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Transcript of Critical Path Analysis. There are no pre-requisites for this Achievement Standard so it can be...
Critical Path Analysis
There are no pre-requisites for this Achievement Standard so it can be placed in any course.No knowledge is pre-supposed.
Methods include a selection from those related to:
precedence tablesnetwork diagramscritical eventsschedulingfloat times
Critical Path Analysis (CPA)
A complex project must be well planned, especially if a number of people are involved.
CPA is used to ensure that the complete scheme is completed in the minimum time.
It is used to schedule the projects.
Any activity can be represented as a project:planning a partybuilding a house/factoryplanning a conference
So what is a project?
What do the projects have in common?
Each project can be broken down into tasks.Each task takes time and uses resources.Tasks are structured
Step 1 – Precedence table
• To identify actual tasks that make up a project• To identify the order these tasks need to be in• To decide how long each task will take
Example: Constructing a garageTask Duration (days)
A prepare foundations 7B Make and position door frame 2C Lay drains, floor base and screed 15D Install services and fittings 8E Erect walls 10F Plaster ceiling 2G Erect roof 5H Install door and windows 8I Fit gutters and pipes 2J Paint outside 3
Some of these activities must be completed before others can start.
Task Duration (days)A prepare foundations 7B Make and position door frame 2C Lay drains, floor base and screed 15D Install services and fittings 8E Erect walls 10F Plaster ceiling 2G Erect roof 5H Install door and windows 8I Fit gutters and pipes 2J Paint outside 3
You can’t erect the roof (G) before you have erected the walls (E)
Task Duration (days)A prepare foundations 7B Make and position door frame 2C Lay drains, floor base and screed 15D Install services and fittings 8E Erect walls 10F Plaster ceiling 2G Erect roof 5H Install door and windows 8I Fit gutters and pipes 2J Paint outside 3
Precedence
D must follow E
Task Duration (days)
A prepare foundations 7B Make and position door frame 2C Lay drains, floor base and screed 15D Install services and fittings 8 EE Erect walls 10F Plaster ceiling 2G Erect roof 5H Install door and windows 8I Fit gutters and pipes 2J Paint outside 3
E must follow A and B
Task Duration (days)
A prepare foundations 7B Make and position door frame 2C Lay drains, floor base and screed 15D Install services and fittings 8 EE Erect walls 10 A, BF Plaster ceiling 2G Erect roof 5H Install door and windows 8I Fit gutters and pipes 2J Paint outside 3
F must follow D and G
Task Duration (days)
A prepare foundations 7B Make and position door frame 2C Lay drains, floor base and screed 15D Install services and fittings 8 EE Erect walls 10 A, BF Plaster ceiling 2 D, GG Erect roof 5H Install door and windows 8I Fit gutters and pipes 2J Paint outside 3
G must follow E
Task Duration (days)
A prepare foundations 7B Make and position door frame 2C Lay drains, floor base and screed 15D Install services and fittings 8 EE Erect walls 10 A, BF Plaster ceiling 2 D, GG Erect roof 5 EH Install door and windows 8I Fit gutters and pipes 2J Paint outside 3
H must follow G
Task Duration (days)
A prepare foundations 7B Make and position door frame 2C Lay drains, floor base and screed 15D Install services and fittings 8 EE Erect walls 10 A, BF Plaster ceiling 2 D, GG Erect roof 5 EH Install door and windows 8 GI Fit gutters and pipes 2J Paint outside 3
I must follow C, F
Task Duration (days)
A prepare foundations 7B Make and position door frame 2C Lay drains, floor base and screed 15D Install services and fittings 8 EE Erect walls 10 A, BF Plaster ceiling 2 D, GG Erect roof 5 EH Install door and windows 8 GI Fit gutters and pipes 2 C, FJ Paint outside 3
J must follow H and I
Task Duration (days)
A prepare foundations 7B Make and position door frame 2C Lay drains, floor base and screed 15D Install services and fittings 8 EE Erect walls 10 A, BF Plaster ceiling 2 D, GG Erect roof 5 EH Install door and windows 8 GI Fit gutters and pipes 2 C, FJ Paint outside 3 I
We call this a precedence table
Task Duration (days)
Precedence
A prepare foundations 7B Make and position door frame 2C Lay drains, floor base and screed 15D Install services and fittings 8 EE Erect walls 10 A, BF Plaster ceiling 2 D, GG Erect roof 5 EH Install door and windows 8 GI Fit gutters and pipes 2 C, FJ Paint outside 3 I
• Precedence diagrams are not that useful.
