Question Consider the following precedence table:

Step 1: Initial Network Construction

• Draw $A$ from the start node.
• Add $B$ and $C$, both depending on $A$.
• Add $D$, which depends on both $B$ and $C$.

Step 2: Identify Dummy Requirement

• Without a dummy, $B$ and $C$ would share the same start and end nodes. This creates ambiguity:
• Does $D$ depend on both $B$ and $C$?
• Or does it depend only on one of them? To resolve this, a dummy is introduced to represent the dependency of $D$ on $B$ and $C$.

Step 3: Add the Dummy Activity

• Insert a dummy activity from the end of $A$ to the start of $C$.
• Label the dummy activity with a dashed line and zero duration.

Final Network

1. $A$ starts at the start node.
2. $B$ depends on $A$
3. $C$ depends on $A$ via a dummy activity.
4. $D$ depends on both $B$ and $C$. The dummy ensures $D's$ dependencies are unambiguously represented.

Common Mistakes

1. Forgetting to Add Dummies Omitting necessary dummy activities leads to ambiguous or incorrect networks.

2. Improper Dummy Placement Placing a dummy where it does not resolve dependency conflicts can confuse the network logic.

3. Incorrect Interpretation Misinterpreting dummy activities as real tasks with duration or resource requirements.

4. Ignoring Precedence Relationships Failing to include all required dependencies in the activity network.

5. Redundant Dummies Adding unnecessary dummy activities that do not resolve ambiguity.

Key Formulas/Theorems

1. Dummy Activity Duration:

2. Dummy Placement Rule: A dummy is required when two or more activities:

• Share the same start and end nodes.
• Have different sets of immediate predecessors.

3. Dependency Representation: Dummies are used to ensure every activity's dependencies are accurately represented.