Project Management - University of Nevada, Renobusiness.unr.edu/faculty/ronlembke/352/OnlineLectures/07-projects/... · Activity on Node (AoN) 2 4? Years Enroll Receive ... • Shortest

Project

Management

Dr. Ron Lembke

Operations Management

What’s a Project?

• Changing something from the way

it is to the desired state

• Never done one exactly like this

• Many related activities

• Focus on the outcome

• Regular teamwork focuses on the

work process

Examples of Projects

• Building construction

• New product introduction

• Software implementation

• Training seminar

• Research project

Why are projects hard?

• Resources-– People, materials

• Planning– What needs to be done?

– How long will it take?

– What sequence?

– Keeping track of who is supposedly doing what, and getting them to do it

IT Projects

• Half finish late and over budget

• Nearly a third are abandoned before

completion– The Standish Group, in Infoworld

• Get & keep users involved & informed

• Watch for scope creep / feature creep

Project Scheduling

• Establishing objectives

• Determining available resources

• Sequencing activities

• Identifying precedence relationships

• Determining activity times & costs

• Estimating material & worker requirements

• Determining critical activities

PERT & CPM

• Network techniques

• Developed in 1950’s

• CPM by DuPont for chemical plants

• PERT by U.S. Navy for Polaris

missile

• Consider precedence relationships

& interdependencies

• Each uses a different estimate of

activity times

• Completion date?

• On schedule? Within budget?

• Probability of completing by ...?

• Critical activities?

• Enough resources available?

• How can the project be finished early at the least cost?

Questions Answered by

PERT & CPM

PERT & CPM Steps

• Identify activities

• Determine sequence

• Create network

• Determine activity times

• Find critical path

• Earliest & latest start times

• Earliest & latest finish times

• Slack

Activity on Node (AoN)

2

4? Years

EnrollReceive

diploma

Project: Obtain a college degree (B.S.)

1 month

Attend class,

study etc.

1

1 day

3

Activity on Arc (AoA)

4,5 ?

Years

Enroll

Receive

diploma


1 month

Attend class, study,

etc.

11 day

2 3 4

AoA Nodes have

meaning

Graduating

SeniorApplicant


1

Aluma

Alumnus

2 3 4

Student

Precedence Relationships

– Scenario 1a

• Hierarchy of what needs to be done, in what order– Time required for each thing

• For me, the hardest part– I’ve never done this before. How do I know

what I’ll do when and how long it’ll take?

– I think in phases

– The farther ahead in time, the less detailed

– Figure out the tricky issues, the rest is details

– A lot will happen between now and then

– It works not badly with no deadline

Precedence Relationships

Mudroom

Mudroom Remodel

• Big-picture sequence easy:

– Demolition

– Framing

– Plumbing

– Electrical

– Drywall, tape & texture

– Slate flooring

– Cabinets, lights, paint

• Hard: can a sink fit?

D

W

DW

Before:

After:

Project Scheduling

Techniques

• Gantt chart

• Critical Path Method (CPM)

• Program Evaluation &

Review Technique (PERT)

Gantt Chart

J F M A M J J

Time PeriodActivity

Design

Build

Test

J F M A M J J

Time PeriodActivity

Design

Build

Test

Day before Thanksgiving, 2015, late afternoon, 27ºF

What do these 3 guys have in common?

Network Example

You’re a project manager for Bechtel.

Construct the network.Activity Predecessors

A --B AC AD BE BF CG DH E, F

Network Example -

AON

A

C

E

F

BD

G

H

Z

Network Example -

AON

A

B

E

D

CF

H

G

Z

Network Example -

AON

A

B

E

D

C

F

HG

Z

Network Example -

AOA

2

4

51

3 6 8

7 9

A

C F

EB

D

H

G

AOA Diagrams

2 31A

C

BD

A precedes B and C, B and C precede D

2 41A C

B

D

3

5

4

Add a phantom arc for clarity.

Scenario 1a

Task Description Days Pred

A Drawings 1 --

B Get & Dye fabric 3 --

C Build stage 4 A

D Sew fabric, frame back 2 B

E Rent, deliver, hang lights 1 A

F Paint stage 2 C

G Test assembly 1 D,F

H disassemble, deliver 1 G

I Assemble, touch-up 1 E,H

Scenario 1a Network

Diagram

3

START

A

1

B

3

E

1

C

4

D

2

F

2

G

1

H

1

I

1 Finish

Scenario 1a Longest

Path

3

START

A

1

B

3

E

1

C

4

D

2

F

2

G

1

H

1

I

1Finish

Paths: Days

AEI 3

ACFGHI 10

BDGHI 8

Critical Path Analysis

• Provides activity information

• Earliest (ES) & latest (LS) start

• Earliest (EF) & latest (LF) finish

• Slack (S): Allowable delay

• Identifies critical path

• Longest path in network

• Shortest time project can be

completed

• Any delay on critical activities delays

the whole project

• Activities have 0 slack

Critical Path

Analysis Example

Event

ID Pred. Description Time

(Wks)

