Task Planning & Logistics · Topic 4 of 4
Precedence Tables & Critical Path
Theory
The Golden Rule: The "minimum time" to complete a massive project is always the longest path through the activity network. This is called the Critical Path. If any job on this path is delayed, the entire project is delayed.
1. Constructing the Network Diagram
A precedence table shows which tasks must be completed before another task can begin. When drawing the diagram, ensure that every preceding task connects with an arrow to its following task.
2. Calculating the Critical Path (Minimum Time)
To find the minimum time for the whole project to be completed:
- Trace every single possible path from start to finish through your diagram.
- Add up the times for each path.
- The path that takes the most time is your minimum project completion time.
⚠️ Common Examiner Traps
- The "Adding Everything" Trap: a frequent error is to simply take the column of times in the table and add them all together to calculate a total time. Because many tasks are done simultaneously (at the same time by different people), adding all numbers together is completely wrong. You must only sum the paths!
- The "Missing Node" Trap: When building the diagram, candidates often miss tasks that have multiple prerequisites (e.g., Task G relies on both C and F). Make sure your box for G has arrows coming from both C and F.
Worked examples
Example 1
Rab modernised a house. The work done is shown in the table.
| Activity | Description | Preceding task | Time in days |
|---|---|---|---|
| A | clear rubbish | none | 7 |
| B | landscape garden | A | 10 |
| C | plaster walls | E, G | 9 |
| D | decorate house | C | 8 |
| E | rewire house | F | 15 |
| F | fix roof | A | 18 |
| G | re-plumb house | F | 11 |
| H | lay flooring | C | 6 |
| I | advertise for sale | B, D, H | 1 |
Calculate the minimum time required for the renovations to be completed. (2 marks)
Step 1: Trace the possible routes from Start (A) to Finish (I) through the network.
Step 2: Calculate the time for each individual path.
- Path 1: A → B → I =
- Path 2: A → F → E → C → D → I =
- Path 3: A → F → E → C → H → I =
- Path 4: A → F → G → C → D → I =
- Path 5: A → F → G → C → H → I =
Step 3: Identify the longest path.
Final Answer: The minimum time required to complete the renovations is 58 days.
Example 2
Identifying the Critical Path
A small event is planned. The activities, their preceding tasks and their durations (in hours) are:
- A (start, none): 4
- B (after A): 6
- C (after A): 3
- D (after B): 5
- E (after C): 9
- F (after D and E): 2
(a) Find the minimum time to complete the event. (b) State which activities are on the critical path.
Step 1: List the paths from A to the finish (F) and total each:
- A → B → D → F =
- A → C → E → F =
(a) The minimum completion time is the longest path: 18 hours.
(b) The critical path is the activities on that longest route: A, C, E, F. A delay to any of these delays the whole event.