelect equipment.Select equipment.DDPrepare final construction plans and layout.Prepare final construction plans and layout.EEBring utilities to the site.Bring utilities to the site.FFInterview applicants and fill positions inInterview applicants and fill positions in

nursing, support staff, maintenance, nursing, support staff, maintenance, and security.and security.

GGPurchase and take delivery of equipment.Purchase and take delivery of equipment.HHConstruct the hospital.Construct the hospital.IIDevelop an information system.Develop an information system.JJInstall the equipment.Install the equipment.KKTrain nurses and support staff.Train nurses and support staff.


St. Adolf’s HospitalSt. Adolf’s HospitalImmediateImmediate

ActivityActivity DescriptionDescription Predecessor(s)Predecessor(s) ResponsibilityResponsibility

AASelect administrative and medical staff.Select administrative and medical staff. ——JohnsonJohnsonBBSelect site and do site survey.Select site and do site survey. ——TaylorTaylorCCSelect equipment.Select equipment. AAAdamsAdamsDDPrepare final construction plans and layout.Prepare final construction plans and layout. BBTaylorTaylorEEBring utilities to the site.Bring utilities to the site. BBBurtonBurtonFFInterview applicants and fill positions inInterview applicants and fill positions in AAJohnsonJohnson


GGPurchase and take delivery of equipment.Purchase and take delivery of equipment. CCAdamsAdamsHHConstruct the hospital.Construct the hospital. DDTaylorTaylorIIDevelop an information system.Develop an information system. AASimmonsSimmonsJJInstall the equipment.Install the equipment. E,G,HE,G,HAdamsAdamsKKTrain nurses and support staff.Train nurses and support staff. F,I,JF,I,JJohnsonJohnson








AON Network








AON Network

Start

A








AON Network

Start

A

B








AON Network

Start

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B

C








AON Network

Start

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B

C

D








AON Network

Start

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B

C

D

E








AON Network

Start

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B

C

D

E

F








AON Network

Start

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B

C

D

E

F

G








AON Network

Start

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B

C

D

E

F

G

H








AON Network

Start

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B

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D

E

F

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I








AON Network

Start

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B

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E

F

G

H

I

J








AON Network

Start

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B

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D

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F

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K








AON Network

FinishStart

A

B

C

D

E

F

G

H

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K

Figure 8.4Example 8.1Example 8.1







AOA Network








AOA Network

A

Start1

2








AOA Network

A

B

Start1

2

4








AOA Network

A

B

C

D

Start1

2

3

5

4








AOA NetworkF

A

B

C

D

H

E

G

I

Start1

82

3 7

65

4








AOA NetworkF

A

B

C

D

H

E

GJ

I

Start1

82

3 7

65

4








AOA NetworkF

A

B

C

D

H

E

GJ

I DummyDummy

Start1

82

3 7

65

4








AOA NetworkF

A

B

C

D

H

E

G

K

J

I

Finish9

DummyDummy

Start1

82

3 7

65

4Figure 8.5








Completion Time

FinishStart

K6

I15

F10

C10

D10

E24

G35

H40

J4

A12

B9







Completion Time

FinishStart

K6

I15

F10

C10

D10

E24

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A12

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Completion Time

FinishStart

K6

I15

F10

C10

D10

E24

G35

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A12

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Completion Time

FinishStart

K6

I15

F10

C10

D10

E24

G35

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A12

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Completion Time

FinishStart

K6

I15

F10

C10

D10

E24

G35

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A12

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Completion Time

FinishStart

K6

I15

F10

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E24

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A12

B9







Completion Time

FinishStart

K6

I15

F10

C10

D10

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G35

H40

J4

A12

B9

Path Expected Time (wks)

A-F-K 28A-I-K 33A-C-G-J-K 67B-D-H-J-K 69B-E-J-K 43







Completion Time

FinishStart

K6

I15

F10

C10

D10

E24

G35

H40

J4

A12

B9

Path Expected Time (wks)

A-F-K 28A-I-K 33A-C-G-J-K 67B-D-H-J-K 69B-E-J-K 43







Completion Time

FinishStart

K6

I15

F10

C10

D10

E24

G35

H40

J4

A12

B9

Figure 8.6






Earliest StartEarliest StartandandEarliest Finish TimesEarliest Finish Times

A

12

K

6

C

10

G

35

J

4

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40

B

9

D

10

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24

I

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10

FinishStart




A

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9

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0

I

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F

10

Earliest start time

FinishStart





A

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9

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0 12

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Earliest start time Earliest finish time

