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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.
14
Task 3 DETERMINE DURATIONS FOR
EACH ACTIVITY
SUMMARY OF ACTIVITIES
16
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
18
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
20
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.
22
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.
23
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.
26
The Critical Path
27
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
28