Chapter 13 Project Management

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna

13-1 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Chapter 13Chapter 13

Project ManagementProject Management



Learning ObjectivesLearning Objectives

Students will be able to

• Understand how to plan, monitor, and control projects with the use of PERT.

• Determine earliest start, earliest finish, latest start, latest finish, and slack times for each activity along with the total project completion time.

• Reduce total project time at the least total cost by crashing the network using manual or linear programming techniques.

• Understand the important role of software in project management.



Chapter OutlineChapter Outline

13.1 Introduction

13.2 PERT

13.3 PERT/COST

13.4 Critical Path Method

13.5 Other Topics in Project

Management



Project Management Project Management ModelsModels

• PERT

• PERT/Cost

• Critical Path Method



Questions Addressed by Questions Addressed by PERT and CPMPERT and CPM

1. When will the project be completed?

2. What are the critical activities or tasks

in the project?

3. Which are the noncritical activities?

4. What is the probability that the project

will be completed by a specific date?

5. Is the project on schedule, ahead of

schedule, or behind schedule?

6. Is the project over or under the budgeted

amount?



Questions - continuedQuestions - continued

7. Are there enough resources

available to finish the project on

time?

8. If the project must be finished in

less than the scheduled amount of

time, what is the best way to

accomplish this at least cost?



Project Planning, Project Planning, Scheduling, and Scheduling, and

ControllingControllingProject Planning1. Setting goals2. Defining the project3. Tying needs into timed project activities4. Organizing the team

Project Scheduling1. Tying resources to specific activities2. Relating activities to each other3. Updating and revising on regular basis

Project Controlling1. Monitoring resources, costs, quality and budgets2. Revising and changing plans3. Shifting resources to meet demands

Before Project

During Project



Six Steps Common toSix Steps Common toPERT and CPMPERT and CPM

1. Define the project and all significant

activities/tasks.

2. Develop relationships among the activities.

Identify precedence relationships.

3. Draw the network.

4. Assign time and/or cost estimates to each

activity.

5. Compute the longest time path (critical path)

through the network.

6. Use the network to help plan, schedule,

monitor, and control the project.



Advantages of Advantages of PERT/CPMPERT/CPM

• Useful at several stages of project management

• Straightforward in concept, not mathematically

complex

• Uses graphical displays employing networks to

help user perceive relationships among project

activities

• Critical path and slack time analyses help

pinpoint activities that need to be closely

watched



Advantages - continuedAdvantages - continued

• Networks generated provide valuable

project documentation and graphically

point out who is responsible for various

project activities

• Applicable to a wide variety of projects

and industries

• Useful in monitoring not only schedules,

but costs as well



Limitations of Limitations of PERT/CPMPERT/CPM

• Project activities must be clearly defined,

independent, and stable in their relationships

• Precedence relationships must be specified and

networked together

• Time activities in PERT are assumed to follow

the beta probability distribution -- must be

verified

• Time estimates tend to be subjective, and are

subject to fudging by managers

• There is inherent danger in too much emphasis

being placed on the critical path



General FoundryGeneral FoundryPERTPERT

Activity Description Immediate

Predecessors

A Build internal components

B Modify roof and floor

C Construct collection stack A

D Pour concrete and install

frame

B

E Build high-temperature

burner

C

F Install control system C

G Install air pollution device D,E

H Inspect and test F,G



General Foundry, Inc.General Foundry, Inc.PERT NetworkPERT Network

Start Finish

A 2 C 2 F 3

B 3 D 4 G 5

E 4 H 2



Beta Probability Beta Probability Distribution with Three Distribution with Three

Time EstimatesTime Estimates



General Foundry, Inc.General Foundry, Inc. Time Estimates Time Estimates

A

B

C

D

E

F

G

H

1

2

1

2

1

1

3

1

2

3

2

4

4

2

4

2

3

4

3

6

7

9

11

3

2

3

2

4

4

3

5

2

Total: 25 weeks

Activity a m b E(t) 2

9

1

6

132

9

25

6

1112

9

16

6

1 92

9

9

6

1 72

9

4

6

2 62

9

1

6

1 32

4

1

6

1 42

9

1

6

1 32



General Foundry, Inc.General Foundry, Inc.PERT Network - with E(t)PERT Network - with E(t)

Start Finish

A 2 C 2 F 3

E 4 H 2

B 3 D 4 G 5

ES EF

LS LF



General Foundry, Inc.General Foundry, Inc.PERT Network ES/EF, PERT Network ES/EF,

LS/LFLS/LF

B 3

0 3

D 3

3 7

G 5

8 13

Start Finish

A 2

0 2

C 2

2 4

F 3

4 7

E 4

4 8

H 2

13 15

ES EF

LS LF



General Foundry, Inc.General Foundry, Inc.PERT Network ES/EF, PERT Network ES/EF,

