Critical Path Method Calculator πŸ₯‡ PERT and CPM Diagram

PM Calculators presents as premium content for our subscribers with membership, our critical path method calculator, and PERT CPM diagram online where you can solve classic project management exercises with a few clicks. In addition, we have included a free version of our tool, limited to exercises of 10 activities, and that only shows the result of the total project time and calculates the critical path.

PERT CPM Diagram - Free Version


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How to use the critical path method calculator and online PERT CPM diagram

To use our tool (pro version) we will follow the following steps:

  • Enter the number of activities for the exercise (For a graphic display issue, we suggest that it enter a maximum of 50 activities; however, the application accepts up to 120 activities).
  • Select the duration option depending on the exercise data (fixed times or three times). You must also choose in which it will enter units the duration data. If you do not have this information, you can leave the default option (hours). Then click on generate model.
  • Record the data of the precedents of each activity and its duration.
  • Click on solve. The page will validate if the data entered is correct. If there is an error, it will show a message at the bottom.
  • If the data entered is valid, the problem results will be calculated and displayed:
    • A table with the details of the relationships between each activity.
    • The graph of the PERT CPM diagram. Clicking on the nodes display the data for each activity. You can also move the nodes to place them in a more suitable position.
    • The red nodes represent the critical path. You can save the image to computer by right clicking on the graphic.
    • It will generate a schedule with the problem data which you can download as an image.
    • It will display the table with the data of nearest start (IP), nearest term (TP), furthest start (IL), furthest term (TL) and slack.
    • If the exercise has 3 times, it will display an additional table with the results of the estimated time, standard deviation and variance.
    • It shows the total results and critical path of the exercise in a green box.
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We will see its use with an example:

Example

A small project consisting of eight activities has the following characteristics:

Activity Preceding activity Most optimistic time (weeks) Most likely time (weeks) Most Pessimistic time (weeks)
A 2 4 12
B 10 12 26
C A 8 9 10
D A 10 15 20
E A 7 7.5 11
F B,C 9 9 9
G D 3 3.5 7
H E,F,G 5 5 5
  1. Draw the PERT network for the project.
  2. Prepare the activity schedule for the project.
  3. Determine the critical path.

Solution:

We enter the number of activities:

PERT CPM diagram online

Later we record the problem data:

Project Problem

Each activity is broken down by its precedents and descendants:

Predecessor Activity Successor
Start β†’ A A A β†’ C
A β†’ D
A β†’ E
Start β†’ B B B β†’ F
A β†’ C C C β†’ F
A β†’ D D D β†’ G
A β†’ E E E β†’ H
B β†’ F
C β†’ F
F F β†’ H
D β†’ G G G β†’ H
E β†’ H
F β†’ H
G β†’ H
H H β†’ End

This table serves as a guide to build our PERT CPM diagram. It added two dummy activities to show the start and end. The activities with 0 (zero) slack are the ones that make up the critical path.

PERT CPM diagram

PERT CPM Diagram

Clicking on the node shows more details:

PERT CPM Online

Likewise, a schedule of activities is generated with the problem data. It takes the current day as the start date when solving the problem.

Critical Path

The following table presents the results to determine the critical path:

  • Early Start (ES): It is equal to the Early Finish to the activity’s precedent. If it has more than one precedent, the highest value is taken.
  • Early Finish (EF): It is equal to the Early Start of the activity plus its duration (t). EF = ES + t.
  • Late Start (LS): It is equal to the Late Finish minus its duration (t). LS = LF – t.
  • Late Finish (LF): It is equal to the late start of the activity that follows. If it has more than one successor, the lowest value is taken.
  • Slack (S): It can be calculated in two ways. S = LS – ES = LF – EF. Activities with zero clearance make up the critical path.
  • When the results include repeating decimal numbers, the periodic part is presented within parentheses. Example: 0.(3) = 0.3333…

For each activity the calculations are made as follows:

  • Time Estimate: Te = (To + 4Γ—Tm + Tp) Γ· 6
  • Standard Deviation: Οƒ = (Tp – To) Γ· 6
  • Variance = Οƒ2
  • Project variance = Σσi2. i=Activities that belong to the critical path. In the case of several critical paths, the one with the greatest variance is chosen.
Activity Optimistic Time (To) Mean Time (Tm) Pessimistic Time (Tp) Time Estimate (Te) Standard Deviation (Οƒ) Variance (Οƒ2)
A 2 4 12 5 1.(6) 2.(7)
B 10 12 26 14 2.(6) 7.(1)
C 8 9 10 9 0.(3) 0.(1)
D 10 15 20 15 1.(6) 2.(7)
E 7 7.5 11 8 0.(6) 0.(4)
F 9 9 9 9 0 0
G 3 3.5 7 4 0.(6) 0.(4)
H 5 5 5 5 0 0

Final reflection

As you can see, this tool is very easy to use as well as having the advantage of being online; so you can use it anywhere with internet access. We hope that you are part of our membership and have access to all our premium material such as this calculator.

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