Answer First
PERT and CPM improve project scheduling by identifying the critical path—the sequence of tasks that determines the minimum project duration. They help managers focus on the activities that matter most, allocate resources efficiently, and predict completion times with or without uncertainty.
Problem Setup
Projects consist of activities with durations and precedence relationships. CPM uses deterministic durations, while PERT uses three-point estimates: \[ t_e = \frac{a + 4m + b}{6}, \] where:
- \(a\) = optimistic time,
- \(m\) = most likely time,
- \(b\) = pessimistic time.
The goal is to compute earliest start times, latest start times, slack, and the critical path.
Step-by-Step Explanation
1. Map the project as a network
Activities become nodes or arcs, and precedence relationships define the structure.
2. Compute earliest start and finish times
A forward pass determines how soon each activity can begin.
3. Compute latest start and finish times
A backward pass determines how late each activity can begin without delaying the project.
4. Identify the critical path
Activities with zero slack form the critical path. Delays in these tasks delay the entire project.
5. Use PERT to incorporate uncertainty
PERT estimates expected duration and variance, allowing managers to compute the probability of finishing by a deadline.
Intuition
PERT and CPM are like creating a roadmap for a project. They show which tasks are flexible, which tasks are bottlenecks, and how long the entire project will take. Managers can then focus on the tasks that truly determine success.
Common Exam Mistakes
- Incorrect forward or backward pass calculations.
- Misidentifying the critical path.
- Confusing slack with float.
- Using the wrong formula for PERT expected time.
Final Summary
PERT and CPM improve project scheduling by identifying the critical path, estimating completion times, and highlighting where managerial attention is most needed. They are essential tools for planning and controlling complex projects.
This explanation belongs to the broader Management Science Tutoring pillar.
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