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Project Management

Introduction to Project Management

- Projects can be simple (planning a company picnic) or complex (planning a space shuttle launch).
- Successfully completing a project requires:
- Knowledge of the tasks involved
- Accurate estimates of time and resources required
- Knowledge of physical and logical relations between the various tasks

- Project management techniques
- Critical Path Method (CPM)
- Program Evaluation and Review Technique (PERT)

- Spreadsheets can be used to manage projects, but dedicated project management software is often more effective.

An Example: Lightner Construction

- Tom Lightner owns Lightner Construction, a general contracting company specializing in the construction of single-family residences and small office buildings.
- Tom frequently has numerous construction projects going on at the same time and needs a formal procedure for planning, monitoring, and controlling each project.
- He is aware of various project scheduling techniques but has never used them.
- He wants to see how he might apply such techniques to one of the home-building projects he will be undertaking in the near future.
- The following slide summarizes each of the major activities required for this project.

Required Predecessor

Activity Description (in days) Activities

A Excavate 3 --

B Lay foundation 4 A

C Rough plumbing 3 B

D Frame 10 B

E Finish exterior 8 D

F Install HVAC 4 D

G Rough electric 6 D

H Sheet rock 8 C, E, F, G

I Install cabinets 5 H

J Paint 5 H

K Final plumbing 4 I

L Final electric 2 J

M Install flooring 4 K, L

Summary of ActivitiesFinal Plumbing

Rough Plumbing

K

I

C

Sheet Rock

Excavate

Lay Foundation

M

H

B

A

Finish Exterior

E

Install

Flooring

L

J

D

Frame

HVAC

Final Electric

Paint

F

Rough Electric

G

An Activity-On-Node (AON) NetworkA Comment of Project Networks

- Projects can also be depicted using Activity-On-Arc (AOA) networks.
- This book uses AON networks (which the author views as superior to AOA).
- Some software packages use AOA networks, so you should at least be aware that they exist.

Install Cabinets

10

K

Lay Foundation

Rough Plumbing

I

B

C

12

13

8

9

2

1

3

M

H

A

Install Flooring

Sheet Rock

Excavate

D

J

L

11

Frame

Paint

Final Electric

Finish Exterior

5

E

4

F

HVAC

G

6

Rough Electric

7

An Activity-on-Arc (AOA) NetworkD

C

B

E

D

A

C

start

finish

E

B

Start and Finish Points- AON networks should have unique start and finish points.

CPM: An Overview

- A Forward Pass through the network determines the earliest times each activity can start and finish.
- A Backward Pass through the network determines the latest times each activity can start and finish without delaying completion of the project.
- The longest path through the network is the “critical path”.

Information Recorded for Each Node

ESTi

EFTi

i

ti

LFTi

LSTi

ti = time required to perform activity i

ESTi = earliest possible start time for activity i

EFTi = earliest possible finish time for activity i

LSTi = latest possible start time for activity i

LFTi = latest possible finish time for activity i

The Forward Pass

- The earliest start time (EST) for the initial activity in a project is “time zero”.
- The EST of an activity is equal to the latest (or maximum) early finish time of the activities directly preceding it.
- The EFT of an activity is equal to its EST plus the time required to perform the activity.

42

33

38

7

10

4

I

5

K

3

C

42

46

25

33

3

7

0

3

4

8

M

4

H

3

B

A

17

25

8

E

33

38

38

40

5

2

J

L

7

17

10

D

17

21

4

F

17

23

6

G

Results of the Forward PassNote:

ESTH=MAX(EFTC,EFTE,EFTF,EFTG)=25

The Backward Pass

- The latest finish time (LFT) for the final activity in a project is equal to its EFT as determined by the forward pass.
- The LFT for any other activity is equal to the earliest (or minimum) LST of the activities directly following (or succeeding) it.
- The LST of an activity is equal to its LFT minus the time required to perform the activity.

42

33

38

7

10

4

5

K

I

3

C

42

46

0

3

3

7

H

4

3

4

M

A

B

17

25

8

E

33

38

38

40

5

2

J

L

D

17

21

4

F

17

23

6

G

Results of the Backward Pass38

42

38

33

22

25

25

33

8

25

33

42

46

0

3

7

3

17

25

7

17

10

35

40

40

42

7

17

Note:

LFTH=MIN(LSTI,LSTJ)=33

LFTD=MIN(LSTE,LSTF ,LSTG)=17

LFTB=MIN(LSTC,LSTD)=7

21

25

19

25

38

38

42

7

10

5

4

I

K

3

C

3

7

0

3

H

4

3

B

A

17

25

8

E

33

38

38

40

5

2

J

L

D

17

21

4

F

17

23

6

G

The Critical Path38

42

38

33

22

25

Slack=15

Slack=0

Slack=0

25

33

42

46

8

M

4

25

33

42

46

0

3

7

3

Slack=0

Slack=0

Slack=0

Slack=0

17

25

7

17

Slack=0

10

35

40

40

42

7

17

Slack=2

Slack=2

Slack=0

21

25

Slack=4

Note:

Slack = LSTi-ESTi or LFTi-EFTi

19

25

Slack=2

Project Management Using Spreadsheets

- The early and late start and finish times for project activities can be done in a spreadsheet using array formulas and circular references.
- See file Fig14-11.xls

Array Formulas

- An array formula can perform multiple calculations using a range of cells and then return either a single result or multiple results.
- You create array formulas in the same way that you create other formulas, except that you press [Ctrl]+[Shift]+[Enter] to enter the formula.

Array Formula Examples

- Let’s compare several standard Excel functions with their equivalent array formulas…
Excel Function

=SUMPRODUCT(E5:E17,F5:F17)

Array Formula

=SUM(E5:E17*F5:F17)

Excel Function

=SUMXMY2(E5:E17,F5:F17)

Array Formula

=SUM((E5:E17-F5:F17)^2)

Gantt Chart

M

L

K

J

I

H

G

F

E

D

Activity Time

C

Slack

B

A

0

5

10

15

20

25

30

35

40

45

50

Time Period

A Gantt Chart for the Example Problem- PERT then estimates expected durationtiand varianceviof each activity’s duration as:

- CPM assumes all activity times are known with certainty or can be estimated accurately.
- PERT accounts for uncertainty in activity times by using three time estimates:
ai= duration of activity i assuming the most favorable conditions

bi = duration of activity i assuming the least favorable conditions

mi = estimate of the most likely duration of activity i

PERT Overview Continued

- The expected (or mean) time required to complete any path in the network is the sum of the expected times (the ti) of the activities on the path.
- Assuming the individual activity times in a project are independent of one another, we may also calculate the variance of the completion time for any path as the sum of the variances (the vi) of the activities on the path.
- PERT considers the path with the largest expected completion time to be the critical path.
- PERT’s reasoning may be flawed...

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