Translate between precedence data and an activity network

Precedence and activity-on-arrow networks

A precedence relation records which activities must finish before another activity starts. In an activity-on-arrow network, nodes are events and arrows are activities

1. Keep events and activities distinct A node marks an event, while an arrow represents an activity with its duration \(\displaystyle \text{node}=\text{event},\quad\text{arrow}=\text{activity}\)
2. Follow the precedence direction An arrow runs from an activity's start event to its finish event \(\displaystyle A\prec B\Rightarrow A\text{ finishes before }B\text{ starts}\)
3. Use immediate predecessors only List the activities directly before an activity, not every earlier activity in the network \(\displaystyle \operatorname{Pred}_{\mathrm{imm}}(D)=\{A,B\}\)
4. Use a zero-duration dummy when needed A dummy preserves a partial overlap without adding work or time \(\displaystyle d=0\)

Worked example

The precedence data are A: none, B: none, C: A and D: A, B. Show the key decisions for an activity-on-arrow network

1. \(\displaystyle \operatorname{Pred}_{\mathrm{imm}}(C)=\{A\}\)C has A as its only immediate predecessor
2. \(\displaystyle \operatorname{Pred}_{\mathrm{imm}}(D)=\{A,B\}\)D must wait for both A and B, so both are direct predecessors
3. \(\displaystyle \{A\}\ne\{A,B\}\)The sets overlap at A: C needs A, while D needs both A and B
4. \(\displaystyle d=0\)Start C at A’s finish event and D at a separate event where B finishes; connect A’s finish event to D’s start event with a zero-duration dummy

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