PERT and MPM
Scheduling a project from its task table: levels, earliest and latest dates, total and free float, critical tasks, minimum project duration, MPM and PERT graphs with dummy tasks.
- 29 cards
- 6 topics
- Free
The outline, topic by topic
Each topic is weighted the way the exam weighs it.
- Concepts
- Questions
- Sort and link
- The numbers
- Scenarios
- Understand
A few cards from the deck
Earliest start: what is it?
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The first date on which a task can begin: the maximum of the earliest finish dates of all its predecessor tasks.
It is the maximum, not the minimum, because the last predecessor must be awaited. A task with no predecessor starts at date 0.
What is the earliest start of task F?
```text
Task Duration Predecessors
A 3 -
B 4 -
C 2 A
D 5 A, B
E 3 C
F 4 C, D
G 2 E, F`- 9, the end of D (4 + 5)
- 5, the end of C (3 + 2)
- 7, the sum of the durations of C and D
- 14, the sum of the ends of C and D
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9, the end of D (4 + 5)
D starts at 4 (it waits for B, finished at 4) and ends at 9. C ends at 5. F waits for both: max(5, 9) = 9. Taking C's end is the error of the minimum; adding the ends makes no sense.
Dates are computed in two passes: the … pass gives the earliest dates, the … pass gives the latest dates.
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Dates are computed in two passes: the forward pass gives the earliest dates, the backward pass gives the latest dates.
The forward pass starts from the beginning and takes maxima; the backward pass starts from the end of the project, at its minimum duration, and takes minima.
Total float: what is it?
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The maximum delay a task can take without pushing back the end of the project: the latest date minus the earliest date.
It is shared with the tasks that follow: if one uses up the float, the others lose theirs. A zero float makes a task critical.