to accompany quantitative analysis for management, 7e by render/stair 13-1 © 2000 by prentice hall,...

To accompany Quantitative Analysis for Management, 7e by Render/Stair

13-1 © 2000 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

Quantitative Analysis Quantitative Analysis for Managementfor Management

Chapter 13Chapter 13Project ManagementProject Management



Chapter OutlineChapter Outline

13.1 Introduction

13.2 PERT

13.3 PERT/COST

13.4 Critical Path Method



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.



Learning Objectives - continuedLearning Objectives - continuedReduce 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.



Project Management ModelsProject Management Models

PERT

PERT/Cost

Critical Path Method



Questions That May Be Questions That May Be Addressed by PERT and CPMAddressed by PERT 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?



Questions - continuedQuestions - continued6. Is the project over or under the budgeted amount?

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 ControllingScheduling, and Controlling

Project 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 PERT/CPMAdvantages of PERT/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 PERT/CPMLimitations of PERT/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 ImmediatePredecessors

A Build internal componentsB Modify roof and floorC Construct collection stack AD Pour concrete and install

frameB

E Build high-temperatureburner

C

F Install control system CG Install air pollution device D,EH Inspect and test F,G



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

1

2 4

53

6

(Build Internal Components)

(ConstructCollection Stack)

(Modify Roof and Floor)

(Pour Concrete andInstall Frame)

(Install Control System)

(Install PollutionDevice)

7(Inspect andTest)

(Build Burner)

A

BD

C

E

F

G

H



Beta Probability Distribution Beta Probability Distribution with Three Time Estimateswith Three Time 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

2Total: 25 weeks

Activity a m b E(t) 2



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

1

2 4

53

6 7

A

BD

C

E

F

G

H

t=2

t=2

t=3

t=4

t=4

t=5

t=3

t=2



General Foundry, Inc.General Foundry, Inc.PERT Network ES/EF, LS/LFPERT Network ES/EF, LS/LF

1

2 4

53

6 7

A

B

D

C

E

F

G

H

t=2

t=2

t=3

t=4

t=4

t=5

t=3

t=2

8 138 13

3 74 8

0 11 4

4 84 8

0 20 2

2 42 4

4 710 13 13 15

13 15

ES EFLS LF



General Foundry, Inc.General Foundry, Inc.PERT Network - Critical PathPERT Network - Critical Path

1

2 4

53

6 7

A

BD

C

E

F

G

H

Total time: 15



General FoundryGeneral FoundrySchedule & SlacksSchedule & Slacks

Activity EarliestStart(ES)

EarliestFinish(EF)

LatestStart(LS)

LatestFinish(LF)

Slack(LS-ES)

OnCriticalPath?

A 0 2 0 2 0 YesB 0 3 1 4 1 NoC 2 4 2 4 0 YesD 3 7 4 8 1 NoE 4 8 4 8 0 YesG 4 7 10 13 6 NoG 8 13 8 13 0 YesH 13 15 13 15 0 Yes



General FoundryGeneral Foundry Meeting a Deadline Meeting a Deadline

Project StandardDeviation, T

= Project Variance

Z = Due Date - Expected Completion DateT

= 16 - 151.76

= 0.570.57 Standard Deviations

1615 Time - weeks

Probability(T 16 Weeks)is 71.6%



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



General FoundryGeneral FoundryPERT - Use of DummyPERT - Use of Dummy

Activity Description ImmediatePredecessors

A Build internal componentsB Modify roof and floorC Construct collection stack AD Pour concrete and install

frameA,B

E Build high-temperatureburner

C

F Install control system CG Install air pollution device D,EH Inspect and test F,G



General Foundry, Inc.General Foundry, Inc.PERT Network - with DummyPERT Network - with Dummy

1

2 4

53

6

(Build Internal Components)

(ConstructCollection Stack)

(Modify Roof and Floor)

(Pour Concrete andInstall Frame)

(Install Control System)

(Install PollutionDevice)

7(Inspect andTest)

(Build Burner)

A

BD

C

E

F

G

H

Du

mm

y



General Foundry, Inc.General Foundry, Inc.PERT Network - with DummyPERT Network - with Dummy

1

2 4

53

6 7

A

BD

C

E

F

G

H

t=2

t=2

t=3

t=4

t=4

t=5

t=3

t=2

Du

mm

yt=

0



PERT - Sensitivity AnalysisPERT - Sensitivity AnalysisImpact of Increase (Decrease) in Critical

Path Activity timeActivity

TimeSuccessorActivity

ParallelActivity

PredecessorActivity

Earlieststart

Increase(decrease)

Nochange

No change

Earliestfinish

Increase(decrease)

Nochange

No change

Lateststart

Increase(decrease)

Increase(decrease)

No change

Latestfinish

Increase(decrease)

Increase(decrease)

No change

Slack Nochange

Increase(decrease)

No change



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

ABCDEFGH

0023448

13

01244

108

13

$11,000 $10,000 $13,000 $12,000 $14,000 $10,000 $16,000 $ 8,000

23244352

ActivityEarliest

Start (ES)Latest

Start (LS)

BudgetedCost per

Week

ExpectedTime, t

TotalBudgeted

Cost

$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 CrashingSteps in Project Crashing

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 & TimesNormal/Crash Costs & Times

Activity NormalTime

CrashTime

NormalCost

CrashCost

CrashCost Per

Week

OnCriticalPath?

A 2 1 22,000 23,000 1,000 YesB 3 1 30,000 34,000 2,000 NoC 2 1 26,000 27,000 1,000 YesD 4 3 48,000 49,000 1,000 NoE 4 2 56,000 58,000 1,000 YesG 3 2 30,000 30,500 500 NoG 5 2 80,000 86,000 2,000 YesH 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 Time Normal Time

Time (Weeks)1 2 3

Normal

Crashweekper

time Crashtime Normal

Cost Normal -Cost Crash

per Week

Cost Crash

to accompany quantitative analysis for management, 7e by render/stair 13-1 © 2000 by prentice hall,...

Documents

total project completion

valuable project documentation

timed project activities4

pertcpmproject activities

noncritical activities

slack time analyses

time andor cost estimates

total cost