Critical Path Analysis

Question 1

Precedence Table

Answer 1

Has the activities listed in the left column and their dependencies on the right.

• Put a - where there are no dependencies
• If an activity is dependent on an activity that depends on others only put the one it is directly dependent on

Question 2

Creating an activity network

Answer 2

Start with a node labelled 0
Point arcs representing activities that aren’t dependent on any others from there
Label each node with an increasing number. connect multiple arcs where one is dependent on multiple
Connect the terminating activity/activities to a sink node at the end
Arcs must be straight

Question 3

Dummy Arcs

Answer 3

Dotted lines from a node to another to show that the activity that is dependent on is needed for the one on the other end of the dummy

Question 4

When do you need a dummy arc?

Answer 4

1. Where two activities at the same node are needed, draw one to a separate node and add the dummy
2. If an activity is needed for one activity on its own and another activity has that and another one needed, draw a dummy from the node where only it is needed

Question 5

Early event time

Answer 5

The earliest time a project can be started based on all events it is dependent on being completed

Question 6

Late event time

Answer 6

The latest time a project can be started without extending the time needed for a project

Question 7

Finding early and late event times

Answer 7

Trace forward from the source node for early, the latest time a needed event is completed
Trace back from the sink for the late, the earliest time from this

Question 8

Critical activity

Answer 8

Any increase in its duration will increase the duration of the whole project
Early start time = late start time where the values on the next node are equal to the values on that node plus the length of the activity

Question 9

Critical path

Answer 9

A path from the source node to the sink node that exclusively follows critical activities

Question 10

Float of an activity

Answer 10

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

Question 11

Float of an activity formula

Answer 11

latest finish time - duration - earliest start time

Question 12

Gantt Diagram

Answer 12

Shows the time each activity can be completed in visually using a diagram with rectangles for each activity

Question 13

Critical activities Gantt diagram

Answer 13

Rectangles across one line for all of them connected

Question 14

Non-critical activities Gantt diagram

Answer 14

Draw a rectangle from the early start time with length the duration. Draw a dotted rectangle from there to the late time.
Each should have a new line

Question 15

When an activity must be at a time Gantt diagrams

Answer 15

No matter how far through the float it is shifted the rectangle will always encompass that time

Question 16

Day 10 Gantt diagram

Answer 16

Between lines 9 and 10

Question 17

Resource histograms

Answer 17

1. Draw your critical path with time the x and workers the y
2. Add non-critical activities from the earliest start time, they should be as low as possible, not necessarily as rectangles
3. Write the letter of the activity in each small square

Question 18

Scheduling diagram

Answer 18

Looks like a Gantt chart

1. The first worker does the critical path
2. Fit each job where it can fit, choosing the one with the earliest late time when given a choice
3. Shade in any gaps

Question 19

Lower bound for the amount of workers required

Answer 19

Sum of all the activity times / critical time of the project and round up to the nearest whole number

Question 20

Where the workers is fewer than the lower bound

Answer 20

Make a scheduling diagram from the activity network by inspection to minimise the run-time. Check for dependencies