Project scheduling helps engineers plan tasks, estimate timelines, assign resources, and track progress from start to finish. This cheat sheet covers CPM, PERT, and Gantt charts, which are common tools for managing engineering projects. Students need these methods to understand how task order, delays, and uncertainty affect a project deadline.
These tools also support clear communication among designers, builders, managers, and clients.
CPM focuses on finding the longest dependent path through a project network, which determines the shortest possible completion time. PERT adds uncertainty by using optimistic, most likely, and pessimistic time estimates to calculate an expected task duration. Gantt charts show tasks on a time scale, making start dates, finish dates, overlap, and progress easy to see.
The most important formulas include expected time te = (a + 4m + b) / 6, slack = LS - ES = LF - EF, and project duration = length of the critical path.
Key Facts
- In CPM, the critical path is the longest path through the project network, and its total duration equals the shortest possible project time.
- A task on the critical path has zero slack, so delaying it delays the entire project unless the schedule is changed.
- Slack or float is calculated by slack = LS - ES = LF - EF, where ES is early start, LS is late start, EF is early finish, and LF is late finish.
- Early finish is calculated by EF = ES + duration, and late start is calculated by LS = LF - duration.
- In PERT, the expected task time is te = (a + 4m + b) / 6, where a is optimistic time, m is most likely time, and b is pessimistic time.
- PERT variance for a task is variance = ((b - a) / 6)^2, which measures schedule uncertainty.
- A Gantt chart displays tasks as horizontal bars on a calendar timeline, showing when each task starts, ends, overlaps, or depends on another task.
- Crashing a schedule means shortening selected task durations, usually at extra cost, and it only reduces total project time if the shortened task is on the critical path.
Vocabulary
- CPM
- The Critical Path Method is a scheduling technique that uses task durations and dependencies to find the longest path and total project duration.
- PERT
- The Program Evaluation and Review Technique is a scheduling method that estimates task time using optimistic, most likely, and pessimistic durations.
- Gantt chart
- A Gantt chart is a timeline chart that shows project tasks as bars across dates or time periods.
- Critical path
- The critical path is the sequence of dependent tasks with the greatest total duration in a project.
- Slack
- Slack is the amount of time a task can be delayed without delaying the project finish date.
- Dependency
- A dependency is a relationship showing that one task must happen before another task can start or finish.
Common Mistakes to Avoid
- Adding all task durations instead of only dependent path durations is wrong because tasks that happen in parallel do not all extend the project finish time.
- Marking the shortest path as the critical path is wrong because the critical path is the longest dependent path, not the fastest one.
- Ignoring zero-slack tasks is wrong because any delay on a zero-slack task directly threatens the final project deadline.
- Using the simple average (a + m + b) / 3 for PERT expected time is wrong because PERT weights the most likely time four times, using te = (a + 4m + b) / 6.
- Assuming a Gantt chart automatically shows dependencies is wrong because dependencies must be drawn or labeled clearly, often with arrows or predecessor notes.
Practice Questions
- 1 A project has two paths: A-B-D with durations 3, 5, and 4 days, and A-C-D with durations 3, 2, and 4 days. What is the critical path and project duration?
- 2 For a PERT activity with optimistic time a = 4 days, most likely time m = 7 days, and pessimistic time b = 16 days, calculate the expected time te.
- 3 A task has ES = 6, EF = 14, LS = 10, and LF = 18. Calculate its slack and decide whether it is on the critical path.
- 4 Explain why shortening a non-critical task may fail to reduce the total project duration, even if that task finishes earlier.
Understanding Project Scheduling (CPM, PERT, Gantt)
A schedule begins with a complete task list, not with a chart. Each task needs a clear result, a duration, and a predecessor. A predecessor is work that must reach a certain point before another task can begin.
For example, a team may need to approve a bridge design before fabrication starts. Some tasks use a finish to start link, where one task must finish before the next begins. Others can run together, such as ordering materials while a site is prepared.
In a network diagram, engineers make a forward pass through the tasks. They find the earliest possible start and finish for each one.
When a task has several predecessors, it must wait for the predecessor that finishes last. This is why one overlooked dependency can make an early schedule unrealistic.
The backward pass starts from the required project completion date and works back toward the beginning. It reveals how long each task can wait without changing that completion date. Slack is useful, but it does not mean a task is unimportant.
A task with some slack may still need workers, equipment, permits, or materials at a particular time. Using all of its slack can create conflicts later. Engineers watch near critical paths too.
These are routes with very little slack. A small delay on one of them can create a new critical path. Students should keep task durations separate from dates.
Duration means working time required. Calendar dates can change because of weekends, holidays, weather, delivery limits, or shifts.
PERT is most useful when a task has uncertain duration. Early design work, testing, field surveys, and approval processes often have this problem. The three estimates should come from real reasons rather than guesses.
The optimistic time assumes that conditions go unusually well. The most likely time reflects normal conditions. The pessimistic time includes realistic trouble, such as failed tests or late information.
The expected time gives extra weight to the most likely estimate because extreme outcomes are less common. Variance shows how widely the estimates spread. A task with a large spread deserves closer attention, even if its expected time seems short.
For a path, uncertainty from its tasks can be combined when the estimates are treated as independent. In real projects, that assumption can fail because bad weather or a supplier problem may delay several tasks at once.
A Gantt chart turns the schedule into a calendar view that a team can use every day. Bars make overlaps visible, but the chart can become crowded on a large project. It may hide the logic of dependencies unless links or notes are included.
A useful Gantt chart has a baseline plan, actual progress, and updated forecasts. Comparing these shows whether a task started late, took longer than planned, or is recovering. Students may meet the same ideas when planning a robotics build, lab investigation, school event, or group presentation.
If a deadline is threatened, shortening work on a noncritical task does not help the final date. Shortening critical work can help, but it may cost more, reduce quality, or shift the critical path to another route. Good scheduling means checking the network again after every major change.