# Further Maths - Critical Path Analysis

## Flashcards

### 2022-02-27

In a precedence table, do you write down any dependency or only direct dependencies?

Only direct dependencies.

What are the two columns in a precedence table?

- Activity
- Depends on

What is the first node in an activity network called?

The source.

What is the last node in an activity network called?

The sink.

What do you label edges with on an activity network?

The activity.

What do edges/activities go between on an activity network?

Events.

Why is it sometimes a good idea to draw an activity network twice?

So you can do a rough and then a neat version.

What notation is used for an activity in an activity network?

A line with an arrow in it connecting two events.

What is sometimes confusing about working out the dependencies at the end of an activity network?

It’s easy to accidentally include additional dependencies for activities that lead to the sink node.

How is a dummy activity denoted on an activity network?

With a dashed arrow.

What condition is there on the layout of activities on an activity network?

There can be at most one activity between any two events.

Why must there only be one activity between any two events on an activity diagram?

Because every activity must be uniquely represented in terms of its events.

How would you represent this so that $D$ can properly depend on $A$, $B$ and $C$?

For what two scenarios do you need dummy activities in an activity network?

- Where one activity depends on multiple other activities
- When two activities start and end at identical nodes

Why aren’t activity networks always unique?

Because there might be choices as to where you can draw the dummy activity.

What are the EET (early event times) and LET (late event times) for the source node?

- EET: 0
- LET: 0

What is true about the EET (early event time) and LET (late event time) at the sink node?

They are equal.

When working out the EETs/early event times via a forward pass on an activity network, do you use the largest or the smallest duration?

The largest duration.

When working out the LETs/late event times via a backward pass on an activity network, do you use the largest or the smallest duration?

The smallest duration.

What is the EET or early event time?

The earliest time of arrival at an event allowing for the completion of all preceding activities.

What is the LET or late event time?

The latest time that the event can be left without extending the time needed for the project.

What is the value of $x$ in this diagram?

What is the value of $y$ in this diagram?

What is always true about the size of the LET compared to the EET?

The LET is always greater than or equal to the EET.

Why is

\[\text{EET}: 10\]
\[\text{LET}: 9\]
not possible?

Because the LET has to always be greater than or equal to the EET.

What is the formula for the float of an activity?

What three things do you subtract right-to-left in this diagram to find the float?

When working out the EET or LET of an event, what must you be considering?

All possible paths to that event.

What is a critical activity?

An activity where any increase in its duration results in a corresponding increase in the duration of the whole project.

What is a critical path?

A path from a source node to a sink node in an activity network which follows critical activities only.

What is true about the length of a critical path in an activity network?

It is the longest path in the network.

What is the float of any critical activity?

Why might an activity not be critical despite having the same EET and LET?

Because its float might not be $0$.

What is the formula for the slack of an event?

What’s the informal definition of float?

The amount of time an activity can be delayed by.

What is a downside of a Gantt chart?

They don’t show dependencies between tasks.

Why must C and D be happening on day 8?

Because there is no room for them to be elsewhere.

What is special about how activities on the critical path appear in a Gantt chart?

They are all perfectly bunched next to eachother at the top.

What is the formula for the lower bound of workers required to finish a project within its critical time?

What’s another name for a Gantt chart?

A cascade chart.

What is a scheduling chart?

A Gantt chart-like diagram that shows the jobs assigned to particular workers at particular times.

By convention, what does worker number $1$ handle on a scheduling chart?

The critical activities.

How can you check that a project won’t finish within its critical time given a certain amount of workers?

See if the number of assigned workers is less than the lower bound.

What is resource levelling?

The process of adjusting start times to optimise the allocation of workers.

What are the three rules for workers?

- Workers can only perform one activity at a time
- Once a worker starts and activity, they must complete it
- Workers become available after finishing instantaneously

What are the two conventions for constructing a scheduling diagram?

- Chose the first available worker
- If there is a choice of activities for a worker, assign the one with the lowest value for its LET (i.e. the most critical).

How can you find the new minimum time of completion for a project given a constraint on workers?

Draw a resource scheduling diagram straight from the activity network, making sure to be careful with dependencies.

### 2022-03-20

What is true about the float of events on the critical path?

It is always zero.