Welcome to PM Calculators, a site dedicated to providing excellent online calculators for business management, including project management. In this post we will use our online critical path method (CPM) calculator and PERT-CPM diagram to develop critical path method examples.
In the following examples, we will perform critical path analysis and CPM network diagrams (Activity-on-node).
We have taken the critical path method problems from the major operations management books used in university teaching as
- Krajewski, L. J., Malhotra, M. K., & Ritzman, L. P. (2015). Operations Management: Processes and Supply Chains, Student Value Edition (11th Edition) (11th ed.). Pearson.
- Heizer, J., & Render, B. (2013). Operations Management (11th Edition) (11th ed.). Pearson.
The following information is known about a project to upgrade a point-of-sale system at Kids and Tots Apparel.
| Activity | Activity Time (days) | Immediate Predecessor(s) |
| A | 8 | – |
| B | 4 | A |
| C | 3 | A |
| D | 5 | B,C |
| E | 4 | D |
| F | 2 | E |
| G | 8 | E |
- Draw a network diagram for this project.
- Determine the critical path and project duration.
- Calculate the slack for each activity.
Solution
a. The network diagram is:
The activity diagram in nodes with all time and float calculations is:
b. The results of the project are:
The critical path is:
A → B → D → E → G
The total project time is: 29 days
c. The following table shows the results for each activity:
| Activity | Time | Early Start (ES) | Early Finish (EF) | Late Start (LS) | Late Finish (LF) | Slack (S) |
|---|---|---|---|---|---|---|
| A | 4 | 0 | 4 | 0 | 4 | 0 |
| B | 5 | 4 | 9 | 4 | 9 | 0 |
| C | 4 | 4 | 8 | 5 | 9 | 1 |
| D | 4 | 9 | 13 | 13 | 17 | 4 |
| E | 1 | 9 | 10 | 16 | 17 | 7 |
| F | 6 | 9 | 15 | 9 | 15 | 0 |
| G | 3 | 13 | 16 | 17 | 20 | 4 |
| H | 2 | 15 | 17 | 18 | 20 | 3 |
| I | 5 | 15 | 20 | 15 | 20 | 0 |
| J | 7 | 20 | 27 | 20 | 27 | 0 |
We got the example from Krajewski’s book (1) Chapter 7, Problem 2.