Develop Project Schedules by Analyzing Network Diagrams

Use the following two rules as you draw and interpret your network diagram. After you understand these rules, analyzing the diagram is a snap:

• Rule 1: After you finish an activity or reach a milestone, you can proceed to the next activity or milestone, as indicated by the arrow(s).
• Rule 2: Before you can start an activity or reach a milestone, you must first complete all activities and reach all milestones with arrows pointing to the activity you want to start or the milestone you want to reach.

The figure illustrates a network diagram. According to Rule 1, from Project Started, you can proceed to work on either Activity 1 or 3, which means you can do either Activity 1 or Activity 3 by itself or both Activities 1 and 3 at the same time. In other words, these two activities are independent of each other.

You may also choose to do neither of the activities. Rule 1 is an allowing relationship, not a forcing (or requiring) relationship. In other words, you can work on any of the activities that the arrows from Project Started lead to, but you don’t have to work on any of them.

For example, suppose a part of your plan includes two activities to build a device: receive parts and assemble parts. As soon as you receive the parts, you can start to assemble them; in fact, you can’t start to assemble them until you receive them. But after you receive all the parts you ordered, neither rule says you must start to assemble them immediately; you can assemble them if you want to, or you can wait. Of course, if you wait, the completion of the assembly will be delayed. But that’s your choice.

According to Rule 2, you can start working on Activity 2 in Figure 1-2 as soon as you complete Activity 1 because the arrow from Activity 1 is the only one leading to Activity 2. Rule 2, therefore, is a forcing relationship, because it forces you to wait until you complete Activity 1 before you can begin working on Activity 2. If arrows from three activities led to Activity 2, you’d have to complete all three activities before starting Activity 2. (The diagram wouldn’t indicate that you could start working on Activity 2 by completing only one or two of the three activities that led to it.)

You can use your network diagram to figure out when to start and end activities and when you’ll finish the entire project if you perform the activities in this way. To find out the schedule that your approach will allow, you need the following information:

• Critical path: A sequence of activities that takes the longest time to complete (this is also the shortest time in which you can complete your project)
• Noncritical path: A sequence of activities in which you can delay activities and still finish your project in the shortest possible time
• Slack time (also called float): The maximum amount of time you can delay an activity and still finish your project in the shortest possible time
• Earliest start date: The earliest date you can start an activity
• Earliest finish date: The earliest date you can finish an activity
• Latest start date: The latest date you can start an activity and still finish your project in the shortest possible time
• Latest finish date: The latest date you can finish an activity and still finish your project in the shortest possible time

You can use the critical path method (CPM) to determine this information and to build your project’s overall schedule. The following sections illustrate how this method works.

The importance of the critical path

The length of your project’s critical path(s) in your network diagram defines your project’s length (hence, the critical path method for determining your project’s schedule). If you want to finish your project in less time, consider ways to shorten its critical path.

Monitor critical-path activities closely during performance because any delay in critical-path activities delays your project’s completion. Also closely monitor any activities on paths that are close to being critical, because any minor delay on those paths can also delay your project’s completion.

Your project can have two or more critical paths at the same time. In fact, every path in your project can be critical if every one of them takes the same amount of time. However, when every path is critical, you have a high-risk situation; a delay in any activity immediately causes a delay in the completion of the project.

Critical paths can change as your project unfolds. Sometimes activities on a critical path finish so early that the path becomes shorter than one or more other paths that were initially considered noncritical. Other times, activities on an initially noncritical path are delayed to the point where the sum of their completion times becomes greater than the length of the current critical path (which turns the initially noncritical path into a critical one).

The forward pass: Determining critical paths, noncritical paths, and earliest start and finish dates

Your first step in analyzing your project’s network diagram is to start at the beginning and see how quickly you can complete the activities along each path. You should determine this information without taking into account any effects that constraints on the availability of personnel or other resources may have. This start-to-finish analysis is called the forward pass.

To help you understand what a forward pass is, you can perform one through the diagram shown. According to Rule 1, you can consider working on either Activity 1 or Activity 3 (or both together) as soon as the project starts. First, consider Activities 1 and 2 on the upper path:

• The earliest you can start Activity 1 is the moment the project starts (the beginning of week 1).
• The earliest you can finish Activity 1 is the end of week 5 (add Activity 1’s estimated duration of five weeks to its earliest start time, which is the start of the project).
• According to Rule 2, the earliest you can start Activity 2 is the beginning of week 6 because the arrow from Activity 1 is the only one leading to Activity 2.
• The earliest you can finish Activity 2 is the end of week 6 (add Activity 2’s estimated duration of one week to its earliest start time at the beginning of week 6).