A None Prepare Site 1

B A Pour fdn. & frame 6

C A Buy shrubs etc. 3

D B Roof 2

E D Do interior work 3

F C Landscape 4

G E,F Move In 1

Network Solution

A

EDB

C F

G

1

6 2 3

1

43

Earliest Start & Finish

Steps

• Begin at starting event & work forward

• ES = 0 for starting activities

• ES is earliest start

• EF = ES + Activity time

• EF is earliest finish

• ES = Maximum EF of all predecessors for

non-starting activities

Activity ES EF LS LF Slack

A 0 1

B

C

D

E

F

Activity A

Earliest Start Solution

For starting activities, ES = 0.

A

EDB

C F

G

1

6 2 3

1

43


A 0 1

B 1 7

C 1 4

D 7 9

E 9 12

F 4 8

G 12 13


A

EDB

C F

G

1

6 2 3

1

43

Latest Start & Finish

Steps

• Begin at ending event & work backward

• LF = Maximum EF for ending activities

• LF is latest finish; EF is earliest finish

• LS = LF - Activity time

• LS is latest start

• LF = Minimum LS of all successors for

non-ending activities


A 0 1

B 1 7

C 1 4

D 7 9

E 9 12

F 4 8

G 12 13 13


A

EDB

C F

G

1

6 2 3

1

43


A 0 1 0 1 B 1 7 1 7 C 1 4 5 8 D 7 9 7 9 E 9 12 9 12 F 4 8 8 12 G 12 13 12 13

Latest Finish

Solution

A

EDB

C F

G

1

6 2 3

1

43


A 0 1 0 1 0

B 1 7 1 7 0

C 1 4 5 8 4

D 7 9 7 9 0

E 9 12 9 12 0

F 4 8 8 12 4

G 12 13 12 13 0

Compute Slack

Critical Path

A

EDB

C F

G

1

6 2 3

1

43

Scenario 1b ES/EF

times

START

A

1

0 1

B

3

0 3

E

1

1 2

C

4

1 5

D

2

3 5

F

2

5 7

G

1

7 8H

1

8 9

I

1

910

Finish

Scenario 1c LF/LS

times

START

A

1

0 1

0 1

B

3

0 3

2 5

E

1

1 2

8 9

C

4

1 5

1 5

D

2

3 5

5 7

F

2

5 7

5 7

G

1

7 8

7 8

H

1

8 9

8 9

I

1

910

9 10 Finish

Scenario 1c

Finish

START

A

1

0 1

0 1

B

3

0 3

2 5

E

1

1 2

8 9

C

4

1 5

1 5

D

2

3 5

5 7

F

2

5 7

5 7

G

1

7 8

7 8

H

1

8 9

8 9

I

1

910

9 10

Other notation

• Compute ES, EF for each

activity, Left to Right

• Compute, LF, LS, Right to Left

C 7LS LF

ES EF

Example #2

A 21

E 5D 2B 4

C 7 F 7

G 2

21 28 28 35

35 37

28 3325 2721 25

0 21

Example #2

A 21

E 5D 2B 4

C 7 F 7

G 2

21 28 28 35

35 37

28 3325 2721 25

0 21

F cannot start until C and D are done.

G cannot start until both E and F are done.

Example #2

A 21

E 5D 2B 4

C 7 F 7

G 2

22 26

0 21

26 28 30 35

35 37

21 28 28 35

21 28 28 35

35 37

28 3325 2721 25

0 21

E just has to be done in time for G to start at 35, so it has slack.

D has to be done in time for F to go at 28, so it has no slack.

Example #2

A 21

E 5D 2B 4

C 7 F 7

G 2

22 26

0 21

26 28 30 35

35 37

21 28 28 35

21 28 28 35

35 37

28 3325 2721 25

0 21

E just has to be done in time for G to start at 35, so it has slack.

D has to be done in time for F to go at 28, so it has no slack.

Gantt Chart - ES

0 5 10 15 20 25 30 35 40

A

B

C

D

E

F

G

Gantt Chart - LS

0 5 10 15 20 25 30 35 40

A

B

C

D

E

F

G

Another Example

A 1

B 4

C 3

D 7

E 6

F 2

H 9

I 4

G 7

Solved Problem 1

A 10 1

0 1

B 41 5

1 5

C 36 9

1 4

D 72 9

1 8

E 65 11

5 11

F 29 11

8 10

H 99 18

8 17

I 418 22

18 22

G 711 18

11 18

Can We Go Faster?

