The critical path method (CPM) is an algorithm for scheduling a set of project activities. It is an important tool for effective project management. It is also guaranteed to show up in one form or another on the PE Exam. Below you will find explanations and examples on how to calculate the CPM for a project.
|Understanding Critical Path Methods (CPM)|
AoN representation has the activitiy inside the node and the arrows represent the precedence relationships. This is used most often in conjunction with computer programs as they allow for easy data entry once precedence has been established. They are also convenient for determining start and finish times by hand.
AoA (also known as Activity on Branch) has the activity represent by the arrows themselves and the nodes represent the precedence as points in time where predecessors have been completed. There are three simple rules to creating the AoA precedence diagram:
The critical path is identified by determining ES, EF, LF, and LS to find activities that have zero slack time. This requires two passes:
For all activities, calculate each activity’s early dates: ES equals the latest (largest) EF of all its immeidate predecessors and EF equals ES plus duration. The EF for the last task is the project duraction.
For all activities, calculate each activity’s late dates: LF equals the earliest (smallest) LS of all it's immediate successors and LS equals LF minus duration. All activities with zero slack are on the critical path.
Solving simple AoA diagrams can be done quickly by calculating the duration of each possible path through the network. The longest path is the project duration and identifies the critical path.