Critical Path Analysis
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1 Critical Path Analysis
2 There are no pre-requisites for this Achievement Standard so it can be placed in any course. No knowledge is pre-supposed.
3 Methods include a selection from those related to: precedence tables network diagrams critical events scheduling float times
4 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.
5 So what is a project? Any activity can be represented as a project: planning a party building a house/factory planning a conference
6 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
7 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
8 Example: Constructing a garage Task Duration (days) A prepare foundations 7 B Make and position door frame C Lay drains, floor base and screed 15 D Install services and fittings 8 E Erect walls 1 F Plaster ceiling G Erect roof 5 H Install door and windows 8 I Fit gutters and pipes J Paint outside 3
9 Some of these activities must be completed before others can start. Task Duration (days) A prepare foundations 7 B Make and position door frame C Lay drains, floor base and screed 15 D Install services and fittings 8 E Erect walls 1 F Plaster ceiling G Erect roof 5 H Install door and windows 8 I Fit gutters and pipes J Paint outside 3
10 You can t erect the roof (G) before you have erected the walls (E) Task Duration (days) A prepare foundations 7 B Make and position door frame C Lay drains, floor base and screed 15 D Install services and fittings 8 E Erect walls 1 F Plaster ceiling G Erect roof 5 H Install door and windows 8 I Fit gutters and pipes J Paint outside 3
11 Precedence
12 D must follow E Task Duration (days) A prepare foundations 7 B Make and position door frame C Lay drains, floor base and screed 15 D Install services and fittings 8 E E Erect walls 1 F Plaster ceiling G Erect roof 5 H Install door and windows 8 I Fit gutters and pipes J Paint outside 3
13 E must follow A and B Task Duration (days) A prepare foundations 7 B Make and position door frame C Lay drains, floor base and screed 15 D Install services and fittings 8 E E Erect walls 1 A, B F Plaster ceiling G Erect roof 5 H Install door and windows 8 I Fit gutters and pipes J Paint outside 3
14 F must follow D and G Task Duration (days) A prepare foundations 7 B Make and position door frame C Lay drains, floor base and screed 15 D Install services and fittings 8 E E Erect walls 1 A, B F Plaster ceiling D, G G Erect roof 5 H Install door and windows 8 I Fit gutters and pipes J Paint outside 3
15 G must follow E Task Duration (days) A prepare foundations 7 B Make and position door frame C Lay drains, floor base and screed 15 D Install services and fittings 8 E E Erect walls 1 A, B F Plaster ceiling D, G G Erect roof 5 E H Install door and windows 8 I Fit gutters and pipes J Paint outside 3
16 H must follow G Task Duration (days) A prepare foundations 7 B Make and position door frame C Lay drains, floor base and screed 15 D Install services and fittings 8 E E Erect walls 1 A, B F Plaster ceiling D, G G Erect roof 5 E H Install door and windows 8 G I Fit gutters and pipes J Paint outside 3
17 I must follow C, F Task Duration (days) A prepare foundations 7 B Make and position door frame C Lay drains, floor base and screed 15 D Install services and fittings 8 E E Erect walls 1 A, B F Plaster ceiling D, G G Erect roof 5 E H Install door and windows 8 G I Fit gutters and pipes C, F J Paint outside 3
18 J must follow H and I Task Duration (days) A prepare foundations 7 B Make and position door frame C Lay drains, floor base and screed 15 D Install services and fittings 8 E E Erect walls 1 A, B F Plaster ceiling D, G G Erect roof 5 E H Install door and windows 8 G I Fit gutters and pipes C, F J Paint outside 3 I
19 We call this a precedence table Task Duration (days) A prepare foundations 7 B Make and position door frame C Lay drains, floor base and screed 15 Precedence D Install services and fittings 8 E E Erect walls 1 A, B F Plaster ceiling D, G G Erect roof 5 E H Install door and windows 8 G I Fit gutters and pipes C, F J Paint outside 3 I
20 Precedence diagrams are not that useful. A useful visual representation of a project is a network diagram.
21 Sequence the most common sequences / dependencies Task A Task B Task B depends upon Task A; B cannot start until A is finished Task A Task A Task B Task B Task C Task C Tasks B and C depend on Task A; neither can start until A is finished, but B and C are independent of each other Task C depends upon Task A and B; C cannot start until both A and B are finished
22 more unusual links and relationships so far all links have been finish-start links... Task A 3 days Task B Task B depends upon Task A, but with a 3 day delay; B cannot start until 3 days after A is finished Task A Task C 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 Task A Task C The finish of Task C depends upon the finish of Task A
23 Drawing a NETWORK how do we get here?
24 Algorithm
25 Draw in the links Task A B C D E F G H I J Precedence E A, B D, G E G C, F I
26 Draw in A, B, C on a rough diagram
27 STEP 1- original vertices with no arcs STEP - delete all arcs incident on A, B, C and redraw as shown STEP 3 - repeat iteration
28
29 STEP 1- original vertices with no arcs STEP - delete all arcs incident on E and redraw as shown STEP 3 - repeat iteration
30
31 STEP 1- original vertices with no arcs STEP - delete all arcs incident on D, G and redraw as shown STEP 3 - repeat iteration
32
33 STEP 1- original vertices with no arcs STEP - delete all arcs incident on F and H and redraw as shown STEP 3 - repeat iteration
34
35 STEP 1- original vertices with no arcs STEP - delete all arcs incident on I and redraw as shown STEP 3 - STOP
36
37 Converting to a usable diagram
38 Proposed method Now draw the network diagram using boxes early start time duration early finish time task number and/or name late start time float late finish time slack
39 Example 15 Task C Duration Task I 7 Task A 1 Task E 8 Task D Task F 3 Task J Task B 5 Task G 8 Task H Finish
40 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.
