Project Management Tools: PERT Analysis and Gantt Charts

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Project Management Tools: PERT Analysis and Gantt Charts

Business Essentials · Chapter 8: Operations Management and Information SystemsSection 8.4 · lesson 45 of 10513 min · free with a free account

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In this lesson

Which delays actually move the finish date?

  • Distinguish a project from an operation
  • Build and read a Gantt chart
  • Find the critical path and the slack in a network
  • Apply PERT estimates and crashing

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Operations Management and Information Systems

Project Management Tools: PERT Analysis and Gantt Charts

Some work is done once, and never repeated. A product launch, an office move, a new warehouse. That kind of work is a project, and it needs its own tools. This section starts with what a project is, the triangle of constraints, and the work breakdown structure. Then two scheduling tools. The Gantt chart, which is easy to read, and the network, which shows dependency. We'll find the critical path for a six-activity launch, and work out how much each activity can slip. Then PERT's three-point estimates, and crashing, which buys time with money. And we'll end with what these tools can't do. The key question throughout is simple. Which delays actually move the finish date?

What a Project Is

Temporary, Unique, Then Closed

A project is a temporary undertaking with a defined objective, a start and an end, and resources assigned to it. Two features set it apart from the continuing operations of section eight point one. It's temporary, and it's unique. An operation repeats the same conversion, again and again. A project is carried out once. When its objective is reached, the project is closed. Building a warehouse is a project. So are launching a product, moving an office, and organizing a conference. Running the warehouse, once it's built, is an operation. Why does the distinction matter? A repeated activity can improve by learning from its repetitions. A project offers few chances to try again. So it has to be planned carefully, in advance.

Triangle and Lifecycle

Linked Constraints, 5 Phases

The project management triangle describes three linked constraints. Scope is the work the project must deliver. Time is the schedule. Cost is the budget. Quality sits at the center, because it suffers when any of the three is pushed. Change one constraint, and the others move. Adding features enlarges the scope, and usually extends the schedule or raises the cost. Shortening the schedule without cutting scope usually raises cost, or lowers quality. So a manager told to deliver more, sooner, and for less is being asked to ignore the triangle. Projects also move through a five-phase lifecycle. Initiation defines the objective, and decides whether to go ahead at all. Planning breaks down the work, sequences it, estimates durations and costs, and assigns resources. Execution carries out the plan. Monitoring runs alongside it, comparing progress with the plan and correcting deviations. Closure confirms delivery, releases resources, and records what was learned. The tools in this section belong mainly to planning and monitoring.

Work Breakdown Structure

Define the Work Before Scheduling It

Nothing can be scheduled until the work is defined. The starting point is the work breakdown structure. It's a hierarchical breakdown of the project's deliverable into smaller and smaller components. You keep dividing until each piece is an activity. An activity is a distinct task, with a clear output, a responsible person, and a duration you can estimate. Take a conference. It might divide first into venue, program, promotion, and logistics. The venue then divides again. Selecting a site, signing a contract, and arranging the room layout. The structure serves three purposes. It makes the scope explicit, so forgotten work is more likely to be noticed. It gives a list of activities to schedule. And it provides units to which costs and responsibility can be assigned.

The Gantt Chart

Easy to Read, Blind to Dependency

A Gantt chart is a bar chart. Activities run down the vertical axis, and time runs along the horizontal. Each activity gets a bar, whose position and length show when it starts, and how long it lasts. It makes three things visible. Sequence, read from left to right. Overlap, since activities running at the same time share the same columns. And progress against plan. Shade the completed part of each bar, and compare it with today's date. That makes the chart easy to read, and useful for communicating with people who aren't planners. Its limitations matter just as much. It doesn't show dependency well in a complex project. That's which activities must finish before others can start. At best, arrows indicate dependencies, and they soon crowd the chart. At worst, they're left out. It also doesn't show how a delay spreads. If one bar slips, the chart won't tell you which later bars must move, or whether the end date is threatened.

Table 8.4.1

Quillon Tools: The Launch as a Gantt Chart

Here's an illustration, with durations constructed for the exercise. Quillon Tools, a fictional company, is launching a product. The work breakdown gives six activities. A, define needs, takes two days. B, design, five. C, order materials, three. D, build, takes six days. E, prepare training, four. And F, launch, two. B and C follow A. D follows both B and C. E follows B. And F follows D and E. To draw the chart, start A on day one, so it fills days one and two. B and C both start on day three, after A. D starts on day eight, once B, ending day seven, and C, ending day five, are both done. E also starts on day eight, after B. F starts on day fourteen, when D and E are both finished. The project ends on day fifteen. Now the limitation shows. B runs alongside C, and D runs alongside E. Nothing in the chart says that B and D are critical, while C and E are not. For that, you need the network.

Figure 8.4.1

The Network and the Critical Path

The network approach draws each activity as a box, with arrows showing which activities must come before which. It puts dependency, the Gantt chart's weak spot, at the center. Every route from start to finish is a path. A path's length is the sum of its activities' durations. A, B, D, F is two plus five plus six plus two, or fifteen days. A, B, E, F is thirteen days. So is A, C, D, F. The critical path is the longest path through the network. Here, that's A, B, D, F, at fifteen days. It sets the minimum time in which the project can be finished. Here's the crucial implication. A delay in any activity on the critical path delays the whole project, by the same amount. A delay off the critical path may not delay the project at all. C and E each have two days to spare. Speeding them up won't shorten the project. That's why the critical path tells a manager where attention belongs.

