Project scheduling tools like MS Project generate critical path with utmost ease. However, it is necessary to know the calculations in critical path analysis. Understanding basic concepts of critical path analysis not only help project managers but also assist pmp certification aspirants. Therefore, solving a critical path method problem improves knowledge of this technique. Hence, this post demonstrates steps in critical path analysis with a solved example.
- 1 Critical Path Analysis – An Overview
- 2 Network Diagram for Critical Path Analysis
- 3 Critical Path Method (CPM) Example
- 4 Critical Path Analysis Steps
- 5 Step – 1 : Calculate the total number of paths and their duration.
- 6 Step – 2 : Indicate the Critical Path
- 7 Step – 3 : Perform Forward Pass on Critical Path
- 8 Step – 4 : Perform Backward Pass on Critical Path
- 9 Step – 5 : Perform Forward Pass on Activities Not On Critical Path
- 10 Step – 6 : Perform Backward Pass on Activities Not On Critical Path.
- 11 Step – 7 : Calculate Total Float
- 12 Step – 8 : Calculate Free Float
- 13 Conclusion
- 14 Author’s Profile
Critical Path Analysis – An Overview
Critical path analysis is the process of identifying the longest path in a schedule network diagram. It not only indicates completeness of project schedule but also helps to ascertain degree of flexibility. Moreover, critical path analysis also reveals the minimum duration required to complete a project.
In order to establish a critical path it is necessary to draw a schedule network diagram. Therefore, critical path analysis also specifies link between project activities. Not all activities can start and finish on time. Hence critical path analysis specifies permissible delays to activities that are not on critical path. Thus schedule flexibility is the permissible delay that does not affect project completion date.
Network Diagram for Critical Path Analysis
Techniques used to construct a project schedule network diagram are Arrow Diagram Method (ADM) and Precedence Diagram Method (PDM).
In order to construct the schedule network diagram, ADM uses Activity-on-Arrow (AOA) technique where as PDM uses Activity-on-Node (AON).
Program Evaluation And Review Technique (PERT) uses Activity-on-Arrow (AOA) where as Critical Path Method (CPM) uses Activity-on-Node (AON).
Most of the scheduling programs use PDM technique to construct schedule network diagram. Hence Critical Path Method (CPM) is the most popular schedule network analysis technique. Therefore, this article will demonstrate steps in critical path analysis with a solved example using CPM.
Critical Path Method (CPM) Example
Activity-on-Node (AON) method of constructing project schedule network diagram represents project activities on nodes. PMBOK uses the following nomenclature.
Critical Path Analysis Steps
To understand the steps involved in critical path analysis, consider the following schedule network diagram.
Step – 1 : Calculate the total number of paths and their duration.
- First path is Start (S) – A – D – E – End (E’) the duration of which is equal to 16 weeks
- The second path is S – A – E – G – E’ the duration of which is also equal to 16 weeks
- The third path is S – B – C – E – G – E’ the duration of which is equal to 22 weeks
- Fourth path is S – B – F – G – E’ the duration of which is equal to 20 weeks
The longest path is S-B-C-E-G-E’ with a duration of 22 weeks hence this is the critical path of the above network diagram.
Step – 2 : Indicate the Critical Path
Indicate the critical path on the network diagram with a bold line. The network diagram will look as follows
Step – 3 : Perform Forward Pass on Critical Path
The next step is to calculate early start and early finish of each activity. We need to start with activities on critical path.
Calculate ES and EF of activities on Critical Path.
The convention used here is that the project starts on day one. Another convention states that the project starts on day zero. We will stick to the convention indicated in PMBOK, which is, the project starts on day 1. Hence ES of first activity B on critical path is 1.
- EF = ES + Activity Duration – 1
- EF of Activity B = 1 + 6 – 1 = 6
- ES = EF of first node + 1 = 6 + 1 = 7
- EF = ES + Activity Duration -1 = 7 + 4 – 1 = 10
Repeat the above step till you reach the last node
Once the forward pass is complete the network diagram will look as follows. The following diagram looks different because of spreadsheet calculations. However, the schedule network logic has not changed.
Step – 4 : Perform Backward Pass on Critical Path
Perform backward pass to calculate Late Start and Late Finish.
Calculate LS and LF of activities on critical path
The total float of activities on critical path is zero. Hence on critical path LS = ES and LF = EF. Therefore, no backward pass calculation for activities on critical path. On completing the backward pass network diagram will look like this.
Step – 5 : Perform Forward Pass on Activities Not On Critical Path
- ES = 1 and EF = 1+4-1 =4
- ES = 4 and EF = 16
For activities with more than one preceding activity ES is latest of the earliest finish times of the preceding activities
When we have ES and EF of a particular node we can calculate the Total Float using the formula
Total Float = LS – ES or LF – EF
Step – 6 : Perform Backward Pass on Activities Not On Critical Path.
- LF = LS of Previous node -1 = 18 – 1 = 17
- LS = LF – Activity Duration + 1 = 17 – 9 + 1 = 9
- LF = 22 since this is the last activity not on critical path it can finish on week 22
- LS = 22 – 12 + 1 = 11
This node has two activities connected to it i.e D and E. In such conditions LF of node A is the earliest of the latest start times of the preceding activity. In this case it is same hence
- LF of node A is 11 – 1 = 10 and
- LS = 10 – 4 + 1 = 7
Step – 7 : Calculate Total Float
The following formula represents total float of an activity.
- Total Float = LS – ES or LF – EF
Upon completion of backward pass and calculation of total float the resultant network diagram will look as follows
Step – 8 : Calculate Free Float
For formula to calculate free float please refer to the following post
To summarize, critical path analysis reveals network information such as critical path, total float, and activity float. This data forms the basis for further project execution. Moreover, other advanced schedule analysis techniques use output of critical path analysis.
For tools and techniques to establish logical relationships between project activities, please read the following post
Visit the following page to know more about the formulas in critical path analysis.
Hope this is a useful post, for any queries you may visit Contact page.