41 Practice Task Task 3 5 Task 7 3 Task 1 6 Task 4 3 Task 5 1 Task 9 Task 6 Task 8
42 Practice Task Task 3 3 Task 1 6 Task 4 3 Task 5 5 Task 7 1 Task 9 Task 6 Task 8
43 Practice Task Task 3 5 Task Task 1 6 Task 4 3 Task 5 1 Task 9 Task 6 Task 8
44 Practice Task 3 Task Task Task 4 3 Task 5 5 Task 7 1 Task 9 3 Task 6 Task 8
45 Practice Task 3 Task Task Task 4 3 Task 5 5 Task 7 1 Task Task 6 Task 8
46 Practice Task 7 3 Task Task Task Task 5 5 Task 7 1 Task Task 6 5 Task 8
47 Practice Task Task Task Task Task 5 5 Task 7 1 Task Task Task 8
48 3 4 7 Task Practice Task 3 Take the largest value 3 3 Task Task Task Task 7 1 Task Task Task 8
49 Practice Task Task Task Task Task Task 7 1 Task Task Task 8
50 3 4 7 Task Practice Task 3 Take the largest value 3 3 Task Task Task Task 7 1 Task Task Task 8
51 Forward pass complete Task Task Task Task Task Task Task 9 3 Task Task 8 Duration = 18
52 Backward pass Task Task Task Task Task Task Task Task Task 8
53 3 4 7 Task Task Task Task Task Task Task Task Task 8 Float
54 3 4 7 Task Task Task Task Task Task Task Task Task 8 17
55 3 4 7 Task Task Task Task Task Task Task Task Task
56 3 3 Task Task Task Task Task Task Task Task Task
57 Forward pass complete Take the smallest 3 3 Task Task Task Task Task Task Task Task Task
58 Critical Path float = 3 3 Task Task Task Task Task Task Task Task Task
59 Your turn 15 Task C Task I 7 Task A 1 Task E 8 Task D Task F 3 Task J Task B 5 Task G 8 Task H Finish
60 Example 1 Forward pass 15 Task C Task I 7 Task A 1 Task E 8 Task D Task F 3 Task J Task B 5 Task G 8 Task H Finish
61 Example 1 Forward pass Task C Task I 7 7 Task A 1 Task E 8 Task D Task F 3 Task J Task B 5 Task G 8 Task H Finish
62 Example 1 Take the largest value Task C? Task I 7 7 Task A 7 1 Task E 8 Task D Task F 3 Task J Task B 5 Task G 8 Task H Finish
63 Example 1 Take the largest value Task C? Task I 7 7 Task A Task E 17 8 Task D Task F 3 Task J Task B 17 5 Task G 8 Task H Finish
64 Example 1 Take the largest value Task C? Task I 7 7 Task A Task E Task D Task F 3 Task J Task B 17 5 Task G 8 Task H Finish
65 Example 1 Take the largest value Task C? Task I 7 7 Task A Task E Task D 5 Task F 3 Task J Task B 17 5 Task G 8 Task H Finish
66 Example 1 Minimum Task C 7 9 Task I 7 7 Task A Task E Task D 5 7 Task F Task J Task B 17 5 Task G 8 3 Task H 3 Finish
67 Example 1 Backward pass Task C 7 9 Task I 7 7 Task A Task E Task D 5 7 Task F Task J Task B 17 5 Task G 8 3 Task H Finish 3 3
68 Example 1 Take lowest value Task C 7 9 Task I 7 7 Task A Task E Task D 5 7 Task F Task J 9 3 Task B 17 5 Task G 8 3 Task H Finish 3
69 Example 1 Take lowest value Task C 7 9 Task I Task A Task E Task D 5 7 Task F Task J 9 3 Task B 17 5 Task G 8 3 Task H Finish 3
70 Example 1 Take lowest value Task C 7 9 Task I Task A Task E Task D 5 7 Task F Task J 9 3 Task B 17 5 Task G 8 3 Task H Finish 3
71 Example 1 Take lowest value Task C 7 9 Task I Task A Task E Task D Task F Task J 9 3 Task B 17 5 Task G Task H Finish 3
72 Example 1 Take lowest value Task C 7 9 Task I Task A Task E Task D Task F Task J 9 3 Task B 17 5 Task G Task H Finish 3
73 Example 1 Take lowest value Task C Task I Task A Task E Task D Task F Task J 9 3 Task B Task G Task H Finish 3
74 Example 1 Critical Path zero float Task C Task I Task A Task E Task D Task F Task J 9 3 Task B Task G Task H Finish 3
75 Example 1 Critical Path A-E-D-F-I-J Task C Task I Task A Task E Task D Task F Task J 9 3 Task B Task G Task H Finish 3
76 Using the outputs Gantt Charts optimising the schedule
77 Gantt: Critical path in red
78 Gantt: Critical path in red
79 Scheduling: Move the critical path along the top
80 Now fit the other activities like a puzzle
81 Now fit the other activities like a puzzle
82 Schedule
83 Any delay on the critical path causes a delay in the entire project
84 There is a -day float on the non-critical path
85 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 = ). 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 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.
86 EES = Earliest early start time LLF = latest late finish time Free 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 = EES successor EF
87 EES = Earliest early start time LLF = latest late finish time Independent 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 = EES successor -LLF predecessor -duration
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