• A useful visual representation of a project is a network diagram.
Sequencethe most common sequences / dependencies
Task A Task B
Task ATask B
Task C
Task C
Task B
Task A
Task B depends upon Task A; B cannot start until A is finished
Task C depends upon Task A and B; C cannot start until both A and B are finished
Tasks B and C depend on Task A; neither can start until A is finished, but B and C are independent of each other
more unusual links and relationships
so far all links have been finish-start links...
Task A Task B
Task A
Task C
Task C
Task A
Task B depends upon Task A, but with a 3 day delay; B cannot start until 3 days after A is finished
The finish of Task C depends upon the finish of Task A
The start of Task C depends on the start of Task A; this is a start-to-start link; it may also incorporate a delay
3 days
Drawing a NETWORK – how do we get here?
Algorithm
Draw in the links Task Precedence
ABCD EE A, BF D, GG EH GI C, FJ I
Draw in A, B, C on a rough diagram
STEP 1- original vertices with no arcsSTEP 2 - delete all arcs incident on A, B, C and redraw as shownSTEP 3 - repeat iteration
STEP 1- original vertices with no arcsSTEP 2 - delete all arcs incident on E and redraw as shownSTEP 3 - repeat iteration
STEP 1- original vertices with no arcsSTEP 2 - delete all arcs incident on D, G and redraw as shownSTEP 3 - repeat iteration
STEP 1- original vertices with no arcsSTEP 2 - delete all arcs incident on F and H and redraw as shownSTEP 3 - repeat iteration
STEP 1- original vertices with no arcsSTEP 2 - delete all arcs incident on I and redraw as shownSTEP 3 - STOP
Converting to a usable diagram
Proposed method
Now draw the network diagram using boxes
task number and/or name
durationearly starttime
late starttime
early finishtime
late finishtimefloat
slack
Example
Task A
7
Task B
2
Task C
15
Task E
10
Task D
8
Task G
5
Task F
2
Task H
8
Task I
2
Task J
3
Finish
Duration
Critical Path
• Find the earliest possible start for each activity, by going forwards through the network.
• Secondly, the latest possible start time for each activity is found by going backwards through the network.
• Activities which have equal earliest and latest start time are on the critical path.
Practice 1
Task 062
Task 01
3Task 04
6
Task 03
3
Task 08
2
Task 02
4
Task 09
1Task 05
3Task 07
5
Practice 1
Task 062
Task 01
30Task 04
6
Task 03
3
Task 08
2
Task 02
4
Task 09
1Task 05
3Task 07
5
Practice 1
Task 062
Task 01
3 30Task 04
6
Task 03
3
Task 08
2
Task 02
4
Task 09
1Task 05
3Task 07
5
Practice 1
Task 062
Task 01
3 30Task 04
63
Task 03
3
Task 08
2
Task 02
43
Task 09
1Task 05
3Task 07
5
3
Practice 1
Task 062
Task 01
3 30Task 04
63 9
Task 03
3
Task 08
2
Task 02
43 7
Task 09
1Task 05
3Task 07
5
3 5
Practice 1
Task 062
Task 01
3 30Task 04
63 9
Task 03
37
Task 08
25
Task 02
43 7
Task 09
1Task 05
39Task 07
