Project Scheduling Mastery: Techniques, Critical Path Analysis, Total Slack, and Free Slack

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Project Scheduling Mastery: Techniques, Critical Path Analysis, Total Slack, and Free Slack

System Analysis and Design · Chapter 9: Project Management, Scheduling, and QualitySection 9.4 · lesson 63 of 698 min · free with a free account

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In this lesson

Dependencies, AON diagrams, PERT estimates, forward and backward passes, and slack.

  • Explain activity dependencies, and read an AON network diagram
  • Apply the three-point PERT formula
  • Perform forward and backward passes to find ES, EF, LS, and LF
  • Distinguish total from free slack, and compare crashing with fast-tracking

Transcript

Everything said in the video, section by section (1,104 words). Read along, or search it.

Project Management, Scheduling, and Quality

Project Scheduling and the Critical Path

A plan becomes a schedule once you know what depends on what, and how long each piece takes. This section works through one small project, step by step. Dependencies and network diagrams, a formula for estimating durations, and the forward and backward passes that find the critical path. Then the two kinds of slack, and two ways to finish a project sooner.

Activity Sequencing

The Worked Example: 6 Activities

A schedule starts with a list of activities, and the dependencies between them. Most dependencies are finish-to-start. An activity cannot start until its predecessor finishes. Other types exist, such as start-to-start, finish-to-finish, and start-to-finish, for activities that overlap in other ways. But finish-to-start is by far the most common. The worked example has six activities. A takes three days, and must finish before B or C can start. B takes five days, and must finish before D, which takes four. C takes four days, and must finish before E, which takes six. And F, the final activity, takes three days, and cannot start until both D and E are finished.

Three-Point Estimates

The PERT Formula

A single duration estimate hides how uncertain it really is. A three-point estimate asks for three numbers instead. An optimistic duration, if everything goes right. A most likely duration. And a pessimistic duration, if things go wrong. The PERT formula combines them into one weighted estimate. Add the optimistic value, four times the most likely value, and the pessimistic value, then divide by six. Weighting the most likely value by four pulls the estimate toward it. For activity B, an analyst gathered an optimistic estimate of three days, a most likely of five, and a pessimistic of nine. Three, plus four times five, plus nine, gives thirty-two. Divided by six, that is about five point three three days. That estimate could replace B's duration in the network. To keep the arithmetic clean, the passes that follow keep B at five days.

Critical Path Method

Forward Pass, Then Backward Pass

The critical path method works through the network twice. The forward pass moves left to right. It finds each activity's early start and early finish, the soonest it could start and finish. An activity's early start is the largest early finish among all of its predecessors. The first activity starts at zero. And its early finish is simply its early start, plus its duration. The backward pass moves right to left, from the project's finish. It finds each activity's late finish and late start, the latest it could run without delaying the whole project. An activity's late finish is the smallest late start among its successors. For the last activity, it is the project's finish. And its late start is its late finish, minus its duration.

Figure 9.1

The Completed Network

Here is the worked example as an activity-on-node diagram. Each activity is a box, and the arrows show the dependencies. This notation has become the standard, largely because each activity's calculated values fit right inside its own box. Each box shows the activity's duration, its early start and early finish, and its late start and late finish. The highlighted boxes and arrows, A, then C, then E, then F, are the critical path.

The Passes, Activity by Activity

Every Value in One Table

Here is how the passes played out. Forward, A starts at zero and finishes at three. B and C can both start at three. B finishes at eight, and C at seven. D starts once B finishes, at eight, and finishes at twelve. E starts once C finishes, at seven, and finishes at thirteen. F needs both D and E. D finishes at twelve, E at thirteen, so F's early start is the larger, thirteen. F finishes at sixteen. That is the project's earliest possible finish. Backward from day sixteen, B's late finish of nine comes from D's late start. And A's late finish of three is the smaller of B's and C's late starts. Total slack is late start minus early start. A, C, E, and F have none. B and D have one day each. The activities with zero slack form the critical path. It is the longest path through the network, and any delay on it delays the whole project.

