Follow the yellow brick road (the critical path)

Abstract

This paper discusses the importance of the schedule critical path (CP) by guiding project managers through the steps needed to create a project schedule. It starts with the work breakdown structure (WBS) and ends with schedule flexibility, which is the real value to project managers.

All project managers should be able to utilize the schedule critical path (CP) because this information is what is necessary to bring a project in on schedule. The CP schedule tells you (relative to the schedule) where you are, where you are headed, and what it is going to look like when you reach the end. If you do not like any of these answers, then you have work to do to change it.

The CP is “the longest (time) sequence of activities in a project plan, which must be completed on time, for the project to be completed by the due date.” This means that if any activity on the CP is delayed, the project end time will be delayed, unless CP activities following the delayed activity are completed earlier than originally planned. The CP will also dictate the shortest time that the project can be completed.

Determining the CP will provide information that will help in:

1. Developing the Human Resources Plan (who I need, when I need them, what percent of their time I need, and when they will return to their functional group).
2. Establishing early and late start times as well as early and late finish times for each activity.
3. Calculating total float, which is an indication of scheduling flexibility.
4. Calculating project float and free float, if any.
5. Establishing a project schedule baseline to measure against.
6. Determining the overall health (status) of the project schedule.

For the purpose of this paper, we will use the following assumptions:

1. The project starts and ends with one activity.
2. The Precedent Diagram Method [PDM, also known as Activity on Node or (AON)] will be used. All activities will be scheduled based on a finish to start (F-S) relationship.
3. The term “activity,” even though it is officially the first level of time decomposition (Level 5 overall), is the name we will use for the lowest level of decomposition (regardless of time decomposition to lower levels).
4. The WBS/time decomposition is accurate and activity durations are reasonable.
5. The network sequencing is reasonable and the resource plan will generally happen as planned.

Finding the project CP starts with the work breakdown structure (WBS). The WBS was first introduced by the Department of Defense in June 1962. Later DOD published MIL-STD-881 for WBS. PMI adopted the concept in 1987 and currently publishes a Practice Standard for Work Breakdown Structures.

In most cases (other than very small and/or short projects), work element decomposition will continue below the work package level (Level 4), which is where the PMI WBS officially stops. Time decomposition will carry on to activities (Level 5), maybe to task (Level 6) and maybe to sub-task (Level 7), or even below, depending on project size, length, and complexity.

As with most schedule network methods, PDM also has its challenges. As the project grows larger, longer, and/or more complex, the sheer number of “activities” can easily get out of control. The ability to use proper PDM relationships degrades with project size. Project managers and their team will have to exercise restraint when it comes to time decomposition and expert judgment when assigning PDM relationships. Too many finish to starts, when other relationship are appropriate, extends the schedule, as do too many starts to starts and times when other relationships are required and the schedule excitability risk increases.

The PDM (AON) scheduling method shows linear progression of the work elements (sequence). Elements of work are put into containers, usually boxes. Lines with arrows are used to connect the boxes, which shows the PDM relationship amongst the activities and the order in which the elements of work will be accomplished. A PDM diagram is NOT time scaled. Neither the size of the box, nor the length of the line has any meaning. PDM also does not show the chronological relationship between elements of work, the amount of work, resource assignments, or importance of the work. PDM also requires additional considerations and constraints. These are dependencies, leads, and lags. Dependencies fall into one of the three following categories:

1. Mandatory dependency—This is sometimes called hard logic. There is a physical relationship between elements of work that requires certain elements to be performed in a certain sequence. An example of this is: packing boxes must be available before you can pack the books for an office move.
2. Discretionary dependency—This is sometimes called soft, preferred, or preferential logic. Discretionary dependencies are usually based upon experience or a best practice approach. An example of this would be to not begin painting walls in a new room before all sheet rock installers were off-site.
3. External dependency—This occurs when project activities are dependent on non-project work. An example of this might be when a project manager must secure senior management approval to proceed to phase two of a project after phase one is complete. The project manager has no control over how long it takes senior management to review phase one results and approve phase two.

Leads and lags are modifications to the finish to start (F – S) relationships.

A “lag” adds “wait time” between when the predecessor activity is completed and its successor can start. “Lags” are shown in one of three ways:

1. On the finish to start line between work elements A and B, you write “+3 days.”
2. On the finish to start line between work elements A and B, you write “3 days lag.”
3. You add an activity that is zero work effort, but 3 days duration between activity A and B.

A “lead” starts the next activity early. “Leads” are shown in one of three ways:

1. On the finish to start line between work elements A and B, you write “-3 days.”
2. On the finish to start line between work elements A and B, you write “3 days lead.”
3. You change the PDM relationship between work element A and B from finish to start (F – S) to start to start (S – S).

PDM relationships include the following four relationships:

Using the PDM logic and relationships allows us to “draw” the PDM (AON) network diagram. An example of a PDM (AON) network diagram is shown in Exhibit 2:

Exhibit 1- PDM Relationships

Remember that “activities,” which may be task, sub-task, etc., are from time decomposition. Activity durations are team estimates, expert judgment, or organizational process assets (OPA) (there could be others). Activity duration represents the amount of time that elapses between the start of an activity and its finish. This is never shorter than work effort and almost always longer.

Exhibit 2 - Example PDM Network Diagram

We shall now use a “Case Study” to illustrate all of these concepts. The project is BUILD A HOUSE. The deliverable we shall focus on is the “Landscape.” We are limiting our scope to one deliverable to keep the number of activities to less than 30. The overall scope of “Landscape” is show in Exhibit 3.

