Define precedence table .

A precedence table lists every activity in a project, alongside its duration and the activities that must already be complete before it can begin. It is the usual starting point for drawing an activity network.

In a precedence table, activity G is preceded by F alone, and F is preceded by E. Why is E not listed against G?

A precedence table lists only the immediately preceding activities, and F already carries E. G still cannot start until E is finished, but that is recorded in F's own row rather than repeated in G's.

Which activities in a project can begin at time 0, and how does a precedence table show them?

The activities with no immediately preceding activities , which the table marks with a dash rather than with letters. Nothing has to be completed before them, so each one has an earliest start time of 0.

True or False? In an activity network, the arrows drawn on the edges are the activities.

False. The boxes , or nodes, are the activities, and an arrow only records that one activity has to be finished before the next can start. This is called an activity-on-node network, and it is the form the specification says will be used.

Activity X has several activities immediately before it. How do you work out X's earliest start time?

For each activity immediately before X, work out earliest start time plus duration , which is the earliest that activity can finish. X's earliest start time is the greatest of those values, because X cannot begin until every one of them is done.

Activity X has several activities immediately after it. How do you work out X's latest finish time?

For each activity immediately after X, work out latest finish time minus duration , which is the latest that activity can start. X's latest finish time is the smallest of those values, because X has to be out of the way in time for all of them.

Which end of an activity network do you work from when filling in earliest start times, and which end for latest finish times?

Earliest start times are filled in from the left , since each one depends on the activities before it. Latest finish times are filled in from the right , since each one depends on the activities after it.

You have drawn an activity network and two activities have nothing following them. What do you add, and why?

Add one extra activity box at the end, with a duration of 0 . It gives the network a single finishing point, so the project has one completion time rather than two loose ends.

Define the float of an activity.

The float of an activity is the slack in its timing: the length of time it can be delayed by without delaying the whole project. An activity with a float of 3 could start up to 3 later than planned and the project would still finish on time.

What does it mean if an activity has a float of 0?

An activity with a float of 0 is a critical activity , meaning there is no slack in its timing at all. Any delay to it, however small, delays the entire project.

Define a critical path .

A critical path is a route through an activity network that runs from the start of the project to the end along critical activities only. Following it gives a chain in which no activity has any slack at all.

True or False? Delaying a non-critical activity by less than its float leaves the project's completion time unchanged.

True. Absorbing a delay of exactly that size is what the float measures. Only once the delay grows beyond the float does the project's completion time move.

A project's critical path has a total length of 28 days. What does that tell you about the project?

The project cannot be completed in less than 28 days , because the length of a critical path is the minimum duration of the whole project. Finishing sooner would need at least one activity on that path to take less time than its stated duration.

Why is it worth knowing which activities in a project are critical?

Critical activities are where a delay costs the project time, so they are where attention and any spare resources should go. A delay to a non-critical activity can often be absorbed instead, so the same effort spent there buys much less.

Define a Gantt chart .

A Gantt chart , also known as a cascade diagram , is a graphical display of the activities making up a project, drawn as horizontal bars against a time axis. The two names refer to the same chart rather than to two different kinds of diagram.

What three things about a project can be read off a Gantt chart?

A Gantt chart shows the critical activities , the total float of each non-critical activity, and the minimum project duration . All three are set against a single time axis, so the shape of the whole project can be taken in at once.

On a Gantt chart, when is each activity assumed to start, and how long is its solid bar?

Each activity is assumed to start at its earliest start time , and its solid bar runs for its duration in a single block with no breaks. An activity with an earliest start time of 4 and a duration of 6 is therefore a solid bar from 4 to 10.

Why can the critical activities on a Gantt chart be drawn back-to-back on a single line?

Critical activities all have a total float of zero , so none of them carries a dotted bar and none needs room to slide. Each one can therefore start at exactly the point where the one before it finished.

On a Gantt chart, what is written on each bar, and what is deliberately left unlabelled?