FinishStart





A

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0 9

FinishStart





A

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9 33

0 9 9 19

FinishStart





A

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0 12

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12 27

12 22

9 33

0 9 9 19

12 22FinishStart





A

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9

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0 12

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12 22

19 59

9 33

0 9 9 19

12 22FinishStart





A

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9

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24

0 12

I

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10

12 27

12 22

22 57

19 59

9 33

0 9 9 19

12 22FinishStart





A

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4

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40

B

9

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10

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24

0 12

I

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12 27

12 22

22 57

59 6319 59

9 33

0 9 9 19

12 22FinishStart





Finish


Earliest start time Earliest finish time

A

12

K

6

C

10

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35

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4

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40

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9

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10

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24

0 12

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12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

Critical path

Start



A

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6

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35

J

4

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B

9

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0 12

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12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

Latest StartLatest StartandandLatest Finish TimesLatest Finish Times


FinishStart




A

12

K

6

C

10

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35

J

4

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40

B

9

D

10

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24

0 12

I

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F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

63 69 LatestfinishtimeFinishStart





A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

63 69Lateststarttime

LatestfinishtimeFinishStart




A

12

K

6

C

10

G

35

J

4

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40

B

9

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10

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24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

53 63 63 69

59 63Latest StartLatest StartandandLatest Finish TimesLatest Finish Times

FinishStart




A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

53 63 63 69

24 59

19 59

35 59


FinishStart




A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

53 63 63 69

14 24 24 59

9 19 19 59

35 59


FinishStart





A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

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24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 69

14 24 24 59

0 9 9 19 19 59

35 59

59 63


Earliest start time Earliest finish timeLatest start time Latest finish time

Critical path

FinishStart


St. Adolf’s HospitalSt. Adolf’s HospitalGantt Charts

Figure 8.9(a)Figure 8.9(a)



Figure 8.9(b)Figure 8.9(b)

Gantt Gantt ChartsCharts




Activity Slack



Activity Slack Activity Slack AnalysisAnalysis

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

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24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 69

14 24 24 59

0 9 9 19 19 59

35 59

59 63

FinishStart




Start

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 69

14 24 24 59

0 9 9 19 19 59

35 59

59 63

Finish


Activity Slack




Start

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 69

14 24 24 59

0 9 9 19 19 59

35 59

59 63

Finish


Activity Slack

Slack = LS – ESor

Slack = LF – EF




Start

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 69

14 24 24 59

0 9 9 19 19 59

35 59

59 63

Finish


Activity Slack

SlackK = 63 – 63

orSlackK = 69 – 69




Start

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 69

14 24 24 59

0 9 9 19 19 59

35 59

59 63

Finish


Activity Slack

SlackK = 0

orSlackK = 0




Start

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 69

14 24 24 59

0 9 9 19 19 59

35 59

59 63

Finish





Start

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 69

14 24 24 59

0 9 9 19 19 59

35 59

59 63

Finish


Node Duration ES LS Slack




Start

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 69

14 24 24 59

0 9 9 19 19 59

35 59

59 63

Finish



A 12 0 2 2B 9 0 0 0C 10 12 14 2D 10 9 9 0E 24 9 35 26F 10 12 53 41G 35 22 24 2H 40 19 19 0I 15 12 48 36J 4 59 59 0K 6 63 63 0




C

10

G

35

E

24

I

15

F

10

12 27

12 22

22 57

9 33

12 22

48 63

53 63

14 24 24 59

35 59

B

90 90 9

D

109 199 19

H

4019 5919 59

J

459 6359 63

K

663 6963 69

Finish

Critical PathCritical Path


A 12 0 2 2BB 99 00 00 00C 10 12 14 2DD 1010 99 99 00E 24 9 35 26F 10 12 53 41G 35 22 24 2HH 4040 1919 1919 00I 15 12 48 36JJ 44 5959 5959 00KK 66 6363 6363 00




C

10

G

35

E

24

I

15

F

10

12 27

12 22

22 57

9 33

12 22

48 63

53 63

14 24 24 59

35 59

B

90 90 9

D

109 199 19

H

4019 5919 59

J

459 6359 63

K

663 6963 69

A

120 122 14

FinishStart

Critical PathCritical PathExample 8.4Example 8.4


Linear cost assumptionLinear cost assumption


8000 —8000 —

7000 —7000 —

6000 —6000 —

5000 —5000 —

4000 —4000 —

3000 —3000 —

0 —0 —

Dire

ct c

ost (

dolla

rs)