Time-Cost Models

1. Identify the critical path

2. Find cost per day to expedite each node on

critical path.

3. For cheapest node to expedite, reduce it as

much as possible, or until critical path

changes.

4. Repeat 1-3 until no feasible savings exist.

Time-Cost Example

• ABC is critical path=30

Crash cost Crash

per week wks avail

A 500 2

B 800 3

C 5,000 2

D 1,100 2

C 10B 10A 10

D 8

Cheapest way to gain 1

Week is to cut A

Time-Cost Example


Crash cost Crash

per week wks avail

A 500 1

B 800 3

C 5,000 2

D 1,100 2

C 10B 10A 9

D 8

Cheapest way to gain 1 wk

Still is to cut A

Wks Incremental Total

Gained Crash $ Crash $

1 500 500

Time-Cost Example


Crash cost Crash

per week wks avail

A 500 0

B 800 3

C 5,000 2

D 1,100 2

C 10B 10A 8

D 8


is to cut B



1 500 500

2 500 1,000

Time-Cost Example


Crash cost Crash

per week wks avail

A 500 0

B 800 2

C 5,000 2

D 1,100 2

C 10B 9A 8

D 8


Still is to cut B



1 500 500

2 500 1,000

3 800 1,800

Time-Cost Example

• Critical paths=26 ADC & ABC

Crash cost Crash

per week wks avail

A 500 0

B 800 1

C 5,000 2

D 1,100 2

C 10B 8A 8

D 8

To gain 1 wk, cut B and D,

Or cut C

Cut B&D = $1,900

Cut C = $5,000

So cut B&D



1 500 500

2 500 1,000

3 800 1,800

4 800 2,600

Time-Cost Example


Crash cost Crash

per week wks avail

A 500 0

B 800 0

C 5,000 2

D 1,100 1

C 10B 7A 8

D 7

Can’t cut B any more.

Only way is to cut C



1 500 500

2 500 1,000

3 800 1,800

4 800 2,600

5 1,900 4,500

Time-Cost Example


Crash cost Crash

per week wks avail

A 500 0

B 800 0

C 5,000 1

D 1,100 1

C 9B 7A 8

D 7

Only way is to cut C



1 500 500

2 500 1,000

3 800 1,800

4 800 2,600

5 1,900 4,500

6 5,000 9,500

Time-Cost Example


Crash cost Crash

per week wks avail

A 500 0

B 800 0

C 5,000 0

D 1,100 1

C 8B 7A 8

D 7

No remaining possibilities to

reduce project length



1 500 500

2 500 1,000

3 800 1,800

4 800 2,600

5 1,900 4,500

6 5,000 9,500

7 5,000 14,500

Time-Cost Example

C 8B 7A 8

D 7

No remaining possibilities to

reduce project length



1 500 500

2 500 1,000

3 800 1,800

4 800 2,600

5 1,900 4,500

6 5,000 9,500

7 5,000 14,500

• Now we know how much it costs us to save any number of weeks

• Customer says he will pay $2,000 per week saved.

• Only reduce 5 weeks.

• We get $10,000 from customer, but pay $4,500 in expediting costs

• Increased profits = $5,500

Ex.

AOA

AON

• Paths:

• ABF: 18

• CDEF: 20

C5

B 10A 6

D 4 E 9

F2

Activity Avail Cost

A 0 ----

B 2 500

C 1 300

D 3 700

E 2 600

F 1 800

Gantt charts to

keep track

• Original

A 6 B 10

C 5 D 4 E 9

2

F 2

Activity Avail Cost

A 0 ----

B 2 500

C 1 300

D 3 700

E 2 600

F 1 800

Consider CDEF

C is cheapest, crash 1 day

A 6 B 10

C 4 D 4 E 9

1

F 2

C5

B10A 6

D 4 E 9

F2

C4

B10A 6

D 4 E 9

F2

Revised Pictures: Activity Avail Cost

A 0 ----

B 2 500

C 0

D 3 700

E 2 600

F 1 800

Consider

DEF

E cheapest

Crash E 1

day

Keep Track with Gantt Charts

A 6 B 10

C 4 D 4 E 8

F 2

C4

B10A 6

D 4 E8

F2

New Pictures:

Activity Avail Cost

A 0 ----

B 2 500

C 0

D 3 700

E 1 600

F 1 800

All Activities

Critical

ABF: 18

CDEF: 18

Options: Crash:

• F $800 – last one

• B, AND D or E

• E is cheaper than D

• $500+$600 =

$1,100 > 1,000

• Cost > Benefit

A 6 B 10

C 4 D 4 E 8

F 1

C4

B10A 6

D 4 E8

F1

Scenario 2

Now, need to do it in 7 days!

