Project Management

Chapter 14

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.

Summary of ActivitiesTime Immediate

RequiredPredecessorActivity Description (in days) Activities

A Excavate 3 --B Lay foundation 4 AC Rough plumbing 3 BD Frame 10 BE Finish exterior 8 DF Install HVAC 4 DG Rough electric 6 DH Sheet rock 8 C, E, F, GI Install cabinets 5 HJ Paint 5 HK Final plumbing 4 IL Final electric 2 JM Install flooring 4 K, L

An Activity-On-Node (AON) NetworkInstall

Cabinets

A B

C

D

E

F

G

H

I

J

K

L

M

Excavate

Lay Foundation

Rough Plumbing

Frame

Finish Exterior

HVAC

Rough Electric

Sheet Rock

Paint

Final Plumbing

Final Electric

InstallFlooring

A 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.

An Activity-on-Arc (AOA) Network

1 2 3

4

5

6

7

8 9

10

11

12 13

Excavate

Lay Foundation

Rough Plumbing

Frame Finish Exterior

HVAC

Rough Electric

Sheet Rock

Paint

Install Cabinets

Final Plumbing

Final Electric

Install Flooring

A

B C

D

G

F

E

H

I

J

K

L

M

Start and Finish Points

AON networks should have unique start and finish points.

A

B

C

D

E

A

B

C

D

E

start finish

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

i ti

ESTi EFTi

LSTi LFTi

ti = time required to perform activity iESTi = earliest possible start time for activity iEFTi = earliest possible finish time for activity iLSTi = latest possible start time for activity iLFTi = 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.

Results of the Forward Pass

H25 33

8

E17 25

8

J33 38

5

I33 38

5 K38 42

4

L38 40

2

M42 46

4A 0 3

3

F17 21

4

G17 23

6

D7 17

10

C7 10

3

B3 7

4

Note: 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.

Results of the Backward Pass

Note: LFTH=MIN(LSTI,LSTJ)=33LFTD=MIN(LSTE,LSTF ,LSTG)=17LFTB=MIN(LSTC,LSTD)=7

H25 33

8

E17 25

8

J33 38

5

I33 38

5 K38 42

4

L38 40

2

M42 46

4A 0 3

3

F17 21

4

G17 23

6

D 7 17

10

C 7 10

3

B 3 7

40 3 3 7

22 25

17 7

17 25

21 25

2519

25 33

33 38

35 40

42

4240

42 46

38

The Critical Path

Note:

Slack = LSTi-ESTi or LFTi-EFTi

H25 33

8

E17 25

8

J33 38

5

I33 38

5 K38 42

4

L38 40

2

M42 46

4A 0 3

3

F17 21

4

G17 23

6

D 7 17

10

C 7 10

3

B 3 7

40 3 3 7

22 25

17 7

17 25

21 25

2519

25 33

33 38

35 40

42

4240

42 46

38

Slack=0 Slack=0

Slack=0

Slack=15

Slack=0

Slack=4

Slack=2

Slack=0

Slack=0 Slack=0

Slack=2 Slack=2

Slack=0

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

0 5 10 15 20 25 30 35 40 45 50

ABCDEFGHI

JKLM

Activity

Time Period

Activity Time

Slack

A Gantt Chart for the Example Problem

PERT: An Overview

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 then estimates expected duration ti and variance vi of each activity’s duration as:

ta m b

ii i i 4

6

vb a

ii i( )2

36

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...