Project Schedule Network Diagramming

Executive Summary

Project Schedule Network Diagrams are an output of the Sequence Activities process in the Project Schedule Management Knowledge Area.  They are generated from a technique called Precedence Diagramming Method.  This technique is used to show the logical dependencies/relationships of activities, which are represented by nodes on the diagram.  This technique is exceptionally important on exam day and should be a big part of your Study Plan.

• Theories at Work
  • Precedence Relationships
  • Critical Path Method
  • Forward Pass
  • Backward Pass
  • Float (also called Total Float or Slack)
  • Free Float
• Critical concepts

As you can see from the “Theories at Work” section, Project Schedule Network Diagrams bring many tools and techniques to bear at one point.  The overall goal is to create a diagram of how activities will need to be sequenced or performed.  It will also allow us to update our Project Documents with details pertaining to Activity Attributes, the Activity List, the Assumption Log, and the Milestone List.  This will feed heavily into the Develop Schedule process, gain more details in the Estimate Activity Durations process, and be revisited for variances in planned versus actual performance in the Control Schedule process.  So… not something to be overlooked or taken lightly…

In order to be successful on the PMP^® exam, you must be able to understand and use the Precedence Diagramming Method.  Let’s run through the “Theories at Work” and put all of the pieces to the puzzle to work for us.

Precedence Relationships describe the logical dependencies between a predecessor and successor activities.  Shown below, Figure 6-9 in the Project Management Body of Knowledge (PMBOK^®) shows the four types of precedence relationships.

These dependencies will help us determine several things.  First, we can outline whether we will be using Activity on Arrow (AOA) diagrams or Activity on Node (AON) diagrams.  While seldom used, the Activity on Arrow diagram outlines the dependencies with (usually) circular nodes and the duration is listed on the arrow.  The AOA diagram can only be used for Finish-to-Start relationships.  The much more commonly used AON diagram can be used for any relationship and outlines the dependencies with the arrow and the duration is listed on the node.

Another thing that the dependencies can tell us (when using the AON diagram) is how the arrows will connect the nodes.  In the example above, all of the relationships are Finish-to-Start relationships because the arrow protrudes from the right (back/finish) of the predecessor and enters the left (front/start) of the successor.  Other relationships are graphically displayed according to their representation from Figure 6-9 of the PMBOK.

NOTE: For the remainder of this article, we will be utilizing an AON diagram with Finish-to-Start relationships.

Once you have laid out the Schedule Network diagram, you are going to need to add some detail from another process, Estimate Activity Durations.  This detail will allow you to determine the amount of time each activity will take based upon its estimate and place it on the diagram.  Once it is present, you can use the Critical Path Method to determine the minimum project duration and determine if any scheduling flexibility exists on all network paths.  Let’s use the AON diagram below to determine the Critical Path of the project.

Tracing from left to right, we need to determine ALL network paths that exist before attempting to determine which path(s) is/are the Critical Path(s).  The network paths are [A-B-D-E], [A-B-D-F-G], [C-D-E], and [C-D-F-G].  We determine which path is the longest in duration (i.e. the shortest amount of time to finish the project) by adding all of the activity estimates together.

A5 + B3 + D4 + E6 = 18

A5 + B3+ D4 + F3 + G1 = 16

C7 + D4 + E6 = 17

C7 + D4 + F3 + G1 = 15

For this diagram, the longest path is [A-B-D-F] which has a duration of 18 days, meaning that the shortest amount of time that this project will take is 18 days.  This is the Critical Path.  It is possible to have more than one Critical Path on a project.

Now let’s add some more details to our AON diagram.  From here, we are going to perform forward and backward passes through the activities to determine the earliest (Forward Pass) and latest (Backward Pass) that activities can start and finish.

For the Forward Pass, the Early Finish (EF) of the predecessor becomes the Early Start (ES) of the successor. The first activity from start always starts at “0.”  In other words, the ES of activities A and C, are 0.  Add the duration to the ES to determine the EF.  Activity A has an ES of 0 and an EF of 5.  Activity C has an ES of 0 and an EF of 7.  Take the EF of Activity A and make that the ES of Activity B. Then add the duration to the ES of Activity B to determine its EF.  So Activity B has an ES of 5 and an EF of 8.  Simple, right?  Now we come to a point where two predecessor activities feed into the same successor activity.  Since the EF of Activity B is actually greater than the EF of Activity C, we need to use the larger number.  This is because of the dependence on both activities to complete before you can start Activity D.  So we see that Activity D has an ES of 8, and after adding the duration, an EF of 12.  This continues until you know the ES and EF of all activities on the Schedule Network Diagram, eventually seeing that the Early Finish of the Project is 18.

