W19_AK_CPM and PERT analysis

1.Problem Definition

We have a project for new server monitoring installation for one of the biggest operator in Indonesia.  We want to create CPM schedule for this project and find out also which path become the critical path.

Please find below list installation activity :


Please find below the activity breakdown structure :


2.Feasible alternatives

We want to analyze the schedule by using this two method :

  • CPM
  • PERT

3. Develop the outcomes

# Activity Path

We try to create the activity path base on the duration time on the previous table to find out the critical path. Please find below the activity path :


# Define the critical path

Four statement will always be true about critical path :

  • It is the longest path in the network
  • It is the path that define the earliest completion date of the project
  • It is usually the path with the least total float
  • It is the path on which any activity expansion or delay will lengthen the total project duration

So by definition above, we can find the critical path is :

Critical Path : B-D-F-G-J-K-L-M-N

Based on our experiences then we can make up the data for low duration, most likely duration and high duration :


# Using CPM Approach

The step involve in assessing the risk of schedule are as follow :

  • Create a complete CPM network
  • Develop three duration estimates (optimis, pessimistic and most likely) for each activity.
  • Identify the duration for all activities
  • Evaluate the result (estimate completion date and identified the highest risk path)
  • Initiate status monitoring

CPM Formula (with triangular distribution):

Expected duration : (Low + Most Likely + High)/3


4. Select Acceptable Criteria

# Using PERT Method

PERT was develop as formal technique by US Navy program in 1958.  PERT was intended not so much to manage a project better , but to determine the mean(average) and standard deviation of the completion date of the project. The basic concept is the pert critical path uses average duration based on the range of possible durations. Pert recalculate activity durations to incorporate the full range of possible duration.

Please find below PERT Formula :

a = best case

m = most likely

b = worst case

te = Expected time = (a + 4m + b)/6

Ϭ = standard deviation = (b – a)/6

Ϭ2 = variance


Base on the table, we can find result as below : (Path :B-D-F-G-J-K-L-M-N)

Ϭ = √0.25+0.09+0.25+0.09+0.09+0.25+0.09+0.36+0.09 = 1.24 round up to 1.5 days

Total Expected time become te = 20


5.  Compare the outcome

# CPM Table

The table summarizes the information from the CPM and risk analysis for duration of critical path, the most likely estimate is 19 days . The risk assessment show that the average duration is 21 days, an “expected” or average schedule slippage of 2 days.

Result of risk analysis :

  • The CPM path duration is not the most likely
  • The most likely duration is 19 days
  • The average duration is 21 days

# PERT Table

Path B-D-F-G-J-K-L-M-N , means that probability that this path shows that it is 68% likely that the project will take between 18.5 and 20 days. It also mean that is is 84% likely (50% + 34%) that this path will be complete within 21.5 days and 97.5% likely (50% + 34% + 13.5%) that it will be complete within 23 days.

6. Best criteria from mimimum

# From CPM by triangular distribution

By triangular distribution, in general it is good assumption and easy distribution to use.  It clearly provide information about risk analysis. That’s why CPM is a the beginning of a complete scheduling exercise not the end result.

# Pert Data

Because we have experience on this project then we can calculate  for low, most likely and high data for the critical path. I think we can use pert for this project, because we have experience data about it and also this Beta distribution is not as risky as the CPM triangular method.  This method will weight all tree values equally , Average in PERT : (Low + 4xMost Likely +High)/6

7. Performance monitoring and post result

We must really take concern on the activities that lies on the critical path, as we know that in some activities management want that the activities finish on the “low time” which is different with our experiences, the activities usually finished on the “most likely time”. We must really take performance and control on those activities.

8. Conclusion

Because I just do analyze using CPM and PERT, then I just made summary about the two method. Please find below about it :



Critical Path Analysis and PERT Charts, Planning & scheduling more complex projects . Retrieved from http://www.mindtools.com/critpath.html. 

Pert and CPM. Retrieved from http://cacareer.weebly.com/uploads/2/0/4/0/2040831/cpm__pert.pdf , web 29 june 2013

Acuna, R. (2009) , ANALYSIS OF PROJECT PLANNING USING CPM AND PERT , In Partial Fulfillment of Math 4395-Senior Project. Retrieved from http://cms.uhd.edu/faculty/redlt/leoaseniorproject.pdf.

Dwivedi, U. Critical Path Method and Critical Chain Project Management , retrieved from http://www.refresher.com/CriticalChainProjectManagement.pdf , web 29 njune 2013.

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1 Response to W19_AK_CPM and PERT analysis

  1. drpdg says:

    Hi Andi,
    Be VERY careful on this……PERT is NOT another form of CPM……. PERT is a RISK ANALYSIS tool that can be “applied” or “adapted” for use in CPM.

    There are only two types or “flavors” of CPM- Activity on Arrow or ADM method and Activity on Node or PDM. Suggest you go back and look over my slides from Day 4 afternoon on scheduling.

    Dr. PDG, Boston MA, USA

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