Dire

ct c

ost (

dolla

rs)

|| || || || || ||55 66 77 88 99 1010 1111

Time (weeks)Time (weeks)Figure 8.11Figure 8.11

Cost-Time Relationships in Cost AnalysisCost-Time Relationships in Cost Analysis

Crash cost (Crash cost (CCCC))

Normal cost (Normal cost (NCNC))

(Crash time)(Crash time) (Normal time)(Normal time)

Estimated costs for Estimated costs for a 2-week reduction, a 2-week reduction, from 10 weeks to from 10 weeks to 8 weeks 8 weeks

52005200


St. Adolf’s HospitalSt. Adolf’s HospitalTABLE 8.1 DIRECT COST AND TIME DATA FOR

THE ST. ADOLF’S HOSPITAL PROJECT

A 12 $ 12,000 11 $ 13,000 1 $ 1,000B 9 50,000 7 64,000 2 7,000C 10 4,000 5 7,000 5 600D 10 16,000 8 20,000 2 2,000E 24 120,000 14 200,000 10 8,000F 10 10,000 6 16,000 4 1,500G 35 500,000 25 530,000 10 3,000H 40 1,200,000 35 1,260,000 5 12,000I 15 40,000 10 52,500 5 2,500J 4 10,000 1 13,000 2 1,000K 6 30,000 5 34,000 1 4,000

TotalsTotals $1,992,000$1,992,000 $2,209,000$2,209,000

MaximumNormal Normal Crash Crash Time Cost of

Time Cost Time Cost Reduction Crashing perActivity (NT) (NC) (CT) (CC) (wk) Week



A-I-K:A-I-K: 33 weeks33 weeks B-D-H-J-K:B-D-H-J-K: 69 weeks69 weeksA-F-K:A-F-K: 28 weeks28 weeks B-E-J-K:B-E-J-K: 43 weeks43 weeksA-C-G-J-K:A-C-G-J-K: 67 weeks67 weeks

Total cost = $2,624,000Total cost = $2,624,000Indirect costs = $8,000/weekIndirect costs = $8,000/weekPenalty cost = $20,000/week after week 65Penalty cost = $20,000/week after week 65

Critical Path B-D-H-J-K: 69 weeksCritical Path B-D-H-J-K: 69 weeksCrash Activity J by 3 weeks @ $1,000/weekCrash Activity J by 3 weeks @ $1,000/week

Minimum-Cost ScheduleMinimum-Cost Schedule









3($28,000) – 3($1,000) = $81,0003($28,000) – 3($1,000) = $81,000






3($28,000) – 3($1,000) = $81,0003($28,000) – 3($1,000) = $81,000$2,624,000 – $81,000 = $2,543,000$2,624,000 – $81,000 = $2,543,000






Total cost = $2,624,000 $2,543,000Total cost = $2,624,000 $2,543,000Indirect costs = $8,000/weekIndirect costs = $8,000/weekPenalty cost = $20,000/week after week 65Penalty cost = $20,000/week after week 65


3($28,000) – 3($1,000) = $81,0003($28,000) – 3($1,000) = $81,000$2,624,000 – $81,000 = $2,543,000$2,624,000 – $81,000 = $2,543,000




St. Adolf’s HospitalSt. Adolf’s HospitalMinimum Cost ScheduleMinimum Cost Schedule




3($28,000) – 3($1,000) = $81,0003($28,000) – 3($1,000) = $81,000$2,624,000 – $81,000 = $2,543,000$2,624,000 – $81,000 = $2,543,000

FinishStart

A12

B9

C10

D10

E24

F10

G35

H40

I15

J1

K6


St. Adolf’s HospitalSt. Adolf’s HospitalMinimum Cost ScheduleMinimum Cost Schedule




3($28,000) – 3($1,000) = $81,0003($28,000) – 3($1,000) = $81,000$2,624,000 – $81,000 = $2,543,000$2,624,000 – $81,000 = $2,543,000

FinishStart

A12

B9

C10

D10

E24

F10

G35

H40

I15

J11

K6





Critical Path B-D-H-J-K: 66 weeksCritical Path B-D-H-J-K: 66 weeksCrash Activity D by 2 weeks @ $2,000/weekCrash Activity D by 2 weeks @ $2,000/week








