2. A Brief Overview ..
Operating System Structure
• The critical path method (CPM) is an algorithm for scheduling
a set of project activities
• Developed in the late 1950s
• By Morgan R. Walker and James E. Kelley
• The US Navy adapted and improved it to manage the Polaris
missile project in the late 1950's
3. Where is it used ?
Operating System Structure
Software Development
Construction
Projects Aerospace and Defence
Research Projects
Product Development
And more …
4. Where is it used ?
Operating System Structure
Software Development
Construction
Projects Aerospace and Defence
Research Projects
Product Development
NASA used the critical path method in 1969 to help determine an efficient schedule
for the tasks that led to the first moon landing. And more …
5. Example : Redesign of a Product
Operating System Structure
Activity Description Predecessor Duration
(weeks)
A Redesign Product - 6
B Redesign Packaging - 2
C Order / Receive components for redesigned product A 3
D Order / Receive components for redesigned packaging B 2
E Assemble products C 4
F Make up packaging D 1
G Package the product E,F 1
H Test market the packaged product G 6
I Revise redesigned product H 3
J Revise redesigned packaging H 1
K Prepare report I,J 1
6. Step 1 – Identify Paths
Operating System Structure
Activity Predecessor Duration
(weeks)
A - 6
B - 2
C A 3
D B 2
E C 4
F D 1
G E,F 1
H G 6
I H 3
J H 1
K I,J 1
7. Step 1 – Identify Paths
Operating System Structure
Activity Predecessor Duration
(weeks)
A - 6
B - 2
C A 3
D B 2
A-C-E-G-H-I-K
E C 4 A-C-E-G-H-J-K
F D 1 B-D-F-G-H-I-K
G E,F 1 B-D-F-G-H-J-K
H G 6
I H 3
J H 1
K I,J 1
8. Step 2 – Network Diagram
Operating System Structure
C
2 5 9
A E J
(Dummy)
G H
1 6 7 8 11
B F I K
3 4 10
D
9. Step 2 – Network Diagram
Operating System Structure
C
2 5 9
A E J
G H
1 6 7 8 11
B F I K
3 4 10
D
Nodes Activities
12. Step 2 – Network Diagram
Operating System Structure
2 5 9
1 6 7 8 11
3 4 10
Merge Event
Where 2 or more activities merge
13. Step 2 – Network Diagram
Operating System Structure
2 5 9
1 6 7 8 11
3 4 10
Burst Event
Where 2 or more activities start
14. Operating System Structure
Step 3 – Calculate Start and End Times
Earliest start time (EST) - The earliest time an activity can start once the
previous dependent activities are over.
Earliest finish time (EFT) – Earliest Start Time (EST) + Activity Duration
Latest finish time (LFT) - The latest time an activity can finish without
delaying the project.
Latest start time (LST) – Latest Finish Time (LFT) - Activity Duration
15. Operating System Structure
Step 3 – Calculate Start and End Times
C [6,9]
2 5 9
G [13,14] H [14,20]
1 6 7 8 11
D [2,4]
3 4 10
Forward Pass
16. Operating System Structure
Step 3 – Calculate Start and End Times
C [6,9] EST EFT
2 5 9
G [13,14] H [14,20]
1 6 7 8 11
D [2,4]
3 4 10
Forward Pass
17. Operating System Structure
Step 3 – Calculate Start and End Times
C [6,9]
2 5 9
G [13,14] H [14,20]
1 6 7 8 11
D [2,4]
3 4 10
Total Project Duration : 24 weeks
18. Operating System Structure
Step 3 – Calculate Start and End Times
C [6,9]
2 5 9
[6,9]
G [13,14] H [14,20]
1 6 7 8 11
[13,14] [14,20]
D [2,4]
3 4 10
[10,12]
Backward Pass
19. Operating System Structure
Step 3 – Calculate Start and End Times
C [6,9] EST EFT
2 5 9
[6,9]
G [13,14] H [14,20]
1 6 7 8 11
[13,14] [14,20]
D [2,4]
3 4 10
[10,12]
LST LFT
Backward Pass
20. Operating System Structure
Step 4 – Find Critical Activities
C [6,9]
2 5 9
[6,9]
G [13,14] H [14,20]
1 6 7 8 11
[13,14] [14,20]
D [2,4]
3 4 10
[10,12]
Critical Activities – Those activities where EST=LST or EFT=LFT
Hence, Critical Activities are – A, C, E, G, H, I, K
21. OperatingFind Critical Path
Step 5 – System Structure
C [6,9]
2 5 9
[6,9]
G [13,14] H [14,20]
1 6 7 8 11
[13,14] [14,20]
D [2,4]
3 4 10
[10,12]
Critical Path : A-C-E-G-H-I-K
22. OperatingFind Critical Path
Step 5 – System Structure
C [6,9]
2 5 9
[6,9]
G [13,14] H [14,20]
1 6 7 8 11
[13,14] [14,20]
D [2,4]
3 4 10
[10,12]
Critical Pathany activity present in the critical path causes delay to the project
A delay in : A-C-E-G-H-I-K
23. Operating System Structure
Summary
Total Project Duration : 24 weeks
Critical Activities : A, C, E, G, H, I, K
Non Critical Activities : B, D, F, J
Critical Path : A-C-E-G-H-I-K
24. Operating System Structure
Float / Slack
Total Float : The total time that a schedule activity may be delayed
Total Float = ( LFT – EFT ) or ( LST-EST)
Free Float : Free Float is the time by which the completion of an activity can
be delayed beyond the EFT without affecting the EST of succeeding activity
Free Float = EST (succeeding) – EFT (present)
Interfering Float : Part of total float that causes reduction in the total float
of successor activity
Interfering Float = LFT (present) – EST (succeeding)
Independent Float : Amount of float that can be used without affecting
either of the succeeding or preceding activity
Independent Float = EST (succeeding) – LFT (preceding) – Duration (present)
25. Activity
Operating System StructureFloat
Total Float Free Float Interfering
Float
Independent
A 0 0 0 0
B 8 0 8 0
C 0 0 0 0
D 8 0 8 0
E 0 0 0 0
F 8 8 0 0
G 0 0 0 0
H 0 0 0 0
I 0 0 0 0
J 2 2 0 2
K 0 0 0 0
* Note that float of all the critical activities = 0