Task Normal Crash $/day

B 3 2 $1,000

C 4 1 2,000

D 2 1 500

F 2 1 800

START

A

1

0 1

0 1

B

3

0 3

2 5

E

1

1 2

8 9

C

4

1 5

1 5

D

2

3 5

5 7

F

2

5 7

5 7

G

1

7 8

7 8

H

1

8 9

8 9

I

1

910

9 10

Not critical

Not critical

Cheapest

$800 gain 1 day

Finish

Scenario 2



B 3 2 $1,000

C 4 1 2,000

D 2 1 500

F 2 1 800

START

A

1

0 1

0 1

B

3

0 3

1 4

E

1

1 2

8 8

C

4

1 5

1 5

D

2

3 5

4 6

F

1

5 6

5 6

G

1

6 7

6 7

H

1

7 8

7 8

I

1

8 9

8 9

Not critical

Not critical

Used up

Only optionDay 1 $800

Day 2 $2,000

Finish

Scenario 2



B 3 2 $1,000

C 3 1 2,000

D 2 1 500

F 2 1 800

START

A

1

0 1

0 1

B

3

0 3

0 3

E

1

1 2

8 8

C

3

1 4

1 4

D

2

3 5

3 5

F

1

4 5

4 5

G

1

5 6

5 6

H

1

6 7

6 7

I

1

7 8

7 8

Used up

Day 1 $800

Day 2 $2,000

Something on both paths

C, and B or D, D cheaper

Day 3 $2,500

Total $5,300

Finish

Scenario 2

Now, Done in 7 days!


B 3 2 $1,000

C 2 1 2,000

D 1 1 500

F 2 1 800

START

A

1

0 1

0 1

B

3

0 3

0 3

E

1

1 2

5 6

C

2

1 3

1 3

D

1

3 4

3 4

F

1

3 4

3 4

G

1

4 5

4 5

H

1

5 6

5 6

I

1

6 7

6 7

Used up

Day 1 $800

Day 2 $2,000Day 3 $2,500

Total $5,300

Used up

Finish

What about

Uncertainty?

PERT Activity Times

• 3 time estimates

• Optimistic times (a)

• Most-likely time (m)

• Pessimistic time (b)

• Follow beta distribution

• Expected time: t = (a + 4m + b)/6

• Variance of times: v = (b - a)2/36

Example Activity

• a = 2, m = 4, b = 6

• E[T] = (2 + 4*4 + 6)/6 = 24/6 = 4.0

• σ2 = (6 – 2)2 / 36 = 16/36 = 0.444

Example

Activity a m b E[T] variance

A 2 4 8 4.33 1

B 3 6.1 11.5 6.48 2

C 4 8 10 7.67 1

Project 18.5 4

Complete in 18.5 days, with a variance

of 4.

CBA

4.33 6.48 7.67

Sum of 3 Normal

Random Numbers

15

20

2

X

35

30

2

X

10

10

2

X

10 20 30 40 50 60

60

60

2

X

Average value of the sum is

equal to the sum of the averages

Variance of the sum is equal to

the sum of the variances

Notice curve of sum is more spread

out because it has large variance

Back to the Example:

Probability of <= 21 wks

18.5 21

Average time = 18.5, st. dev = 2

21 is how many standard deviations

above the mean?

21-18.5 = 2.5.

St. Dev = 2,

so 21 is 2.5/2 = 1.25 standard

deviations above the mean

Book Table says area between

Z=1.25 and –infinity is 0.8944

Probability <= 21 wks

= 0.8944 = 89.44%

Benefits

of PERT/CPM

• Useful at many stages of project

management

• Mathematically simple

• Use graphical displays

• Give critical path & slack time

• Provide project documentation

• Useful in monitoring costs

Limitations

of PERT/CPM

• Clearly defined, independent, &

stable activities

• Specified precedence

relationships

• Activity times (PERT) follow

beta distribution

• Subjective time estimates

• Over emphasis on critical path

Conclusion

• Explained what a project is

• Drew project networks

• Compared PERT & CPM

• Determined slack & critical path

• Found profit-maximizing crash decision

• Computed project probabilities

Documents

Project Management - University of Nevada, Renobusiness.unr.edu/faculty/ronlembke/352/OnlineLectures/07-projects/... · Activity on Node (AoN) 2 4? Years Enroll Receive ... • Shortest