$28,000 + $8,000 – 2($2,000) = $32,000$28,000 + $8,000 – 2($2,000) = $32,000$2,543,000 – $32,000 = $2,511,000$2,543,000 – $32,000 = $2,511,000








$28,000 + $8,000 – 2($2,000) = $32,000$28,000 + $8,000 – 2($2,000) = $32,000$2,543,000 – $32,000 = $2,511,000$2,543,000 – $32,000 = $2,511,000







$28,000 + $8,000 – 2($2,000) = $32,000$28,000 + $8,000 – 2($2,000) = $32,000$2,543,000 – $32,000 = $2,511,000$2,543,000 – $32,000 = $2,511,000

Minimum-Cost ScheduleMinimum-Cost ScheduleSt. Adolf’s HospitalSt. Adolf’s Hospital

FinishStart

A12

B9

C10

D10

E24

F10

G35

H40

I15

J11

K6





$28,000 + $8,000 – 2($2,000) = $32,000$28,000 + $8,000 – 2($2,000) = $32,000$2,543,000 – $32,000 = $2,511,000$2,543,000 – $32,000 = $2,511,000


Start

A12

B9

D10

E24

F10

FinishC10

G35

H40

I15

J11

K6





Critical Paths B-D-H-J-K and A-C-G-J-K: 64 weeksCritical Paths B-D-H-J-K and A-C-G-J-K: 64 weeksCrash Activity K by 1 week @ $4,000/weekCrash Activity K by 1 week @ $4,000/week








$8,000 – $4,000 = $4,000$8,000 – $4,000 = $4,000$2,511,000 – $4,000 = $2,507,000$2,511,000 – $4,000 = $2,507,000








$8,000 – $4,000 = $4,000$8,000 – $4,000 = $4,000$2,511,000 – $4,000 = $2,507,000$2,511,000 – $4,000 = $2,507,000







$8,000 – $4,000 = $4,000$8,000 – $4,000 = $4,000$2,511,000 – $4,000 = $2,507,000$2,511,000 – $4,000 = $2,507,000


FinishStart

A12

B9

C10

D88

E24

F10

G35

H40

I15

J11

K6





$8,000 – $4,000 = $4,000$8,000 – $4,000 = $4,000$2,511,000 – $4,000 = $2,507,000$2,511,000 – $4,000 = $2,507,000


FinishStart

A12

B9

C10

D88

E24

F10

G35

H40

I15

J11

K55



Critical Paths B-D-H-J-K and A-C-G-J-K: 63 weeksCritical Paths B-D-H-J-K and A-C-G-J-K: 63 weeksCrash Activities B and C by 2 weeks Crash Activities B and C by 2 weeks @ $7,000/week and $600/week@ $7,000/week and $600/week










2($8,000) – 2($7,600) = $8002($8,000) – 2($7,600) = $800$2,507,000 – $800 = $2,506,200$2,507,000 – $800 = $2,506,200








2($8,000) – 2($7,600) = $8002($8,000) – 2($7,600) = $800$2,507,000 – $800 = $2,506,200$2,507,000 – $800 = $2,506,200







2($8,000) – 2($7,600) = $8002($8,000) – 2($7,600) = $800$2,507,000 – $800 = $2,506,200$2,507,000 – $800 = $2,506,200


FinishStart

A12

B9

C10

D88

E24

F10

G35

H40

I15

J11

K55





2($8,000) – 2($7,600) = $8002($8,000) – 2($7,600) = $800$2,507,000 – $800 = $2,506,200$2,507,000 – $800 = $2,506,200


FinishStart

A12

B77

C88

D88

E24

F10

G35

H40

I15

J11

K55


Coors FieldCoors Field


Probabilistic Time EstimatesProbabilistic Time Estimates

Figure 8.12 (a) Beta DistributionFigure 8.12 (a) Beta Distribution

MeanMeanmmaa bb TimeTime

Prob

abili

tyPr

obab

ility


Probabilistic Time EstimatesProbabilistic Time Estimates

TimeTime

Prob

abili

tyPr

obab

ility

Figure 8.12 (b) Normal DistributionFigure 8.12 (b) Normal DistributionMeanMean

aa bbmm33 33

Area under curve Area under curve between between aa and and bb is 99.74%is 99.74%


St. Adolf’s HospitalSt. Adolf’s HospitalProbabilistic Probabilistic Time EstimatesTime Estimates

