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.
Understanding Engineering: Project Scheduling (CPM and PERT)
A useful schedule starts by breaking a large job into activities that produce clear results. For a bridge project, activities may include surveying the site, designing foundations, ordering steel, building supports, and installing the deck. Each activity needs a realistic duration and a clear dependency.
A dependency states what must be complete before another activity can begin. Most are finish to start links, such as completing excavation before pouring concrete.
Some work can overlap, but only when the technical risk is understood. Starting steel fabrication before final design approval may save time, yet it can create expensive rework if the design changes.
Engineers calculate a schedule by making two passes through the activity network. The forward pass begins at the project start and finds the earliest possible time for every activity. When an activity has several predecessors, it must wait for the predecessor that finishes last.
The backward pass begins at the required completion date and works back through the network. It finds how late each activity can start or finish without affecting the overall completion date.
Comparing the early and late times reveals which activities have no room for delay. Those activities form one critical path, though a project can have more than one critical path when several routes take the same total time.
Slack is not simply spare time that can be wasted. It is a planning buffer attached to a specific activity. A task with three days of slack can slip by three days under the current assumptions, but a larger delay will affect later work.
Slack can disappear when an earlier activity takes longer than planned or when a resource is moved elsewhere. For example, a crane may be needed for both placing beams and lifting equipment.
The network may show that the tasks are independent, but the shared crane creates a resource conflict. Good schedules account for these practical limits rather than treating every available worker and machine as unlimited.
PERT is helpful when durations are uncertain, especially during design, research, testing, or work in unfamiliar ground conditions. Instead of pretending that one duration is certain, a team estimates a short outcome, a most likely outcome, and a long outcome. The most likely estimate receives more weight because extreme outcomes should not dominate the expected time.
The gap between the short and long estimates shows uncertainty. A wide gap means the activity needs closer attention. Teams may investigate the risk, collect better data, add contingency, or plan an alternative method.
PERT does not remove uncertainty. It makes uncertainty visible enough to discuss.
When learning these methods, draw the network carefully before doing any calculations. Check that every activity has the right predecessors and that no task is missing. A perfect calculation based on a wrong dependency gives a misleading answer.
Label activities clearly and keep units consistent, using days or weeks throughout. Recheck the schedule whenever scope, resources, weather assumptions, or delivery dates change.
In real projects, the critical path can move from design work to procurement or construction as conditions change. The schedule is therefore a living model for making decisions, not a one-time chart made for a report.
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.