What is a dummy activity?

A dummy activity is an arc in an activity network with **duration zero**. It has no letter name, is drawn as a **dotted line**, and is used only to show precedence relationships in more complex networks.

What are the two situations that require a dummy activity?

1) **Unique start-end pairs**: When two activities would share the same (start, end) nodes, a dummy gives one a different pair. 2) **Split predecessors**: When activity D needs both B and C but activity E needs only B, a dummy shows D depends on both.

How are dummy activities represented on an activity network?

Dummies are drawn as **dotted lines** (not solid). They have **no letter label** and **no duration** shown (duration is 0).

What is the 'unique pair' rule and why does it require dummies?

Each activity must have a **unique** (start node, end node) pair. If B and C both go from node 1 to node 2, they violate this. A dummy creates an extra node so B is (1,3) and C is (1,2), for example.

What is meant by 'split immediate predecessors'?

When activity D has immediate predecessors B and C, but activity E has only B. D needs both B and C; E needs only B. A dummy is used to show that D cannot start until both B and C are complete.

What duration do dummy activities have in earliest and latest event time calculations?

Dummy activities have **duration 0**. So for earliest event time: early_end = early_start + 0. For latest: late_start = late_end - 0.

Why should you use the minimum number of dummies?

Activity networks should be **concise and efficient**. Using more dummies than necessary makes the diagram harder to read and may indicate an inefficient layout. Exam questions often specify the exact number required.

Can the dummy go in either direction between two nodes?

Yes. E.g. if B and C both precede D, the dummy can go from 2 to 3 (with D starting at 3) or from 3 to 2 (with D starting at 2). Either preserves the correct precedence.

If G and H both depend on C and I depends on both G and H, why is a dummy needed?

G and H would both start at the same node (after C) and end at the same node (before I), giving them the same (start, end) pair. A dummy creates an extra node so G and H have **unique** pairs.

If E depends on A and D but C depends only on A, why is a dummy needed?

This is a **split predecessors** case. E needs both A and D; C needs only A. A dummy ensures the network shows that E cannot start until both A and D are complete.

Dummy Activities | Pearson Edexcel International AS Maths

Critical Path Analysis

Dummy Activities

Summary

Dummy activities are zero-duration arcs used in activity networks to represent precedence relationships when the network structure requires them. They are drawn as dotted lines, have no letter designation, and serve two main purposes: ensuring each activity has a unique start-end node pair, and showing split immediate predecessors when one activity depends on multiple others with different dependency patterns.

1. Definition and Properties

A dummy activity is an activity with weight (duration) of zero. It consumes no time or resources.

Dummies are not assigned names (letters like A, B, C). They are represented by dotted lines on the activity network.

Dummies are used only to show precedences in more complicated activity networks. They have no physical meaning.

In calculations (e.g. earliest/latest event times), dummies count as arcs with duration 0.

2. Situation 1: Unique Start-End Node Pairs

Each activity (arc) in an activity network must have a unique pair of start and end nodes.

When two activities (e.g. B and C) both have the same immediate predecessor and lead to the same successor, they would otherwise share the same start and end nodes.

A dummy is used to give one activity a different end node. E.g. B gets pair (1, 3) and C gets pair (1, 2), or the dummy goes from 2 to 3 with D starting from 3.

Example: Activity D has predecessors B and C. Without a dummy, B and C could both be (1, 2). A dummy ensures B is (1, 3) and C is (1, 2).

3. Situation 2: Split Immediate Predecessors

When one activity depends on both of two predecessors, but another activity depends on only one of them, a dummy is needed.

Example: D depends on B and C; E depends only on B. A dummy shows that D requires both B and C to be complete, while E requires only B.

The dummy creates the correct dependency structure so that D cannot start until both B and C finish.

This situation arises when predecessors 'split' — some activities need one, others need both.

4. Drawing Dummies Correctly

Start with a rough sketch of the network to identify where dummies are needed.

Look ahead: check which activities depend on each node and whether unique pairs or split predecessors apply.

Use the minimum number of dummies. Exam questions often specify exactly how many to use.

If you think you need more dummies than specified, reconsider the layout — a more efficient network may avoid extra dummies.

5. Worked Example: Two Dummies

6. Examiner Tips

Dummy Activities

Summary

1. Definition and Properties

A dummy activity is an activity with weight (duration) of zero. It consumes no time or resources.

Dummies are not assigned names (letters like A, B, C). They are represented by dotted lines on the activity network.

Dummies are used only to show precedences in more complicated activity networks. They have no physical meaning.

In calculations (e.g. earliest/latest event times), dummies count as arcs with duration 0.

2. Situation 1: Unique Start-End Node Pairs

Each activity (arc) in an activity network must have a unique pair of start and end nodes.

When two activities (e.g. B and C) both have the same immediate predecessor and lead to the same successor, they would otherwise share the same start and end nodes.

A dummy is used to give one activity a different end node. E.g. B gets pair (1, 3) and C gets pair (1, 2), or the dummy goes from 2 to 3 with D starting from 3.

Example: Activity D has predecessors B and C. Without a dummy, B and C could both be (1, 2). A dummy ensures B is (1, 3) and C is (1, 2).

3. Situation 2: Split Immediate Predecessors

When one activity depends on both of two predecessors, but another activity depends on only one of them, a dummy is needed.

Example: D depends on B and C; E depends only on B. A dummy shows that D requires both B and C to be complete, while E requires only B.

The dummy creates the correct dependency structure so that D cannot start until both B and C finish.

This situation arises when predecessors 'split' — some activities need one, others need both.

4. Drawing Dummies Correctly

Start with a rough sketch of the network to identify where dummies are needed.

Look ahead: check which activities depend on each node and whether unique pairs or split predecessors apply.

Use the minimum number of dummies. Exam questions often specify exactly how many to use.

If you think you need more dummies than specified, reconsider the layout — a more efficient network may avoid extra dummies.

5. Worked Example: Two Dummies

Given activities with E depending on A and D (split: C depends only on A), use one dummy between A/D and C.

Given G and H both depending on C, and I depending on both G and H (unique pairs), use one dummy so G and H have distinct end nodes before I.

The dummy for split predecessors: draw from the node where A and D meet to where E starts, ensuring E waits for both.

The dummy for unique pairs: insert a node between C and the merge for G and H so G and H have different (start, end) pairs.

6. Examiner Tips

Exam questions may give a partially completed network. Complete it using the specified number of dummies.

Always verify: each activity has a unique (start, end) node pair; all precedence relationships from the table are correctly represented.

Dummies still participate in forwards and backwards passes — treat them as arcs with duration 0.