Exhibit 3 - “Landscape” Deliverable Scope

Duration estimates and sequencing the activities by the team yields the following chart:

Exhibit 4 - Duration and Sequencing the Activities

The “Landscape” deliverable PDM (AON) diagram looks like:

Exhibit 5 - “Landscape” Deliverable PDM Diagram

Once the PDM (AON) diagram is developed, there are several methods to determine the critical path. For simple, short, and less complex projects, inspection might work. For larger, more complex, and/or longer projects, software analysis might be called for.

For our Case Study, we shall use the critical path method (CPM) by hand. The CPM can use a single-point duration estimate and calculates the early and late start times for each activity. We shall calculate these early start times, for each activity, by performing what is called the Forward Pass. The late start times shall be calculated by performing what is called The Backward Pass, for each activity. We can then calculate total float (sometimes called slack) for each activity. Then we can identify the critical path, which has zero (Ø) total float.

In order to perform the forward and backward passes, we need to expand our network diagram “boxes” as shown in Exhibit 6.

Exhibit 6 - PDM “Box” Nomenclature

For the purpose of this paper and The Case Study, we will assume the deliverable “Landscape” starts with activity 25 on the morning of day zero (Ø). We will use the following equation: ES_s = ES_p + DUR_p (early start of the successor is the early start of the predecessor plus the duration of the predecessor).

We shall also use the equation: EF_c = ES_c + DUR_c (early finish of the current activity equals the early start of the current activity plus the duration of the current activity).

Starting with the first activity, work your way through the network diagram (left to right), from the first activity to the last activity. This will establish the ES and EF times for each activity. On path splits, pass the same value to all activities. On path convergences, pass the largest value to the successor. See the charts in Exhibit 7 and 8.

Exhibit 7 - The Forward Pass, Sheet 1

Exhibit 8 - The Forward Pass, Sheet 2

Now, we are ready to perform the Backward Pass. Transfer the ES value to the LS slot for the last activity. The justification for this is that our network diagram has all paths converging through activity 29. Activity 29 must be on the CP, as all paths go through it. If an activity is on the CP, its total float must be zero. Total float is equal to the late start time minus the early start time (TF = LS – ES). In order for TF to be zero (as it must be) LS and ES must be equal. Now start the Backward Pass using the following equation: LS_p = LS_s - DUR_p (late start of the predecessor is equal to the late start of the successor minus the duration of the predecessor).

We shall also use the equation: LF_c = LS_c + DUR_c (late finish for the current activity is equal to the late start of the current activity plus the duration of the current activity).

Starting with the last activity, work your way back through the network diagram (right to left), from the last activity to the first activity. This will establish the LS and LF for each activity. On path splits, calculate each path separately. On path convergences, pass the smallest value to the successor. See the charts in Exhibit 9 and 10:

Exhibit 9 - The Backward Pass, Sheet 1

Exhibit 10 - The Backward Pass, Sheet 2

Now that we have ES, LS, EF, and LF for each activity, we can calculate TF using the equation TF = LS – ES (total float equals late start time minus early start time) or LF – EF (late finish time minus late finish time). The path with zero TF is the critical path. It is possible to have more than one critical path. We will add the TF, in green, above our “boxes.” We will add a red underline under the critical path. See the charts in Exhibit 11 and 12,

Exhibit 11 - Calculate Total Float and ID the CP, Sheet 1

Exhibit 12 - Calculate Total Float and ID the CP, Sheet 2

There are two other types of float:

1. Project Float—Occurs (rarely) when the CPM project end date is shorter than the required end date. The equation is PF = CPMED – RED where:
   PF = Project float
   CPMED = CPM end date
   RED = Required end date
2. Free Float—The amount of time that a scheduled activity can be delayed without delaying the early start time of any immediate successor activity. It is given by the equation FF = ES_s - EF_p (free float is equal to the early start of the successor activity minus the early finish of the predecessor activity).

The last steps of developing a schedule are to:

1. Assign resources (people, materials, equipment, money, supplies, etc.) to each activity.
2. Level resources, as necessary.
3. Analyze the effect of resource assignment and leveling on the network diagram and project end time.
4. Consider:
   1. Changing PDM relationships
   2. Fast tracking the project
   3. Crashing the project
   4. Changing out resources
   5. Moving the end time out
   6. Reducing scope (non-PMI method)
5. Analyze the effect of the considerations in #4.
6. Establish a project start calendar date for activity 25, zero start time.
7. Convert the network diagram to a calendar-based, resource-loaded chart.

The completed CPM network diagram will give us information on options when scheduled activities go wrong or are about to go wrong. If a critical path activity is in danger of slipping or has slipped, for any reason (resources, allocations, durations, etc.), the critical path network schedule will provide information about what we might do to correct the problem. We should consider the following:

1. Move resources (if correct skills and they are available) from a non-critical path activity to the problem area. We can not leave the moved resource on the new assignment for longer than the TF on the non-critical path activity, or else the “left” non-critical path activity will become a parallel critical path.
2. Assign more resources (if correct skills are available) to later critical path activities to “make up” the previous slip. If we follow this method, we should consider the source of these resources in this order:
   1. a. First, from inside the project.
   2. Second, from outside the project, but within the organization.
   3. Third, from outside the organization.
3. Reconsider the list above, 4a through 4f from the previous paragraph.

The Yellow Brick Road (the Critical Path) is a powerful tool to develop and control a project schedule. Spend the time to develop it, execute it, and then to monitor and control the project schedule! Remember, the schedule critical path tells you (relative to the project schedule) where you are, where you are headed, and what it is going to look like when you reach project end. If you do not like the picture, then you have work to do to change it.