Project scheduling helps engineers plan complex work by showing which tasks must happen first, which can occur in parallel, and when the whole project can finish. CPM, the Critical Path Method, uses activity durations and dependencies to find the longest required chain of work. PERT, the Program Evaluation and Review Technique, adds uncertainty by estimating likely activity times from optimistic, most likely, and pessimistic values.
These tools matter because a small delay in the wrong activity can move the entire project deadline.
Key Facts
- CPM project duration = length of the critical path.
- Slack = LS - ES = LF - EF.
- Earliest finish: EF = ES + duration.
- Latest start: LS = LF - duration.
- PERT expected time: te = (a + 4m + b) / 6.
- PERT variance: sigma^2 = ((b - a) / 6)^2.
Vocabulary
- Activity
- An activity is a task in a project that takes time and may require resources.
- Dependency
- A dependency is a required order relationship in which one activity must finish before another can start.
- Critical path
- The critical path is the longest path through the project network and determines the shortest possible project completion time.
- Slack
- Slack is the amount of time an activity can be delayed without delaying the whole project.
- PERT expected time
- PERT expected time is a weighted average activity duration based on optimistic, most likely, and pessimistic estimates.
Common Mistakes to Avoid
- Adding all activity durations instead of only the durations along a path is wrong because parallel tasks do not all extend the project finish time.
- Calling the shortest path the critical path is wrong because the critical path is the longest dependent chain that controls the completion date.
- Ignoring slack on noncritical activities is wrong because slack shows how much delay can occur before that activity becomes critical.
- Using PERT estimates as exact deadlines is wrong because PERT models uncertainty and should be interpreted with expected values and variation.
Practice Questions
- 1 A project has paths A-B-D with durations 4, 6, and 5 days, and A-C-D with durations 4, 3, and 5 days. What is the project duration and which path is critical?
- 2 An activity has ES = 8 days, EF = 14 days, LS = 11 days, and LF = 17 days. Find its duration and slack.
- 3 A noncritical activity has 3 days of slack, but its supplier delay is expected to be 5 days. Explain how this delay may affect the project schedule and the critical path.