5
3 5
Practice 1
Task 062
Task 01
3 30Task 04
63 9
Task 03
3 107
Task 08
2 75
Task 02
43 7
Task 09
1Task 05
39 12Task 07
5
3 5
Practice 1
Task 062
Task 01
3 30Task 04
63 9
Task 03
3 107
Task 08
2 75
Task 02
43 7
Task 09
1Task 05
39 12Task 07
512
3 5
Take the largest value
Practice 1
Task 062
Task 01
3 30Task 04
63 9
Task 03
3 107
Task 08
2 75
Task 02
43 7
Task 09
1Task 05
39 12Task 07
512 17
3 5
Practice 1
Task 062
Task 01
3 30Task 04
63 9
Task 03
3 107
Task 08
2 75
Task 02
43 7
Task 09
1Task 05
39 12Task 07
512 17
3 5
Take the largest value
Forward pass complete
Duration = 18
Task 062
Task 01
3 30
3
Task 04
63 9
Task 03
3 107
5Task 08
2 75
Task 02
43 7
Task 09
1 1817Task 05
39 12Task 07
512 17
Backward pass
Task 062
Task 01
3 30
3
Task 04
63 9
Task 03
3 107
5Task 08
2 75
Task 02
43 7
Task 09
1 1817Task 05
39 12Task 07
512 17
18
Task 062
Task 01
3 30
3
Task 04
63 9
Task 03
3 107
5Task 08
2 75
Task 02
43 7
Task 09
1 1817Task 05
39 12Task 07
512 17
1817 0
Float
Task 062
Task 01
3 30
3
Task 04
63 9
Task 03
3 107
5Task 08
2 75
Task 02
43 7
Task 09
1 1817Task 05
39 12Task 07
512 17
1817 0
17
17
Task 062
Task 01
3 30
3
Task 04
63 9
Task 03
3 107
5Task 08
2 75
Task 02
43 7
Task 09
1 1817Task 05
39 12Task 07
512 17
1817 0
17
17
12
15
0
10
Task 062
Task 01
3 30
3
Task 04
63 9
Task 03
3 107
5Task 08
2 75
Task 02
43 7
Task 09
1 1817Task 05
39 12Task 07
512 17
1817 0
17
17
12
15
0
10
12
12
9
9 0
2
1513 10
9
93 0
5 2
Forward pass complete
Task 062
Task 01
3 30
3
Task 04
63 9
Task 03
3 107
5Task 08
2 75
Task 02
43 7
Task 09
1 1817Task 05
39 12Task 07
512 17
1817 0
17
17
12
15
0
10
12
12
9
9 0
2
1513 10
9
93 0
5 2
Take the smallest
Critical Path – float = 0
Task 0623 5
13 1510
Task 09
1 1817
1817 0
Task 07
512 17
1712 0Task 05
39 12
129 0
Task 04
63 9
93 0
Task 01
3 30
30 0
Task 08
2 75
1715 10
Task 03
3 107
129 2
Task 02
43 7
95 2
Your turn
Task A
7
Task B
2
Task C
15
Task E
10
Task D
8
Task G
5
Task F
2
Task H
8
Task I
2
Task J
3
Finish
Example 1 – Forward pass
Task A
70
Task B
20
Task C
150
Task E
10
Task D
8
Task G
5
Task F
2
Task H
8
Task I
2
Task J
3
Finish
Example 1 – Forward pass
Task A
7 70
Task B
2 20
Task C
15 150
Task E
10
Task D
8
Task G
5
Task F
2
Task H
8
Task I
2
Task J
3
Finish
Example 1 – Take the largest value
Task A
7 70
Task B
2 20
Task C
15 150
Task E
107
Task D
8
Task G
5
Task F
2
Task H
8
Task I
2?
Task J
3
Finish
Example 1 – Take the largest value
Task A
7 70
Task B
2 20
Task C
15 150
Task E
10 177
Task D
817
Task G
517
Task F
2
Task H
8
Task I
2?
Task J
3
Finish
Example 1 – Take the largest value
Task A
7 70
Task B
2 20
Task C
15 150
Task E
10 177
Task D
8 2517
Task G
5 2217
Task F
2
Task H
8
Task I
2?
Task J
3
Finish
Example 1 – Take the largest value
Task A
7 70
Task B
2 20
Task C
15 150
Task E
10 177
Task D
8 2517
Task G
5 2217
Task F
225
Task H
822
Task I
2?
