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Critical Path Analysis

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There are no pre-requisites for this Achievement Standard so it can be placed in any course. No knowledge is pre-supposed.

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Methods include a selection from those related to: precedence tables network diagrams critical events scheduling float times

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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.

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Any activity can be represented as a project: planning a party building a house/factory planning a conference So what is a project?

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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

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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

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Example: Constructing a garage TaskDuration (days) Aprepare foundations7 BMake and position door frame2 CLay drains, floor base and screed15 DInstall services and fittings8 EErect walls10 FPlaster ceiling2 GErect roof5 HInstall door and windows8 IFit gutters and pipes2 JPaint outside3

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Some of these activities must be completed before others can start. TaskDuration (days) Aprepare foundations7 BMake and position door frame2 CLay drains, floor base and screed15 DInstall services and fittings8 EErect walls10 FPlaster ceiling2 GErect roof5 HInstall door and windows8 IFit gutters and pipes2 JPaint outside3

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You can’t erect the roof (G) before you have erected the walls (E) TaskDuration (days) Aprepare foundations7 BMake and position door frame2 CLay drains, floor base and screed15 DInstall services and fittings8 EErect walls10 FPlaster ceiling2 GErect roof5 HInstall door and windows8 IFit gutters and pipes2 JPaint outside3

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Precedence

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D must follow E TaskDuration (days) Aprepare foundations7 BMake and position door frame2 CLay drains, floor base and screed15 DInstall services and fittings8E EErect walls10 FPlaster ceiling2 GErect roof5 HInstall door and windows8 IFit gutters and pipes2 JPaint outside3

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E must follow A and B TaskDuration (days) Aprepare foundations7 BMake and position door frame2 CLay drains, floor base and screed15 DInstall services and fittings8E EErect walls10A, B FPlaster ceiling2 GErect roof5 HInstall door and windows8 IFit gutters and pipes2 JPaint outside3

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F must follow D and G TaskDuration (days) Aprepare foundations7 BMake and position door frame2 CLay drains, floor base and screed15 DInstall services and fittings8E EErect walls10A, B FPlaster ceiling2D, G GErect roof5 HInstall door and windows8 IFit gutters and pipes2 JPaint outside3

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G must follow E TaskDuration (days) Aprepare foundations7 BMake and position door frame2 CLay drains, floor base and screed15 DInstall services and fittings8E EErect walls10A, B FPlaster ceiling2D, G GErect roof5E HInstall door and windows8 IFit gutters and pipes2 JPaint outside3

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H must follow G TaskDuration (days) Aprepare foundations7 BMake and position door frame2 CLay drains, floor base and screed15 DInstall services and fittings8E EErect walls10A, B FPlaster ceiling2D, G GErect roof5E HInstall door and windows8G IFit gutters and pipes2 JPaint outside3

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I must follow C, F TaskDuration (days) Aprepare foundations7 BMake and position door frame2 CLay drains, floor base and screed15 DInstall services and fittings8E EErect walls10A, B FPlaster ceiling2D, G GErect roof5E HInstall door and windows8G IFit gutters and pipes2C, F JPaint outside3

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J must follow H and I TaskDuration (days) Aprepare foundations7 BMake and position door frame2 CLay drains, floor base and screed15 DInstall services and fittings8E EErect walls10A, B FPlaster ceiling2D, G GErect roof5E HInstall door and windows8G IFit gutters and pipes2C, F JPaint outside3I

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We call this a precedence table TaskDuration (days) Precedence Aprepare foundations7 BMake and position door frame2 CLay drains, floor base and screed15 DInstall services and fittings8E EErect walls10A, B FPlaster ceiling2D, G GErect roof5E HInstall door and windows8G IFit gutters and pipes2C, F JPaint outside3I

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Precedence diagrams are not that useful. A useful visual representation of a project is a network diagram.

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Sequence the most common sequences / dependencies Task ATask B Task A Task B 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

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more unusual links and relationships so far all links have been finish-start links... Task ATask B Task A 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

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Drawing a NETWORK – how do we get here?

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Algorithm

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Draw in the links TaskPrecedence A B C DE EA, B FD, G GE HG IC, F JI

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Draw in A, B, C on a rough diagram

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STEP 1- original vertices with no arcs STEP 2 - delete all arcs incident on A, B, C and redraw as shown STEP 3 - repeat iteration

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STEP 1- original vertices with no arcs STEP 2 - delete all arcs incident on E and redraw as shown STEP 3 - repeat iteration

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STEP 1- original vertices with no arcs STEP 2 - delete all arcs incident on D, G and redraw as shown STEP 3 - repeat iteration

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STEP 1- original vertices with no arcs STEP 2 - delete all arcs incident on F and H and redraw as shown STEP 3 - repeat iteration

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STEP 1- original vertices with no arcs STEP 2 - delete all arcs incident on I and redraw as shown STEP 3 - STOP

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Converting to a usable diagram

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Proposed method Now draw the network diagram using boxes task number and/or name duration early start time late start time early finish time late finish time float slack

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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

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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.