2 Kinds of Slack

Total Slack vs. Free Slack

Slack comes in two kinds. Total slack is how much an activity can slip without delaying the project's finish. Free slack is stricter. It is how much an activity can slip without delaying the early start of its very next successor. It is the successor's early start, minus the activity's own early finish. B and D show why the difference matters. Both have one day of total slack. But B's free slack is zero. D's early start sits exactly at B's early finish, day eight. So any delay to B pushes D out immediately, even though the project as a whole absorbs it. D's free slack is the full day. F cannot start until day thirteen regardless, so it makes no difference whether D finishes on day twelve or thirteen.

Schedule Compression

Crashing vs. Fast-Tracking

When a project has to finish sooner than the critical path allows, two compression techniques are common. Crashing adds resources to a critical path activity, to shorten its duration. Assigning two more developers to activity E, so it takes four days instead of six, is crashing. It usually costs more, and the benefit shrinks the further an activity is crashed. Fast-tracking overlaps activities that would normally run one after another, doing them in parallel. Starting E before C is fully finished, based on C's partial results, is fast-tracking. The trade-off is a higher risk of rework. Both only work on the critical path. Shortening B or D would not shorten the project at all.

Key Terms

The Vocabulary of This Section

Let's lock in the key terms. A finish-to-start dependency means a successor cannot begin until its predecessor is done. An activity-on-node diagram shows activities as nodes, and dependencies as arrows. A PERT estimate is the optimistic value, plus four times the most likely, plus the pessimistic, all divided by six. The critical path is the zero-slack path that sets the shortest possible duration. Total slack is delay tolerance against the project finish. Free slack is delay tolerance against the next activity. And crashing adds resources, while fast-tracking overlaps activities.

Key Takeaways

What to Carry Forward

To pull this together. Most activity dependencies are finish-to-start, and an activity-on-node diagram shows them as nodes and arrows. A PERT estimate blends optimistic, most likely, and pessimistic durations into one weighted number. The forward pass finds each activity's early start and finish. The backward pass, from the project's finish, finds its late start and finish. Total slack measures tolerance against the project finish, free slack against the next activity, and the critical path is the chain with zero total slack. And crashing adds resources, while fast-tracking overlaps activities. Both apply only to the critical path.

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FAQ

Questions students ask us

About Project Scheduling Mastery: Techniques, Critical Path Analysis, Total Slack, and Free Slack

How do you calculate a PERT estimate?
A PERT estimate adds the optimistic duration, four times the most likely duration, and the pessimistic duration, then divides by six. Weighting the most likely value pulls the estimate toward it. For example, with an optimistic estimate of 3 days, a most likely of 5, and a pessimistic of 9, the sum is 3 + 20 + 9 = 32, and 32 divided by 6 is about 5.33 days.
How do you find the critical path using forward and backward passes?
The forward pass moves left to right, setting each activity's early start to the largest early finish of its predecessors and adding its duration to get early finish. The backward pass moves from the project finish, setting each late finish to the smallest late start of its successors and subtracting duration for late start. Activities with zero slack, late start minus early start, form the critical path.
What is the difference between total slack and free slack?
Total slack is how long an activity can slip without delaying the project's finish, while free slack is how long it can slip without delaying the early start of its next activity. Free slack equals the successor's early start minus the activity's early finish. An activity can have a day of total slack but zero free slack if its successor starts the moment it finishes.
What is the difference between crashing and fast-tracking a schedule?
Crashing adds resources to a critical path activity to shorten it, while fast-tracking overlaps activities that would normally run in sequence. Assigning extra developers so a task takes four days instead of six is crashing, which usually costs more. Starting a task based on a predecessor's partial results is fast-tracking, which raises the risk of rework. Shortening activities off the critical path does not shorten the project.

About the System Analysis and Design course

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System Analysis and Design (Computer Science 390) carries a NCCRS credit recommendation for 3 semester credits. ACE and NCCRS have over 2,100 cooperating colleges that will consider accepting credits; the final decision is with the universities.
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