Task J
3
Finish
Example 1 – Minimum 32
Task A
7 70
Task B
2 20
Task C
15 150
Task E
10 177
Task D
8 2517
Task G
5 2217
Task F
2 2725
Task H
8 3022
Task I
2 2927
Task J
3 3229
Finish32
Example 1 – Backward pass
Task A
7 70
Task B
2 20
Task C
15 150
Task E
10 177
Task D
8 2517
Task G
5 2217
Task F
2 2725
Task H
8 3022
Task I
2 2927
Task J
3 3229
Finish32
32
Example 1 – Take lowest value
Task A
7 70
Task B
2 20
Task C
15 150
Task E
10 177
Task D
8 2517
Task G
5 2217
Task F
2 2725
Task H
8 3022
Task I
2 2927
Task J
3 3229
Finish32
32
32
32
29 0
24 2
Example 1 – Take lowest value
Task A
7 70
Task B
2 20
Task C
15 150
Task E
10 177
Task D
8 2517
Task G
5 2217
Task F
2 2725
Task H
8 3022
Task I
2 2927
Task J
3 3229
Finish32
32
32
32
29 0
24 2
2927 0
Example 1 – Take lowest value
Task A
7 70
Task B
2 20
Task C
15 150
Task E
10 177
Task D
8 2517
Task G
5 2217
Task F
2 2725
Task H
8 3022
Task I
2 2927
Task J
3 3229
Finish32
32
32
32
29 0
24 2
2927 0
2725 0
Example 1 – Take lowest value
Task A
7 70
Task B
2 20
Task C
15 150
Task E
10 177
Task D
8 2517
Task G
5 2217
Task F
2 2725
Task H
8 3022
Task I
2 2927
Task J
3 3229
Finish32
32
32
32
29 0
24 2
2927 0
2725 02517 0
2419 2
Example 1 – Take lowest value
Task A
7 70
Task B
2 20
Task C
15 150
Task E
10 177
Task D
8 2517
Task G
5 2217
Task F
2 2725
Task H
8 3022
Task I
2 2927
Task J
3 3229
Finish32
32
32
32
29 0
24 2
2927 0
2725 02517 0
2419 2
177 0
Example 1 – Take lowest value
Task A
7 70
Task B
2 20
Task C
15 150
Task E
10 177
Task D
8 2517
Task G
5 2217
Task F
2 2725
Task H
8 3022
Task I
2 2927
Task J
3 3229
Finish32
32
32
32
29 0
24 2
2927 0
2725 02517 0
2419 2
177 0
2712 12
70 0
7 5 5
Example 1 – Critical Path – zero float
Task A
7 70
Task B
2 20
Task C
15 150
Task E
10 177
Task D
8 2517
Task G
5 2217
Task F
2 2725
Task H
8 3022
Task I
2 2927
Task J
3 3229
Finish32
32
32
32
29 0
24 2
2927 0
2725 02517 0
2419 2
177 0
2712 12
70 0
7 5 5
Example 1 – Critical Path – A-E-D-F-I-J
Task A
7 70
Task B
2 20
Task C
15 150
Task E
10 177
Task D
8 2517
Task G
5 2217
Task F
2 2725
Task H
8 3022
Task I
2 2927
Task J
3 3229
Finish32
32
32
32
29 0
24 2
2927 0
2725 02517 0
2419 2
177 0
2712 12
70 0
7 5 5
Using the outputs• Gantt Charts• optimising the schedule
Gantt: Critical path in red
Gantt: Critical path in red
Scheduling: Move the critical path along the top
Now fit the other activities like a puzzle
Now fit the other activities like a puzzle
Schedule
Any delay on the critical path causes a delay in the entire project
There is a 2-day float on the non-critical path
Definitions
• Critical Path Those activities that can not over run without effecting the total length of the project, are those where the EST = LFT (Total float = 0).
• Total Float LFT of the activity- the duration- EST of the activity. This shows how much ´slack´ there is on a particular route of the network. If the total float is 0 then an activity lies on the critical path.
• Free Float EST of the next activity – Duration – EST of this activity. This shows the ´slack´ on an individual activity before it delays the start of the next activity.
• EES = Earliest early start time• LLF = latest late finish timeFree float: The amount of time that a schedule activity can be delayed without delaying the early start date of any immediately following schedule activities.
Free Float = EESsuccessor – EF
• EES = Earliest early start time• LLF = latest late finish timeIndependent float is that portion of the total float within which an activity can be delayed for start without affecting the float of the preceding activities.
Independent Float = EESsuccessor-LLFpredecessor-duration