Now it’s time to perform a backward pass on our activity paths.  Here we will work from right to left to determine the late finish (LF) and late start (LS) of each activity.  We still take into consideration the larger number for activities when more than one predecessor activity feeds into the successor activity.  Since we know the EF of the project is 18, it is automatically the LF for the project.  Moving left, we use 18 as the LF for Activity E and Activity G.  Subtract the duration of the activity to determine its LS.  Activity E has an LF of 18 and an LS of 12.  Activity E has an LF of 18 and an LS of 17.  This continues until we have the LF and LS of each activity.  If you’re drawing this out on your own, you should have the below as your ‘answer key.’  Notice that the previously defined Critical Path of [A-B-D-F] has the same ES and LS and the same EF and LF.  We’ll get to why that is significant in just a second…

The next item on our “Theories at Work” list is to determine Float (or Total Float/Slack).  Float is the amount of time that an activity can be delayed from its scheduled start without delaying the completion date.  We determine the float of an activity by subtracting either the ES from the LS or by subtracting the EF from the LF.  EXAM TIP: Items on the Critical Path will always have a Float of “0.”

Let’s put it into practice and determine the Float of our activities.  For all activities, use the formula above to determine the Float.  Once complete, your answer key should look like the below picture.  Take note that any activity that has an identical EF and LF or ES and LS will have a Total Float of “0” and be on the Critical Path.

Next, we’ll talk about Free Float.  Free Float is different from Float.  Free Float considers how long a predecessor activity can be delayed AND extended beyond its EF without delaying the ES of its immediate successor.  In the example we have been using so far, we don’t have an ‘easy example’ of Free Float.  We will use a much more easily identifiable example of Free Float to explain this concept.  In the picture below, you can see that Activity A has an EF of 2, and Activity B has an EF of 5.  Activity E is dependent on both Activity A and Activity B and therefore has an ES of 5.  This means that Activity A can be delayed or extended for up to 3 days without affecting Activity E.

Frequently Asked Questions

Q: Will I have to perform this for all of my projects?

A: That depends…  You need to be able to perform this in a rudimentary fashion for the test, but in most cases, you will have some form of scheduling software for “real world” projects.  This is an important concept to understand, but oftentimes it is not practiced on actual projects.  A solid understanding of the basics of Schedule Network Diagrams will help you on real projects after the PMP exam to determine strategic points for Schedule Compression techniques.  If project timeline constraints require it, you may need to perform either Crashing or Fast-Tracking of the schedule to reduce the overall duration.  Just remember that when you perform schedule compression techniques that you may change the Critical Path, create more than one Critical Path, or be forced to Crash or Fast-Track more than one path to achieve your goals.  This is also true on exam day…

What to Memorize

There is not much that you can add to your Brain Dump for the exam in this area.  Adding the formula for determining Float and Free Float may be handy, or you may want to include a quick graphic on how to perform a Forward and Backward Pass to the Brain Dump.  This area requires practice to become efficient.  You will likely see a few test questions that require you to quickly draw a Schedule Network Diagram to answer the question.

KA Critical Reasoning & Testing Skills

Q: You are the Project Manager on a project to refurbish an office space.  You are preparing a Schedule Network Diagram for the project to graphically display this for your Project Sponsor and the project team.  Given the activity list below, you determine that the fastest the project can be completed is ____ days and the Critical Path is _______________________.

Activity	Predecessor	Duration (in days)
A	Start	3
B	Start	5
C	B	4
D	A, C	7
E	D	3
F	E, G	7
G	C	11

1. 27, [B-C-F-G]
2. 20, [A-D-E-F]
3. 27, [B-C-G-F]
4. 26, [B-C-D-E-F]

EXPLANATION: In order to complete this scenario, we need to create a Schedule Network Diagram to graphically show the relationships and duration of each activity.  After drawing, the diagram and calculating the duration, we can see that there are four paths; [A-D-E-F], [B-C-D-E-F], and [B-C-G-F].  After adding the duration of each activity for each path, we see that [A-D-E-F] has a duration of 20 days,  [B-C-D-E-F] has a duration of 26 days, and [B-C-G-F] has a duration of 27 days.  This means that the shortest amount of time the project can be completed in is 27 days, so answers B and D are out.  Now, look at the two remaining answers, A and C.  They have the correct duration, but the incorrect order.  The order of the activities is [B-C-G-F], so answer D is our correct answer here.

Closing Summary

Schedule Network Diagrams are an important tool for a variety of reasons.  The most obvious of which is the ability to take apart a question on exam day to determine the Critical Path, the Free Float, Total Float, or perform Schedule Compression on an activity list.  This HAS TO BE a part of your Study Plan, and you should attempt to become efficient at drawing these correctly.  Many of the examples in this article are oversimplified in order to assist with helping you understand the concepts.  The questions on the exam will not be quite so simple and may even contain distracting information that prevents you from achieving the success you need to pass the exam.  Make sure that you enlist the help of a few experts, like the team at PM-ProLearn, to help you perform your best on test day!