So far, so good. Now consider Activities 3 and 4 on the lower path of the diagram:

• The earliest you can start Activity 3 is the moment the project starts (the beginning of week 1).
• The earliest you can finish Activity 3 is the end of week 1.
• The earliest you can start Activity 4 is the beginning of week 2.
• The earliest you can finish Activity 4 is the end of week 4.

You have to be careful when you try to determine the earliest you can start Activity 5. According to Rule 2, the two arrows entering Activity 5 indicate you must finish both Activity 1 and Activity 4 before you begin Activity 5. Even though you can finish Activity 4 by the end of week 4, you can’t finish Activity 1 until the end of week 5. Therefore, the earliest you can start Activity 5 is the beginning of week 6.

If two or more activities or milestones lead to the same activity, the earliest you can start that activity is the latest of the earliest finish dates for those preceding activities or milestones.

Is your head spinning yet? Take heart; the end is in sight.

• The earliest you can start Activity 5 is the beginning of week 6.
• The earliest you can finish Activity 5 is the end of week 7.
• The earliest you can finish Activity 2 is the end of week 6. Therefore, the earliest you can finish the entire project (and reach the milestone called Project Ended) is the end of week 7.

So far, you have the following information about your project:

• The length of the critical path (the shortest time in which you can complete the project) is seven weeks. Only one critical path takes seven weeks; it includes the milestone Project Started, Activity 1, Activity 5, and the milestone Project Ended.
• Activity 2, Activity 3, and Activity 4 aren’t on critical paths.

The backward pass: Calculating the latest start and finish dates and slack times

You’re halfway home. In case resource conflicts or unexpected delays prevent you from beginning all the project activities at their earliest possible start times, you want to know how much you can delay the activities along each path and still finish the project at the earliest possible date. This finish-to-start analysis is called the backward pass.

To expand on the example introduced in the preceding section, the forward pass indicates that the earliest date you can reach the milestone Project Ended is the end of week 7. However, Rule 2 in the earlier section “Reading a network diagram” says you can’t reach the milestone Project Ended until you’ve completed Activities 2 and 5. Therefore, to finish your project by the end of week 7, the latest you can finish Activities 2 and 5 is the end of week 7. Consider the lower path on the diagram with Activities 3, 4, and 5:

• You must start Activity 5 by the beginning of week 6 to finish it by the end of week 7 (because Activity 5’s estimated duration is two weeks).
• According to Rule 2, you can’t start Activity 5 until you finish Activities 1 and 4. So you must finish Activities 1 and 4 by the end of week 5.
• You must start Activity 4 by the beginning of week 3.
• You must finish Activity 3 before you can work on Activity 4. Therefore, you must finish Activity 3 by the end of week 2.
• You must start Activity 3 by the beginning of week 2.

Finally, consider the upper path on the network diagram:

• You must start Activity 2 by the beginning of week 7.
• You can’t work on Activity 2 until you finish Activity 1. Therefore, you must finish Activity 1 by the end of week 6.

Be careful in your calculations. You must finish Activity 1 by the end of week 5 to start Activity 5 at the beginning of week 6. But to start work on Activity 2 at the beginning of week 7, you must finish Activity 1 by the end of week 6. So, finishing Activity 1 by the end of week 5 satisfies both requirements.

If two or more arrows leave the same activity or milestone, the latest date you can finish the activity or reach the milestone is the earliest of the latest dates that you must start the next activities or reach the next milestones.

In the figure, the latest start dates for Activities 2 and 5 are the beginnings of week 7 and week 6, respectively. Therefore, the latest date to finish Activity 1 is the end of week 5. The rest is straightforward: You must start Activity 1 by the beginning of week 1 at the latest.

To organize the dates you calculate in the forward and backward passes, consider writing the earliest and latest start dates and the earliest and latest finish dates at the top of each milestone or activity box in the project’s network diagram. The following figure illustrates how this looks for the example shown.

Now that you have all the earliest and latest start and finish dates for your milestones and activities, you need to determine the slack time for each activity or milestone. You can determine slack time in one of two ways:

• Subtract the earliest possible start date from the latest allowable start date.
• Subtract the earliest possible finish date from the latest allowable finish date.

Thus, you can determine that Activities 2, 3, and 4 have slack times of one week, while Activities 1 and 5 have no slack time.

If an activity’s slack time is zero, the activity is on a critical path.

Although slack time is defined as the amount of time an activity or milestone can be delayed without delaying your project’s completion date, slack time is actually associated with a path of activities rather than with an individual activity. The information in the preceding figure indicates that both Activity 3 and Activity 4 (which are on the same path) have slack times of one week. However, if the start of Activity 3 is delayed by a week to the beginning of week 2, the earliest that Activity 4 can start will be the beginning of week 3, and it will have zero slack time.