Each bar is labelled with its activity name and its duration . Floats are left unlabelled, so a float has to be read off the time axis rather than looked up.

True or False? A Gantt chart assumes, in the first instance, that one worker is assigned to each activity.

True. That single-worker assumption is where a chart starts, and it is what makes the chart usable for resource levelling and scheduling problems. Those problems can then be worked once the number of workers each activity really needs is known.

Where is the time axis drawn on a Gantt chart, and how far must it run?

The time axis is drawn horizontally along the bottom of the chart, usually starting at 0. It has to run at least as far as the minimum project duration, since every bar drawn above it has to fit within that range.

Level 3MathsAQAMathematical Studies (Core Maths)Paper 2B: Critical Path & Risk AnalysisFlashcardsCritical Paths AnalysisCritical Paths Analysis

Critical Paths Analysis (AQA Level 3 Mathematical Studies (Core Maths): Paper 2B: Critical Path & Risk Analysis): Flashcards

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FrontCompound Projects & Activity Networks
Define precedence table.

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Cards in this collection (28)

Define precedence table.
A precedence table lists every activity in a project, alongside its duration and the activities that must already be complete before it can begin.
It is the usual starting point for drawing an activity network.
In a precedence table, activity G is preceded by F alone, and F is preceded by E. Why is E not listed against G?
A precedence table lists only the immediately preceding activities, and F already carries E.
G still cannot start until E is finished, but that is recorded in F's own row rather than repeated in G's.
Which activities in a project can begin at time 0, and how does a precedence table show them?
The activities with no immediately preceding activities, which the table marks with a dash rather than with letters.
Nothing has to be completed before them, so each one has an earliest start time of 0.
True or False?
In an activity network, the arrows drawn on the edges are the activities.
False.
The boxes, or nodes, are the activities, and an arrow only records that one activity has to be finished before the next can start.
This is called an activity-on-node network, and it is the form the specification says will be used.
An activity box carries the activity letter above a row of three numbers. Fill in the two missing entries, reading that row from left to right.
- the $______$ start time
- the duration
- the $______$ finish time
The completed row is:
- the earliest start time
- the duration
- the latest finish time
So a box labelled D above the numbers 3, 2 and 7 means activity D can start as early as 3, takes 2, and must be finished by 7.
Activity X has several activities immediately before it. How do you work out X's earliest start time?
For each activity immediately before X, work out earliest start time plus duration, which is the earliest that activity can finish.
X's earliest start time is the greatest of those values, because X cannot begin until every one of them is done.
Activity X has several activities immediately after it. How do you work out X's latest finish time?
For each activity immediately after X, work out latest finish time minus duration, which is the latest that activity can start.
X's latest finish time is the smallest of those values, because X has to be out of the way in time for all of them.
Which end of an activity network do you work from when filling in earliest start times, and which end for latest finish times?
Earliest start times are filled in from the left, since each one depends on the activities before it.
Latest finish times are filled in from the right, since each one depends on the activities after it.
Activity F follows C, D and E, where C starts at 4 and lasts 3, D starts at 4 and lasts 6, and E starts at 5 and lasts 4. What is F's earliest start time?
F's earliest start time is 10.
C finishes at $4 + 3 = 7$ , D at $4 + 6 = 10$ and E at $5 + 4 = 9$ , and F has to wait for the last of those three.
You have drawn an activity network and two activities have nothing following them. What do you add, and why?
Add one extra activity box at the end, with a duration of 0.
It gives the network a single finishing point, so the project has one completion time rather than two loose ends.
Define the float of an activity.
The float of an activity is the slack in its timing: the length of time it can be delayed by without delaying the whole project.
An activity with a float of 3 could start up to 3 later than planned and the project would still finish on time.
Complete the formula for the float of an activity, using the three numbers written in its own box.
$float =______- earliest start time -______$
The completed formula is:
$float = latest finish time - earliest start time - duration$
