DEVELOPMENT OF THE NETWORK DIAGRAM AND

CRITICAL PATHAcknowledgement - A

Practical Introduction to Management Science

4th edition

BUILDING A HOUSE

2

THE NETWORK DIAGRAM IS

ABOUT CREATING

RELATIONSHIPSBETWEEN

ACTIVITIES

THE NETWORK DIAGRAM IS

ABOUT CREATING

RELATIONSHIPSBETWEEN

ACTIVITIES

BUILDING A HOUSE

3

RELATIONSHIPS ARE ALSO

REFERRED TO AS DEPENDENCIES – THE MOST BASIC

IS “FINISH TO START”

RELATIONSHIPS ARE ALSO

REFERRED TO AS DEPENDENCIES – THE MOST BASIC

IS “FINISH TO START”

BUILDING A HOUSE

4

THUS THE BASIC QUESTION IS

WHICH ACTIVITIES MUST

BE FINISHED BEFORE WHICH ACTIVITIES CAN

START

THUS THE BASIC QUESTION IS

WHICH ACTIVITIES MUST

BE FINISHED BEFORE WHICH ACTIVITIES CAN

START

BUILDING A HOUSE

5

THE USE OF AN ARROW

(SPECIFICALLY IN THE NOTATION USED IN THIS

EXAMPLE) SHOWS THIS

RELATIONSHIP

THE USE OF AN ARROW

(SPECIFICALLY IN THE NOTATION USED IN THIS

EXAMPLE) SHOWS THIS

RELATIONSHIP

A B

Activity A Must Be Finished Before B Can Start

BUILDING A HOUSE

6

THE USE OF AN ARROW

(SPECIFICALLY IN THE NOTATION USED IN THIS

EXAMPLE) SHOWS THIS

RELATIONSHIP

THE USE OF AN ARROW

(SPECIFICALLY IN THE NOTATION USED IN THIS

EXAMPLE) SHOWS THIS

RELATIONSHIP

But Activity E, F and G Don’t Have to Wait for Each Other

D

E

F

G

FrameHVAC

Rough Electric

H

Sheet Rock

BUILDING A HOUSE

7

THE USE OF AN ARROW

(SPECIFICALLY IN THE NOTATION USED IN THIS

EXAMPLE) SHOWS THIS

RELATIONSHIP

THE USE OF AN ARROW

(SPECIFICALLY IN THE NOTATION USED IN THIS

EXAMPLE) SHOWS THIS

RELATIONSHIP

Note That E, F and G Don’t Have to Start and Finish At The Same Time

D

E

F

G

FrameHVAC

Rough Electric

H

Sheet Rock

BUILDING A HOUSE

8

THE USE OF AN ARROW

(SPECIFICALLY IN THE NOTATION USED IN THIS

EXAMPLE) SHOWS THIS

RELATIONSHIP

THE USE OF AN ARROW

(SPECIFICALLY IN THE NOTATION USED IN THIS

EXAMPLE) SHOWS THIS

RELATIONSHIP

TheY However Need to Be Finished Before H Can Start

D

E

F

G

FrameHVAC

Rough Electric

H

Sheet Rock

Task 1 Is to Create These Dependencies By Indicating the Predecessors For Each Activity

SUMMARY OF ACTIVITIES

10

Time ImmediateRequiredPredecessor

Activity Description (in days) ActivitiesA ExcavateB Lay foundationC Rough plumbingD FrameE Finish exteriorF Install HVACG Rough electricH Sheet rockI Install cabinetsJ PaintK Final plumbingL Final electricM Install flooring

SUMMARY OF ACTIVITIES

11

Time ImmediateRequiredPredecessor

Activity Description (in days) ActivitiesA Excavate --B Lay foundation AC Rough plumbing BD Frame BE Finish exterior DF Install HVAC DG Rough electric DH Sheet rock C, E, F, GI Install cabinets HJ Paint HK Final plumbing IL Final electric JM Install flooring K, L

Task 2 TEST THE LOGIC BY

CONSTRUCTING THE NETWORK DIAGRAM

An Activity-On-Node (AON) Network

13

Install 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

Basic Rules for Constructing the Network Diagram

•Networks typically flow from left to right;•An activity cannot begin until all of its

preceding activities are complete;•Arrows indicate precedence and flow and

can cross over each other;• Identify each activity with a unique

number; this number must be greater than its predecessors;

•Looping is not allowed;•Conditional statements are not allowed;•Use unique start and stop nodes.

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Task 3 DETERMINE DURATIONS FOR

EACH ACTIVITY

SUMMARY OF ACTIVITIES

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Time ImmediateRequiredPredecessor

Activity Description (in days) ActivitiesA 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

Task 4FILL EACH NODE AS FOLLOWS

Information Recorded for Each Node

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i ti

ESTi EFTi

LSTi LFTi

ti = DURATION required to perform activity iESTi = earliest possible start for activity i

EFTi = earliest possible finish for activity iLSTi = latest possible start for activity i

LFTi = latest possible finish for activity i

Task 5CALCULATE THE FORWARD AND

THE BACKWARD PASS

•A Forward Pass through the network determines the earliest times each activity can start and finish – ALSO DETERMINE THE TOTAL DURATION OF THE PROJECT

•A Backward Pass through the network determines the latest times each activity can start and finish without delaying completion of the project – WITH THIS INFORMATION WE CAN DETERMINE WHERE WE CAN DELAY ACTIVITIES (HAVE SLACK) AND WHERE WE CANNOT

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21

The Forward Pass

•The earliest start (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 of the activities directly preceding it;

•The EFT of an activity is equal to its EST plus the duration required to perform the activity.

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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 (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.

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Results of the Backward Pass

24

Note: LFTH=MIN(LSTI,LSTJ)=33

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

LFTB=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

3

Task 6DETERMINE THE CRITICAL PATH

Determining The Critical Path

• Critical activities have zero slack and cannot be delayed without delaying the completion of the project;

• The slack for non-critical activities represents the amount of time by which the start of these activities can be delayed without delaying the completion of the entire project (assuming that all predecessor activities start at their earliest start times);

• The longest path on the network;• Could also be those activities with the least

slack.

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The Critical Path

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Note:

Slack = LSTi-ESTi and 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

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