D1 - Critical Path Analysis

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Precedence Table

Columns: 'Activity' column and 'depends on' column

What is it for: Shows all the activities of an activity network and which activities each of them depend on.

Used to draw an activity network 

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Nodes

What are they: Nodes are used between activities to mark the start or end of an activity

Source node: Always 0, at the start of an activity network

Sink node: At the end of an activity network

Remember: An activity can never start with a larger node and finish at a smaller node

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Early and late event times

Latest start time: Perform a forward pass. Always check each route to a node and select the longest route.

Earliest finish time: Perform a backward pass. Always check each route to a node and select the shortest route.

Use the nodes to write the early and late times.

Total float: Latest finish time - activity duration - earliest start time

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Critical Path

Critical activites: Always have the same early and late event time

Critical path: The path formed by the critical activities

Critical time: The duration of the critical path

Lower bound of workers: Total time for all activities / critical time

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Dummies

What are they: These are arcs in an activity network with no duration. Always shown by a dotted line

When are they needed: When there are activities with complex dependance (many situtations). Most common - When two activities from the same node also need to end at the same node.

And when an activity depends upon two activities from different nodes that already have activities dependant upon them.

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Cascade Charts

AKA: Gantt charts

Method: Always put critical activities on the top row. Put all other activities on seperate rows and draw their duration in a solid box with their total float extended as a dotted line.

Scheduling diagram: A special gantt chart that assigns workers to activites. Need to present lower bound of workers on the left, each with their own row. Arrange activities, moving them within their total float to use the minimal amount of workers.

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