Critical path analysis

Question 1

What is a precedence table?

Answer 1

A table which shows the activities that each activity is dependent on

Question 2

What is an event?

Answer 2

The completion of an activity

Question 3

What is an activity on arc network?

Answer 3

A way of representing each activity’s dependencies in network form

Question 4

Describe an activity on arc network

Answer 4

The activities are represented by edges, and the events are represented by vertices. Each edge has an arrow defining its direction. It is convention to use straight lines for edges

Question 5

What is a source vertex?

Answer 5

A vertex with an indegree of 0

Question 6

What is a sink vertex?

Answer 6

A vertex with an outdegree of 0

Question 7

What is a dummy activity?

Answer 7

An activity which has no weight, but is used when it is otherwise impossible to show an activity being dependent on several events, or to avoid two activities sharing an edge

Question 8

What is the early event time of an event?

Answer 8

The earliest possible time that it can occur

Question 9

How can the early event time of an event be calculated?

Answer 9

Starting from the source vertex and working forwards, it is the longest possible path into the event

Question 10

What is the late event time of an event?

Answer 10

The latest time that it can occur without delaying the overall time of the project

Question 11

How can the late event time of an event be calculated?

Answer 11

Starting from the sink vertex and working backwards, it the longest possible path into the event subtracted from the sink vertex’s early event time

Question 12

What is the float of an activity?

Answer 12

The amount of time that its start may be delayed without affecting the duration of the project

Question 13

How can the float of an activity be calculated?

Answer 13

Latest finish time - duration - earliest start time

Question 14

What is a critical activity?

Answer 14

An activity with a float of 0

Question 15

What is a critical path?

Answer 15

A path from the source vertex to the sink vertex which entirely follows critical activities

Question 16

What can be said about the vertices on a critical path?

Answer 16

The early event times and the late event times are equal

Question 17

Describe a Gantt chart

Answer 17

The number scale represents elapsed time. The critical activities are all shown on the same line at the top. All other activities are shown on their own line, with a solid box representing the earliest start time and the duration, while a dotted box extends to the latest finish time, showing its float

Question 18

How can one work out which activities must be happening on a certain day from a Gantt chart?

Answer 18

It is all activities whose solid box must lie on the imaginary vertical line drawn on the appropriate time

Question 19

How can one work out which activities may be happening on a certain day from a Gantt chart?

Answer 19

It is all activities whose solid box may lie on the imaginary vertical line drawn down the appropriate time after being moved around within its dotted box

Question 20

What assumptions must be made when scheduling?

Answer 20

• Each activity is completed by a single worker in the time given as the duration of the activity
• Once an activity has started, it must be completed by the worker
• Once a worker has completed an activity, they become immediately available to start another activity

Question 21

Which worker should always be used when scheduling?

Answer 21

The first available one

Question 22

What should be done if there is a choice of tasks for a worker?

Answer 22

Assign the one with the lowest latest finish time