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Practice 1 Task 06 2 Task 01 3 Task 04 6 Task 03 3 Task 08 2 Task 02 4 Task 09 1 Task 05 3 Task 07 5

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Practice 1 Task 06 2 Task 01 3 0 Task 04 6 Task 03 3 Task 08 2 Task 02 4 Task 09 1 Task 05 3 Task 07 5

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Practice 1 Task 06 2 Task 01 3 30 Task 04 6 Task 03 3 Task 08 2 Task 02 4 Task 09 1 Task 05 3 Task 07 5

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Practice 1 Task 06 2 Task 01 3 3 0 Task 04 6 3 Task 03 3 Task 08 2 Task 02 4 3 Task 09 1 Task 05 3 Task 07 5 3

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Practice 1 Task 06 2 Task 01 3 3 0 Task 04 6 39 Task 03 3 Task 08 2 Task 02 4 37 Task 09 1 Task 05 3 Task 07 5 3 5

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Practice 1 Task 06 2 Task 01 3 3 0 Task 04 6 39 Task 03 3 7 Task 08 2 5 Task 02 4 37 Task 09 1 Task 05 3 9 Task 07 5 3 5

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Practice 1 Task 06 2 Task 01 3 3 0 Task 04 6 39 Task 03 3 107 Task 08 2 75 Task 02 4 37 Task 09 1 Task 05 3 912 Task 07 5 3 5

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Practice 1 Task 06 2 Task 01 3 3 0 Task 04 6 39 Task 03 3 107 Task 08 2 75 Task 02 4 37 Task 09 1 Task 05 3 912 Task 07 5 12 3 5 Take the largest value

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Practice 1 Task 06 2 Task 01 3 3 0 Task 04 6 39 Task 03 3 107 Task 08 2 75 Task 02 4 37 Task 09 1 Task 05 3 912 Task 07 5 12 17 3 5

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Practice 1 Task 06 2 Task 01 3 3 0 Task 04 6 39 Task 03 3 107 Task 08 2 75 Task 02 4 37 Task 09 1 Task 05 3 912 Task 07 5 12 17 3 5 Take the largest value

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Forward pass complete Duration = 18 Task 06 2 Task 01 3 30 3 Task 04 6 3 9 Task 03 3 10 7 5 Task 08 2 7 5 Task 02 4 3 7 Task 09 1 18 17 Task 05 3 9 12 Task 07 5 12 17

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Backward pass Task 06 2 Task 01 3 30 3 Task 04 6 3 9 Task 03 3 10 7 5 Task 08 2 7 5 Task 02 4 3 7 Task 09 1 18 17 Task 05 3 9 12 Task 07 5 12 17 18

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Task 06 2 Task 01 3 30 3 Task 04 6 3 9 Task 03 3 10 7 5 Task 08 2 7 5 Task 02 4 3 7 Task 09 1 18 17 Task 05 3 9 12 Task 07 5 12 17 18 170 Float

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Task 06 2 Task 01 3 30 3 Task 04 6 3 9 Task 03 3 10 7 5 Task 08 2 7 5 Task 02 4 3 7 Task 09 1 18 17 Task 05 3 9 12 Task 07 5 12 17 18 170

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Task 06 2 Task 01 3 30 3 Task 04 6 3 9 Task 03 3 10 7 5 Task 08 2 7 5 Task 02 4 3 7 Task 09 1 18 17 Task 05 3 9 12 Task 07 5 12 17 18 170 12 15 0 10

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Task 06 2 Task 01 3 30 3 Task 04 6 3 9 Task 03 3 10 7 5 Task 08 2 7 5 Task 02 4 3 7 Task 09 1 18 17 Task 05 3 9 12 Task 07 5 12 17 18 170 12 15 0 10 12 9 9 0 2 15 1310 9 9 3 0 5 2

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Forward pass complete Task 06 2 Task 01 3 30 3 Task 04 6 3 9 Task 03 3 10 7 5 Task 08 2 7 5 Task 02 4 3 7 Task 09 1 18 17 Task 05 3 9 12 Task 07 5 12 17 18 170 12 15 0 10 12 9 9 0 2 15 1310 9 9 3 0 5 2 Take the smallest

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Critical Path – float = 0 Task 06 2 3 5 13 15 10 Task 09 1 18 17 18 17 0 Task 07 5 12 17 12 0 Task 05 3 9 12 9 0 Task 04 6 3 9 9 3 0 Task 01 3 30 3 0 0 Task 08 2 7 5 171510 Task 03 3 10 7 12 9 2 Task 02 4 3 7 9 5 2

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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

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Example 1 – Forward pass Task A 7 0 Task B 2 0 Task C 15 0 Task E 10 Task D 8 Task G 5 Task F 2 Task H 8 Task I 2 Task J 3 Finish

