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A Level Further Maths Decision 1 > Critical Path Analysis > Flashcards

Flashcards in Critical Path Analysis Deck (20)
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Precedence Table

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


Creating an activity network

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


Dummy Arcs

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


When do you need a dummy arc?

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


Early event time

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


Late event time

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


Finding early and late event times

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


Critical activity

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


Critical path

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


Float of an activity

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


Float of an activity formula

latest finish time - duration - earliest start time


Gantt Diagram

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


Critical activities Gantt diagram

Rectangles across one line for all of them connected


Non-critical activities Gantt diagram

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


When an activity must be at a time Gantt diagrams

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


Day 10 Gantt diagram

Between lines 9 and 10


Resource histograms

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


Scheduling diagram

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


Lower bound for the amount of workers required

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


Where the workers is fewer than the lower bound

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