Dependency Table Example Task ID Name Predecessors 1 A 2 B 3 C 4 D 1 5 E 1;2 6 F 1;2 7 G 5;6 8 H 4;5
Dependent tasks Dependency Matrix 1 2 3 4 5 6 7 8 9 10 1 x 2 x x 3 x x 4 x 5 x x 6 x 7 x 8 x 9 x x 10 x
Network Diagram Task C Task F Start Task B Task A Task E Task D Task G Task H End
Dependency Table with durations Task ID Name Duration Predecessors 1 A 5 2 B 2 3 C 4 4 D 4 1 5 E 5 1;2 6 F 2 1;2 7 G 2 5;6 8 H 1 4;5
Network Diagram with durations Task C 4 days Start Task B 2 days Task A 5 days Task F 2 days Task E 5 days Task D 4 days Task G 2 days Task H 1 day End
Network Diagram node Early start (ES) Late start (LS) Task name (duration) Early finish (EF) Late finish (LF)
0 0 Start 0 0 Network Diagram B (2) A (5) 0 4 C (4) 8 12 0 2 3 5 0 5 5 7 F (2) 8 10 5 10 E (5) 5 10 0 5 5 9 7 D (4) 11 Project duration 10 12 G (2) 10 12 10 11 11 H (1) 12 ES LS End EF Task (days) 12 12 12 LF 12
0 0 Network Diagram (highlighted) Start 0 0 0 3 0 0 B (2) A (5) Critical path 2 5 5 5 0 4 8 C (4) 12 5 7 F (2) 5 10 5 E (5) 5 9 7 8 D (4) 10 11 10 10 2 G (2) 10 10 1 11 H (1) ES LS End EF Task (days) Project duration 12 12 12 12 12 LF 12
How to create a network diagram - 1 (Forward pass) 1. Create a start task. Set its duration, ES and EF to 0. 2. For each task that doesn't have a predecessor: 1. Create the task, and set its duration. 2. Draw the dependency from the start task to the new task. 3. Set its early start to 0. 4. Set its early finish to its early start + its duration. 3. For each task that has only predecessors already drawn: 1. Create the task, and set its duration. 2. Draw the dependency from each predecessor to the new task. 3. Set its early start to max(ef of its predecessors). 4. Set its early finish to its early start + its duration. 4. Repeat step 3 until all tasks are drawn. 5. Add an end task. Set its duration to 0. 1. Connect all tasks that don't have successors to the end task. 2. Set its early start and early finish to max(ef of its predecessors).
How to create a network diagram - 2 (Backward pass) 1. Set the end task's LF = EF, LS = LF. 2. For each task that immediately precedes the end task: 1. Set its late finish to the end task's late start. 2. Set its late start to its late finish its duration. 3. For each task that has only successors with an LS: 1. Set its late finish = min(ls of its successors). 2. Set its late start to its late finish its duration. 4. Repeat step 3 until all tasks have an LS and an LF. 5. Verify that the start tasks has all values set to 0. 6. Highlight the critical path(s).
It s your turn
Exercise Network Diagram Task ID Name Duration Predecessors 1 A 5 2 B 4 3 C 2 2 4 D 4 3 5 E 6 1 6 F 1 5 7 G 2 1;3 8 H 1 7 9 I 6 2 10 J 3 4;8
Network Diagram Solution
Project Diagrams Network Diagram (PERT / CPM) 1 Activity-On-Node Activity-On-Arrow Gantt Chart (Bar chart) Start Task B 2 days Task A 5 days Task C 4 days Task F 2 days Task E 5 days Task D 4 days Task G 2 days Task H 1 day End 1 PERT = Program Evaluation and Review Technique; CPM=Critical Path Method
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It s your turn
Example with task durations Task ID Name Duration Predecessors 1 A 5 2 B 4 3 C 2 2 4 D 4 3 5 E 6 1 6 F 1 5 7 G 2 1;3 8 H 1 7 9 I 6 2 10 J 3 4;8
Gantt Chart (MS Project) Total duration of the project Project summary task Critical path in red
Milestones control points to evaluate progress and adjust plans illustrate progress to the customer may be intermediate sign-offs or stage payments should be chosen carefully Good practice: make them coincide with a significant deliverable
Types of task dependencies Finish-to-start Start-to-start Start-to-finish Finish-to-finish
Scheduling - ASAP or ALAP? ASAP + - Slack Resources are needed early Lower risk of delay Early costs ALAP + - Resources are needed late No slack Late costs Higher risk of delay ASAP ALAP Cost Time