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Example 1 – Forward pass Task A 7 0 Task B 2 0 Task C 15 0 Task E 10 Task D 8 Task G 5 Task F 2 Task H 8 Task I 2 Task J 3 Finish

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Example 1 – Take the largest value Task A 7 0 Task B 2 0 Task C 15 0 Task E 10 7 Task D 8 Task G 5 Task F 2 Task H 8 Task I 2 ? Task J 3 Finish

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Example 1 – Take the largest value Task A 7 0 Task B 2 0 Task C 15 0 Task E 10 17 7 Task D 8 17 Task G 5 17 Task F 2 Task H 8 Task I 2 ? Task J 3 Finish

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Example 1 – Take the largest value Task A 7 0 Task B 2 0 Task C 15 0 Task E 10 17 7 Task D 8 25 17 Task G 5 22 17 Task F 2 Task H 8 Task I 2 ? Task J 3 Finish

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Example 1 – Take the largest value Task A 7 0 Task B 2 0 Task C 15 0 Task E 10 17 7 Task D 8 25 17 Task G 5 22 17 Task F 2 25 Task H 8 22 Task I 2 ? Task J 3 Finish

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Example 1 – Minimum 32 Task A 7 0 Task B 2 0 Task C 15 0 Task E 10 17 7 Task D 8 25 17 Task G 5 22 17 Task F 2 27 25 Task H 8 30 22 Task I 2 29 27 Task J 3 32 29 Finish 32

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Example 1 – Backward pass Task A 7 0 Task B 2 0 Task C 15 0 Task E 10 17 7 Task D 8 25 17 Task G 5 22 17 Task F 2 27 25 Task H 8 30 22 Task I 2 29 27 Task J 3 32 29 Finish 32

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Example 1 – Take lowest value Task A 7 0 Task B 2 0 Task C 15 0 Task E 10 17 7 Task D 8 25 17 Task G 5 22 17 Task F 2 27 25 Task H 8 30 22 Task I 2 29 27 Task J 3 32 29 Finish 32 2929 0 24 2

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Example 1 – Take lowest value Task A 7 0 Task B 2 0 Task C 15 0 Task E 10 17 7 Task D 8 25 17 Task G 5 22 17 Task F 2 27 25 Task H 8 30 22 Task I 2 29 27 Task J 3 32 29 Finish 32 2929 0 24 2 2927 0

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Example 1 – Take lowest value Task A 7 0 Task B 2 0 Task C 15 0 Task E 10 17 7 Task D 8 25 17 Task G 5 22 17 Task F 2 27 25 Task H 8 30 22 Task I 2 29 27 Task J 3 32 29 Finish 32 2929 0 24 2 2927 0 25 0

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Example 1 – Take lowest value Task A 7 0 Task B 2 0 Task C 15 0 Task E 10 17 7 Task D 8 25 17 Task G 5 22 17 Task F 2 27 25 Task H 8 30 22 Task I 2 29 27 Task J 3 32 29 Finish 32 2929 0 24 2 2927 0 25 0 17 0 24 19 2

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Example 1 – Take lowest value Task A 7 0 Task B 2 0 Task C 15 0 Task E 10 17 7 Task D 8 25 17 Task G 5 22 17 Task F 2 27 25 Task H 8 30 22 Task I 2 29 27 Task J 3 32 29 Finish 32 2929 0 24 2 2927 0 25 0 17 0 24 19 2 177 0

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Example 1 – Take lowest value Task A 7 0 Task B 2 0 Task C 15 0 Task E 10 17 7 Task D 8 25 17 Task G 5 22 17 Task F 2 27 25 Task H 8 30 22 Task I 2 29 27 Task J 3 32 29 Finish 32 2929 0 24 2 2927 0 25 0 17 0 24 19 2 177 0 2712 7 0 0 7 5 5

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Example 1 – Critical Path – zero float Task A 7 0 Task B 2 0 Task C 15 0 Task E 10 17 7 Task D 8 25 17 Task G 5 22 17 Task F 2 27 25 Task H 8 30 22 Task I 2 29 27 Task J 3 32 29 Finish 32 2929 0 24 2 2927 0 25 0 17 0 24 19 2 177 0 2712 7 0 0 7 5 5

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Example 1 – Critical Path – A-E-D-F-I-J Task A 7 0 Task B 2 0 Task C 15 0 Task E 10 17 7 Task D 8 25 17 Task G 5 22 17 Task F 2 27 25 Task H 8 30 22 Task I 2 29 27 Task J 3 32 29 Finish 32 2929 0 24 2 2927 0 25 0 17 0 24 19 2 177 0 2712 7 0 0 7 5 5

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Using the outputs Gantt Charts optimising the schedule

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Gantt: Critical path in red

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Scheduling: Move the critical path along the top

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Now fit the other activities like a puzzle

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Schedule

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Any delay on the critical path causes a delay in the entire project

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There is a 2-day float on the non-critical path

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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.

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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

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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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