# Critical Path Method Examples – Problems with Solution π₯

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

1. Krajewski, L. J., Malhotra, M. K., & Ritzman, L. P. (2015). Operations Management: Processes and Supply Chains, Student Value Edition (11th Edition) (11th ed.). Pearson.
2. Heizer, J., & Render, B. (2013). Operations Management (11th Edition) (11th ed.). Pearson.

## Example 1: Project in a high school

Consider the following data for a project to install a new server at a local high school:

 Activity Activity Time (days) Immediate Predecessor(s) A 4 – B 5 A C 4 A D 4 B E 1 B F 6 B,C G 3 D,E H 2 F I 5 F J 7 G,H,I
1. Draw a network diagram.
2. Calculate the critical path for this project.
3. How much slack is in each of the activities G, H, and I?

### Solution

a. The network diagram is:

Next we have the CPM diagram with the corresponding calculations:

b. The results of the project are:

The critical path is:
A β B β F β I β J

The total project time is: 27 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

I took the solved problem from Krajewski's book (1), Chapter 7, Exercise 1.