A F

I

C G Finish

D

E

HB J

K

Start

ttee = =aa + 4 + 4mm + + bb

66

MeanMean

22 = = ( )( )bb –– aa66

22

VarianceVariance



Activity BActivity BMostMost

OptimisticOptimistic LikelyLikely PessimisticPessimistic((aa)) ((mm)) ((bb))77 88 1515

Probabilistic Probabilistic Time EstimatesTime Estimates

A F

I

C G Finish

D

E

HB J

K

Start




Activity BActivity BMostMost

OptimisticOptimistic LikelyLikely PessimisticPessimistic((aa)) ((mm)) ((bb))77 88 1515

Probabilistic Probabilistic Time EstimatesTime Estimates

ttee = = 9 weeks = = 9 weeks7 + 4(8) + 157 + 4(8) + 1566

22 = = 1.78 = = 1.78( )( )15 - 715 - 766

22

A F

I

C G Finish

D

E

HB J

K

Start





Optimistic Likely Pessimistic Expected VarianceActivity (a) (m) (b) Time (te ) (2 )

Time Estimates (wk) Activity Statistics

A 11 12 13 12 0.11B 7 8 15 9 1.78C 5 10 15 10 2.78D 8 9 16 10 1.78E 14 25 30 24 7.11F 6 9 18 10 4.00G 25 36 41 35 7.11H 35 40 45 40 2.78I 10 13 28 15 9.00J 1 2 15 4 5.44K 5 6 7 6 0.11



2 = (variances of activities) z = T – TE

2

2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89

z = 72 – 69 11.89

ProbabilitiesCritical Path = B - D - H - J - K

T = 72 days TE = 69 days





2

2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89

z = = 0.8772 – 69 11.89



From Appendix 2Pz = .8078 .81






2

2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89

z = = 0.8772 – 69 11.89



From Appendix 2Pz = .8078 .81Project duration (weeks)Project duration (weeks)

6969 7272

Probability of Probability of meeting the meeting the schedule is schedule is 0.80780.8078

Length of Length of critical pathcritical path

Normal distribution: Normal distribution: Mean = 69 weeks; Mean = 69 weeks; = 3.45 weeks = 3.45 weeks

Probability of Probability of exceeding 72 exceeding 72 weeks is 0.1922 weeks is 0.1922





2

2 = 0.11 + 2.78 + 7.11 + 5.44 + 0.11 = 15.55

z = = 1.2772 – 67 15.55

ProbabilitiesPath = A - C - G - J - K


From Appendix 2Pz = .8980 .90



A F

I

C G Finish

D

E

HB J

K

Start


Activity Duration Earliest Start Latest Start Slack

C 10 16 14 –2G 35 26 24 –2J 4 61 59 –2K 6 65 63 –2D 10 10 9 –1H 40 20 19 –1E 24 10 35 25I 15 16 48 32F 10 16 53 37

TABLE 8.2 SLACK CALCULATIONS AFTER ACTIVITIES AAND B HAVE BEEN COMPLETED


Project Life CycleProject Life Cycle

StartStart FinishFinish

Res

ourc

e re

quire

men

tsR

esou

rce

requ

irem

ents

TimeTimeFigure 8.14Figure 8.14

Definition Definition and and

organizationorganization

PlanningPlanning ExecutionExecution Close outClose out


Solved Problem 1Solved Problem 1

Finish

Start

A4

B7

C5

D6

E3

F11

G4

H3




Finish

Start

A

B

C

D

E

F

G

Figure 8.16(a) AON NetworkFigure 8.16(a) AON Network



Figure 8.16(b) AOA NetworkFigure 8.16(b) AOA Network

Finish

Start

1

2

3

F

A

B C

D

E

F

G

DummyDummy



Finish

Start


A

4.0

0.04.0

4.08.0

D

12.0

4.08.0

16.020.0

E

6.5

9.09.0

15.515.5

G

4.5

15.515.5

20.020.0

C

3.55.55.5

9.09.0

F

9.0

5.56.5

14.515.5

B

5.50.00.0

5.55.5



Finish

Start


A

4.0

0.04.0

4.08.0

D

12.0

4.08.0

16.020.0

E

6.5

9.09.0

15.515.5

G

4.5

15.515.5

20.020.0

C

3.55.55.5

9.09.0

F

9.0

5.56.5

14.515.5

B

5.50.00.0

5.55.5

Start

1

ES EF

LS LF

0 4

4 8

A

Documents

To Accompany Krajewski Ritzman Operations Management: Strategy and Analysis, Seventh Edition 2004 Prentice Hall, Inc. All rights reserved. Planning