Relationshipsbetween Activities

• A project is a sequence of activities.– Large projects have interrelated sequences.

• These are called Precedent activities– They must be defined before the project

begins.

Step 2 Develop a Network Model

• A Network Diagram visually displays the interrelated activities using nodes (circles) and arcs (arrows) that depict the relationships between activities.

• It is a graphical diagram.• Two types of Graphical Network Models

– Activity On Arc (AOA)– Activity On Node (AON) (We will use AON)

Two Types of Network Models

Activity-on-Arc (AOA)

Activity-on-Node (AON)

Activity Activity

Link

We will use this!D E

Time Time

Activity E

Time

Activity D

What AON Nodes look like.

Early Start

Early Finish

Late Finish

Late Start

Activity

Activity Duration

Slack

The earliest you can complete an activity--determined by adding the activity time (duration) to the early start time.

This is the latest you can finish an activity without delaying project completion. It is the same as the Late Start time of the next activity. If there are two or more subsequent activities, this time is the same as the earliest of those “Late Start” times.

The is the earliest you can start an activity. It is determined by the early finish time of the precedent activity. If there are two or more precedent activities, this time is the same as precedent activity with the latest “Early Finish” time.

This is the Late-Finish time minus the activity duration.

Slack (S) is the difference, if any, between the early start (ES) and late start times (LS) or the early finish (EF) and late finish (EF) times.

S = LS - ES or S = LF - EF

© 2011 Lew Hofmann

Precedent Relationships

Precedent relationships determine a sequence for accomplishing activities. They specify that any given activity cannot start until its preceding activity or activities have been completed.

In our AON approach, the nodes (circles) represent activities, and the arcs represent the sequential relationships between them.

AON

S T U

Activity On Node approach

“S” precedes “T” which precedes “U”

Nodes are simplified in the following examples.

Activity Relationships

T

U

S

T & U cannot begin until S has been completed.

S

T

U

S & T must be completed before U can be started.

Activity Relationships

S

T

U

V

U & V can’t begin until S & T have been completed.

S

T

U

V

U cannot begin until S & T have been completed. V cannot begin until T has been completed.

Activity Relationships

S T V

U

T & U cannot begin until S has been completed; V cannot begin until both T & U have been completed.

A Select administrative and medical staff. — JohnsonB Select site and do site survey. — TaylorC Select equipment. A AdamsD Prepare final construction plans & layout. B TaylorE Bring utilities to the site. B BurtonF Interview applicants and fill positions in A Johnson

nursing, support staff, maintenance, and security.

G Purchase and take delivery of equipment. C AdamsH Construct the hospital. D TaylorI Develop an information system. A SimmonsJ Install the equipment. E,G,H AdamsK Train nurses and support staff. F,I,J Johnson

St. Adolf’s Hospital(A sample project)

ImmediateActivity Description Predecessor(s) *Responsibility

*We won’t be using the “Responsibility” data, but it is important in project management.

St. Adolf’s HospitalDiagramming the Network

FinishStart

A

B

C

D

E

F

G

H

I

J

K

Immediate Predecessors

A – 12

B – 9

C A 10

D B 10

E B 24

F A 10

G C 35

H D 40

I A 15

J E,G,H 4

K F,I,J 6

Activity Times (wks)

St. Adolf’s Hospital

FinishStart

A

B

C

D

E

F

G

H

I

J

K

Path Time (wks)

A-I-K33A-F-K28A-C-G-J-K 67B-D-H-J-K 69B-E-J-K 43

Paths are sequences of activities between a project’s start and finish.

St. Adolf’s Hospital

FinishStart

A

B

C

D

E

F

G

H

I

J

KPath Time (wks)

A-I-K33A-F-K28A-C-G-J-K 67B-D-H-J-K 69B-E-J-K 43

Project Expected Time is 69 wks.

The longest path is the critical path!

3. Develop the schedule

• Now we insert the time estimates.– This is where we distinguish between PERT & CPM.

• CPM is used when activity times are Certain.• It is Decision making under Certainty

• You are certain of the time each activity will require to complete.

• PERT is used when activity times are not certain. (Decision making under risk)

Using PERT

• PERT is used when activity times are uncertain.– Decision making under risk (“P” for probabilistic)– Three time estimates are required for each activity.

• OPTIMISTIC TIME: Best time if everything goes perfectly• REALISTIC TIME: Most likely time• PESSIMISTIC TIME: A worst-case situation

B + 4M + PExpected Time = -------------------

6

In this example, the most likely time is given a weight of 4, and the other two times (pessimistic and optimistic) are each given weights of 1. Software allows you to change these as needed, but the denominator must be the total of the weights given.

• Earliest Start Time (ES) for an activity is the earliest finish time of the immediately preceding activity.

• Earliest Finish Time (EF) for an activity is its earliest start time plus how long it takes to do it (estimated duration).

• Latest Start Time (LS) is the latest you can finish the activity minus the activity’s estimated duration.

• Latest Finish Time (LF) is the latest start time of the activity that immediately follows it. (Latest start and finish times for each activity are computed starting at the project’s last activity completion time and working forward.)

St. Adolf’s HospitalDeveloping the schedule

Earliest Start and Earliest Finish Times

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

I

15

FinishStart

A

12

F

10

0

Earliest start time

12

Earliest finish time

0 9

9 33

9 19 19 59

22 5712 22

59 63

12 27

12 22 63 69

© 2012 Lew Hofmann

Earliest Start and Earliest Finish Times

Critical Path

The Critical Path takes 69 weeks

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

I

15

FinishStart

A

12

F

10

0 9

9 33

9 19 19 59

22 5712 22

59 63

12 27

12 22 63 690 12

Path Time (wks)

A-I-K33A-F-K28A-C-G-J-K 67B-D-H-J-K 69B-E-J-K 43

© 2012 Lew Hofmann

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

I

15

FinishStart

A

12

F

10

0 9

9 33

9 19 19 59

22 5712 22

59 63

12 27

12 22 63 690 12

Latest Start and Latest Finish Times(Working from the last activity toward the first activity)

48 63

53 63

59 63

24 59

19 59

35 59

14 24

9 19

2 14

0 9

Latestfinishtime

63 69Lateststarttime

© 2012 Lew Hofmann

Activity Slack Analysis

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

I

15

FinishStart

A

12

F

10

0 9

9 33

9 19 19 59

22 5712 22

59 63

12 27

12 22 63 690 12

48 63

53 63

59 63

24 59

19 59

35 59

14 24

9 19

2 14

0 9

63 69

Slack is the difference between LS and ES or the EF and LF.

Node Duration ES LS Slack

A 12 0 2 2

B 9 0 0 0

C 10 12 14 2

D 10 9 9 0

E 24 9 35 26

F 10 12 53 41

G 35 22 24 2

H 40 19 19 0

I 15 12 48 36

J 4 59 59 0

K 6 63 63 0

© 2012 Lew Hofmann

Sample GanttChart Printout