Planning & Decision Making · Topic 3 of 11
Constructing PERT Charts
Theory
A PERT Chart (Programme Evaluation and Review Technique) is a visual activity network that is highly useful in project planning. Instead of just showing the order of tasks, it calculates the exact timeline of the project.
1. The Node Structure
In a PERT chart, every activity is represented by a box (a node) that usually contains three vital pieces of numerical information:
- Duration: How long the task takes to complete.
- Earliest Start Time (EST): The absolute earliest time a task can begin.
- Latest End Time (LET): The latest time a task must be completely finished by to avoid delaying the entire project.
2. The Forward Scan (Finding the EST)
To find the Earliest Start Times, we perform a forward scan, working from left to right across the diagram:
- For the very first activities with no predecessors, the EST is always 0.
- For an activity with a single predecessor, the EST is simply the sum of the predecessor's EST and its duration.
- The 'Maximum' Rule: If an activity has multiple predecessors (arrows merging into it), you must calculate the sum (EST + duration) for every preceding task and take the maximum value. You must wait for the longest task to finish before moving on.
3. The Backward Scan (Finding the LET)
To find the Latest End Times, we perform a backward scan, working backwards from right to left:
- For the final activities with no successors, the LET is the total length of the project (the highest number found at the end of your forward scan).
- For an activity with a single successor, the LET is the difference between its successor's LET and its duration.
- The 'Minimum' Rule: If an activity has multiple successors (arrows splitting out from it), you must calculate the difference (LET − duration) for every succeeding task and take the minimum value.
4. Start and End Boxes
It is highly recommended to add a "START" box at the beginning of your diagram and an "END" box at the finish. These are not real activities, so they have a duration of 0. Using an END box guarantees you use the correct final LET for your backward scan and avoids costly exam mistakes.
Worked examples
Example 1
Example 1: The Forward Scan (The 'Maximum' Rule)
A school is organising a theatrical play. Task E (Hold Dress Rehearsal) cannot begin until both Task C (Build Set) and Task D (Finalise Costumes) are completed.
- Task C has an Earliest Start Time of 12 days and a duration of 5 days.
- Task D has an Earliest Start Time of 14 days and a duration of 2 days.
Calculate the Earliest Start Time (EST) for Task E.
We must apply the 'Maximum' rule because Task E has multiple predecessors.
- Path C finishes at: 12 + 5 = 17 days.
- Path D finishes at: 14 + 2 = 16 days.
We take the highest number. Therefore, the EST for Task E is 17 days.
Example 2
Example 2: The Backward Scan (The 'Minimum' Rule)
A film director is planning a shoot. Task B (Draft Script) must be completely finished before Task C (Film Scene 1) and Task D (Film Scene 2) can begin.
- Task C takes 4 days and has a Latest End Time of 20 days.
- Task D takes 6 days and has a Latest End Time of 25 days.
Calculate the Latest End Time (LET) for Task B.
We must apply the 'Minimum' rule because Task B has multiple successors.
- Path C calculation: 20 − 4 = 16 days.
- Path D calculation: 25 − 6 = 19 days.
We take the lowest number. Therefore, the LET for Task B is 16 days.
Example 3
Example 3: Constructing a Full PERT Chart
A small business is launching a new product. The table below lists the tasks, their dependencies, and durations in weeks.
| Task | Description | Preceding Task | Duration (weeks) |
|---|---|---|---|
| A | Market Research | None | 3 |
| B | Design Product | A | 4 |
| C | Order Materials | A | 2 |
| D | Manufacture | B, C | 5 |
| E | Launch Marketing | B | 3 |
| F | Deliver to Stores | D, E | 1 |
Using the data, perform a forward and backward scan to determine the Earliest Start Time and Latest End Time for all tasks.
To construct this, draw a START node leading to A. From A, arrows split to B and C. Both B and C merge into D. However, an arrow also goes from B to E. Finally, both D and E merge into F, which leads to an END node.
Forward Scan (Left to Right - finding EST):
- START: EST = 0, Dur = 0.
- A: Preceded by START. EST = 0.
- B: Preceded by A (0 + 3 = 3). EST = 3.
- C: Preceded by A (0 + 3 = 3). EST = 3.
- D: Preceded by B (3 + 4 = 7) and C (3 + 2 = 5). Max is 7. EST = 7.
- E: Preceded by B (3 + 4 = 7). EST = 7.
- F: Preceded by D (7 + 5 = 12) and E (7 + 3 = 10). Max is 12. EST = 12.
- END: Preceded by F (12 + 1 = 13). Total project time is 13 weeks.
Backward Scan (Right to Left - finding LET):
- END: LET = 13, Dur = 0.
- F: Succeeded by END (13 − 0 = 13). LET = 13.
- E: Succeeded by F (13 − 1 = 12). LET = 12.
- D: Succeeded by F (13 − 1 = 12). LET = 12.
- C: Succeeded by D (12 − 5 = 7). LET = 7.
- B: Succeeded by D (12 − 5 = 7) and E (12 − 3 = 9). Min is 7. LET = 7.
- A: Succeeded by B (7 − 4 = 3) and C (7 − 2 = 5). Min is 3. LET = 3.