Forward and Backward Pass

Finding the Slack

Slack, also called float, is how long an activity can be delayed without delaying the project. It's found by comparing the earliest and latest times each activity can start, in days from the start. The forward pass runs from start to finish. An activity can start only when all its predecessors are done. A runs from zero to two. B and C both start at two, finishing at seven and five. D waits for the later of B and C, so it starts at seven, and finishes at thirteen. E runs from seven to eleven. F waits for D, so it runs from thirteen to fifteen. The backward pass runs from the end. F must finish by fifteen, so it must start by thirteen. D must start by seven, and E by nine. So B must finish by seven, and start by two. C must finish by seven, so it can start as late as four. A must start at zero. Slack is latest start minus earliest start. It's zero for A, B, D, and F. They're critical. For C, it's four minus two, or two days. For E, nine minus seven, also two days. A slack activity can start late, slow down, or use fewer people, freeing resources for critical work. But slack is shared along a path. If C uses its two days, nothing is left for what follows it.

PERT

3 Estimates for Uncertain Durations

So far, each activity has had a single duration, as if the estimate were certain. Real durations aren't. The program evaluation and review technique, known as PERT, asks for three estimates of each duration. An optimistic time, a, if everything goes well. A most likely time, m. And a pessimistic time, b, if things go badly. The expected time is a, plus four times m, plus b, all divided by six. That gives the most likely time four times the weight of each extreme. There's a measure of spread too. The variance is b minus a, divided by six, then squared. So activities with wide ranges are flagged as more uncertain. Suppose activity D has estimates of four, six, and fourteen days. These figures are illustrative. The expected time is four, plus twenty-four, plus fourteen, divided by six. That's seven days, not six. The pessimistic side sits far from the most likely, so it pulls the expected time up. With the other durations unchanged, the critical path becomes sixteen days. The lesson is that a schedule built on most likely values alone is probably optimistic, when outcomes skew toward delay.

Crashing

Buying Time, Cheapest Day First

Crashing shortens a project by adding resources to selected activities, at a cost. Each day saved has a price, and that price differs by activity. The principle has two parts. Shorten only critical activities, since shortening anything else doesn't shorten the project. And start with the one whose cost per day saved is lowest. Here are illustrative figures. B can be shortened by up to one day, at three hundred dollars a day. D can be shortened by up to two days, at four hundred dollars a day. Crashing B by one day cuts the critical path to fourteen days, for three hundred dollars. Crashing D by one day cuts it to thirteen, for another four hundred. A second day of D cuts it to twelve, for another four hundred. Three days saved, for one thousand one hundred dollars. But there's a limit. As the critical path shortens, other paths become critical. At twelve days, A, B, D, F and A, B, E, F are both critical. Any further cut would have to shorten an activity on both paths.

Limits

What the Tools Cannot Do

These tools are powerful, but it's worth being clear about what they can't do. They schedule work. They don't manage the people who do it. A perfect network says nothing about whether the team has the skills, agrees about the objective, or is motivated. The group dynamics from section seven point four remain the manager's job. A plan is also only as good as the estimates inside it. A network built on carelessly guessed durations produces a schedule that looks precise, and is wrong. And a critical path computed from those durations may point the manager at the wrong activities. Finally, the tools assume the list of activities and dependencies is complete. Work left out of the work breakdown structure doesn't appear in any chart.

Case Vignette (Composite)

The Rush Order

Here's a composite case. The organization and the person are fictional. Noor is a project manager at Quillon Tools, running the fifteen-day product launch we just analyzed. Her sponsor wants it finished sooner. The materials supplier will deliver in one day instead of three, for an extra fee. Noor pays it, expecting to save two days. The launch happens on day fifteen, exactly as planned. Her options at the outset were the rush order, finding a way to shorten design or build, or asking for a later date. Her acceleration budget was small. The trade-off was the cost of speeding up an activity, against a shorter project. The reasoning turns on the critical path. Ordering materials is activity C. It has two days of slack, and sits off the critical path. Finishing it early didn't change when D could start. D still waited for design to finish on day seven. Only shortening B, D, or another critical activity could have moved the finish date. The money would have been well spent only on a critical activity.

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FAQ

Questions students ask us

About Project Management Tools: PERT Analysis and Gantt Charts

What is the critical path in project management?
The critical path is the longest path of dependent activities through a project network, and its length sets the minimum time needed to finish the project. Any delay to a critical activity delays the whole project by the same amount, while activities off the path may have time to spare. If a network's paths take 15, 13, and 13 days, the 15-day path is critical, and speeding up activities only on the other paths will not shorten the project.
How do you calculate slack or float for a project activity?
Slack equals an activity's latest start time minus its earliest start time. Earliest starts come from a forward pass through the network, where each activity begins once all its predecessors finish. Latest starts come from a backward pass from the project's end date. An activity that can start on day 2 at the earliest and day 4 at the latest has two days of slack. Critical activities have zero slack.
What is the PERT formula for expected activity time?
PERT's expected time is (a + 4m + b) / 6, where a is the optimistic estimate, m the most likely, and b the pessimistic. The variance is ((b - a) / 6) squared. With estimates of 4, 6, and 14 days, the expected time is (4 + 24 + 14) / 6 = 7 days, not 6, because the long pessimistic tail pulls it upward. Schedules built only on most likely times therefore tend to be optimistic.
What is the difference between a Gantt chart and a project network diagram?
A Gantt chart is a bar chart with activities listed down the side and time along the bottom, showing when each activity starts, how long it lasts, and progress against plan. It is easy to read but shows dependencies poorly and cannot reveal how one delay spreads. A network diagram draws activities as boxes linked by arrows, putting dependencies at the center, so it can identify the critical path and each activity's slack.

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