The latest finish time is the last moment the activity may end, so taking off the duration and the earliest start leaves the slack in between.
What does it mean if an activity has a float of 0?
An activity with a float of 0 is a critical activity, meaning there is no slack in its timing at all.
Any delay to it, however small, delays the entire project.
Activity F has an earliest start time of 4, a duration of 6 and a latest finish time of 19. By how long could F be delayed without delaying the project?
F could be delayed by up to 9 without pushing the project back.
Its three box entries give $19 - 4 - 6 = 9$ , which is the float of F.
Define a critical path.
A critical path is a route through an activity network that runs from the start of the project to the end along critical activities only.
Following it gives a chain in which no activity has any slack at all.
True or False?
Delaying a non-critical activity by less than its float leaves the project's completion time unchanged.
True.
Absorbing a delay of exactly that size is what the float measures.
Only once the delay grows beyond the float does the project's completion time move.
A project's critical path has a total length of 28 days. What does that tell you about the project?
The project cannot be completed in less than 28 days, because the length of a critical path is the minimum duration of the whole project.
Finishing sooner would need at least one activity on that path to take less time than its stated duration.
For a critical activity, how do the three numbers in its box fit together?
The three numbers fit together exactly, so that $earliest start time + duration = latest finish time$ .
There is no room to spare between the earliest the activity can start and the latest it can finish.
Why is it worth knowing which activities in a project are critical?
Critical activities are where a delay costs the project time, so they are where attention and any spare resources should go.
A delay to a non-critical activity can often be absorbed instead, so the same effort spent there buys much less.
Define a Gantt chart.
A Gantt chart, also known as a cascade diagram, is a graphical display of the activities making up a project, drawn as horizontal bars against a time axis.
The two names refer to the same chart rather than to two different kinds of diagram.
What three things about a project can be read off a Gantt chart?
A Gantt chart shows the critical activities, the total float of each non-critical activity, and the minimum project duration.
All three are set against a single time axis, so the shape of the whole project can be taken in at once.
On a Gantt chart, when is each activity assumed to start, and how long is its solid bar?
Each activity is assumed to start at its earliest start time, and its solid bar runs for its duration in a single block with no breaks.
An activity with an earliest start time of 4 and a duration of 6 is therefore a solid bar from 4 to 10.
On a Gantt chart, the solid bar of a non-critical activity is followed by a bar drawn with a dotted line. Complete the quantity that fixes where that dotted bar ends.
$end of the dotted bar = earliest start time + duration +______$
The completed rule is:
$end of the dotted bar = earliest start time + duration + total float$
The dotted bar is the room the solid bar can slide back and forth along, which is why its length is the float itself.
Why can the critical activities on a Gantt chart be drawn back-to-back on a single line?
Critical activities all have a total float of zero, so none of them carries a dotted bar and none needs room to slide.
Each one can therefore start at exactly the point where the one before it finished.
On a Gantt chart, what is written on each bar, and what is deliberately left unlabelled?
Each bar is labelled with its activity name and its duration.
Floats are left unlabelled, so a float has to be read off the time axis rather than looked up.
On a Gantt chart with a time axis in hours, activity E is a solid bar from 18 to 24 with a dotted bar running on to 26. What is E's latest finish time, and what is its float?
E must be finished by 26 hours, which is the far end of the dotted bar.
Its float is the length of that dotted bar, $26 - 24 = 2$ hours.
True or False?
A Gantt chart assumes, in the first instance, that one worker is assigned to each activity.
True.
That single-worker assumption is where a chart starts, and it is what makes the chart usable for resource levelling and scheduling problems.
Those problems can then be worked once the number of workers each activity really needs is known.
Where is the time axis drawn on a Gantt chart, and how far must it run?
The time axis is drawn horizontally along the bottom of the chart, usually starting at 0.
It has to run at least as far as the minimum project duration, since every bar drawn above it has to fit within that range.

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