LS/LFLS/LF

B 3

0 3

1 4

D 4

3 7

4 8

G 5

8 13

8 13

Start Finish

A 2

0 2

0 2

C 2

2 4

2 4

F 3

4 7

10 13

E 4

4 8

4 8

H 2

13 15

13 15

ES EF

LS LF



General Foundry, Inc.General Foundry, Inc.Critical PathCritical Path

B 3

0 3

1 4

D 4

3 7

4 8

G 5

8 13

8 13

Start Finish

A 2

0 2

0 2

C 2

2 4

2 4

F 3

4 7

10 13

E 4

4 8

4 8

H 2

13 15

13 15

ES LF

LS LF

Total Time = 15



General FoundryGeneral FoundrySchedule & SlacksSchedule & Slacks

Act

ivit

y ES EF LS LF LS-ES OnCriticalPath?

A 0 2 0 2 0 Yes

B 0 3 1 4 1 No

C 2 4 2 4 0 Yes

D 3 7 4 8 1 No

E 4 8 4 8 0 Yes

G 4 7 10 13 6 No

G 8 13 8 13 0 Yes

H 13 15 13 15 0 Yes



General FoundryGeneral Foundry Meeting a Deadline Meeting a Deadline

0.57 Standard Deviations

1615 Time - weeks

0.57 1.76

15-16

date completion Expected - date Due z

rianceproject va deviation, Standard

71.6%

weeks)16P(t



PERT ProvidedPERT Provided

• Project expected completion date: 15

weeks

• Probability of finishing in 16 or fewer

days: 71.6%

• Identity of activities on critical path: A,

C, E, G, and H

• Identity of activities with slack: B, D,

and F

• Detailed schedule of start/finish dates



PERT - Sensitivity PERT - Sensitivity AnalysisAnalysis

Impact of Increase (Decrease) in Critical

Path Activity time

Activity

Time

Successor

Activity

Parallel

Activity

Predecessor Activity

ESIncrease

(decrease)No change No change

EFIncrease

(decrease)No change No change

LSIncrease

(decrease)

Increase(Decrease) No change

LFIncrease

(decrease)


SlackNo

change




Gantt Chart for Gantt Chart for General FoundryGeneral Foundry

Activity 1 2 3 4 5 6 7 8 9 10

11

12

13

14

15

A

B

C

D

E

F

G

H



General Foundry, Inc. General Foundry, Inc. PERT & BudgetingPERT & Budgeting

A

B

C

D

E

F

G

H

0

0

2

3

4

4

8

13

0

1

2

4

4

10

8

13

$11,000

$10,000

$13,000

$12,000

$14,000

$10,000

$16,000

$ 8,000

2

3

2

4

4

3

5

2

ActivityES LS)

BudgetedCost per

Week

E(t)Total

BudgetedCost

$22,000

$30,000

$26,000

$48,000

$56,000

$30,000

$80,000

$16,000

Total $308,000



General FoundryGeneral FoundryBudget RangesBudget Ranges



General FoundryGeneral FoundryMonitoring & ControllingMonitoring & Controlling



Critical Path MethodCritical Path MethodSteps in Project Steps in Project

CrashingCrashing

1. Find normal critical path and identify

critical activities.

2. Compute crash cost per week for all

activities.

3. Select critical activity with smallest

crash cost per week. Crash this activity

4. Check to make sure critical path is still

critical. If not, find the new one.

Return to step 3.



General FoundryGeneral FoundryNormal/Crash Costs & Normal/Crash Costs &

TimesTimesA

ctiv

ity

Nor

mal

T

ime

Cra

sh

Tim

e

Nor

mal

C

ost

Nor

mal

C

ost

Cra

sh C

ost

Per

Wee

k

On the Critical Path?

A 2 1 22,000 23,000 1,000 Yes

B 3 1 30,000 34,000 2,000 No

C 2 1 26,000 27,000 1,000 Yes

D 4 3 48,000 49,000 1,000 No

E 4 2 56,000 58,000 1,000 Yes

G 3 2 30,000 30,500 500 No

G 5 2 80,000 86,000 2,000 Yes

H 2 1 16,000 19,000 3,000 Yes



Crash & NormalCrash & NormalTimes and CostsTimes and Costs

$34,000

$33,000

$32,000

$31,000

$30,000

ActivityCost

CrashCost

NormalCost

Crash TimeNormal Time

Time (Weeks)1 2 3

Normal

Crash

per week 20002000

4000

1 - 3

30000 - 34000

TimeCrash Time Normal

Cost Normal -Cost Crash

Week

PerCost

Crash

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Chapter 13 Project Management