---
title: "Dummy activity and float definitions"
subject: "Project Engineering"
chapter: 3
key: "semester_7/project_engineering:float-definitions-dummy"
source: https://www.bctengineer.com/q/semester_7/project_engineering/float-definitions-dummy
site: BCT Engineering
---

# Dummy activity and float definitions

Project Engineering · Chapter 3: Project Planning and Scheduling

- Asked in: 2070 Chaitra (old course), 2+2+2+2 marks
- Video: [Determine Total Float & Free Float (AKA "Slack") of activities in a network diagram](https://www.youtube.com/watch?v=NDa-Fq5jeuM) — Engineer4Free
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/project_engineering/float-definitions-dummy
- Whole chapter: https://www.bctengineer.com/md/semester_7/project_engineering/chapter-3

## Question

Define the terms dummy activity, total float, free float and independent float.

## Short answer

A dummy activity is a zero-duration, zero-resource arrow used only to maintain logic. Total float is the maximum delay an activity can have without delaying the project (LST – EST). Free float is the delay allowed without affecting the earliest start of any successor. Independent float is the delay possible when all predecessors finish as late as possible and successors start as early as possible.

## Answer

Example network used below (days): A = 4 and B = 3 are start activities; C = 5 and D = 2 follow A; E = 3 follows C and D; F = 4 follows B. Project duration = 12 days.

```text
(1) --A(4)--> (2)
(1) --B(3)--> (3)
(2) --D(2)--> (4)
(2) --C(5)--> (5)
(3) --F(4)--> (6)
(4) - - dummy - -> (5)
(5) --E(3)--> (6)
```

| Activity | D | EST | EFT | LST | LFT | TF | FF | Int.F | Ind.F |
|---|---|---|---|---|---|---|---|---|---|
| A | 4 | 0 | 4 | 0 | 4 | 0 | 0 | 0 | 0 |
| B | 3 | 0 | 3 | 5 | 8 | 5 | 0 | 5 | 0 |
| C | 5 | 4 | 9 | 4 | 9 | 0 | 0 | 0 | 0 |
| D | 2 | 4 | 6 | 7 | 9 | 3 | 3 | 0 | 3 |
| E | 3 | 9 | 12 | 9 | 12 | 0 | 0 | 0 | 0 |
| F | 4 | 3 | 7 | 8 | 12 | 5 | 5 | 0 | 0 |

#### Dummy activity

A **dummy activity** is an imaginary activity with zero duration and zero resource, shown by a dashed arrow, used to maintain correct logic or give unique event numbers (the dashed arrow (4)-(5) in the example keeps E dependent on both C and D).

#### Total float

**Total float** is the time by which an activity can be delayed without delaying the project completion date.
$TF = LST - EST = LFT - EFT$. Example: B has TF = 8 - 3 = 5 days; critical activities have TF = 0.

#### Free float

**Free float** is the time by which an activity can be delayed without affecting the earliest start of any succeeding activity.
$FF = \min(EST\ \text{of successors}) - EFT$. Example: D has FF = 9 - 6 = 3 days (E starts at 9).

#### Independent float

**Independent float** is the time by which an activity can be delayed even when all its predecessors finish as late as possible and its successors start as early as possible; it affects neither predecessors nor successors.
$IndF = \max(0,\ \min(EST\ \text{of successors}) - \max(LFT\ \text{of predecessors}) - D)$. Example: D has IndF = 9 - 4 - 2 = 3 days; B has IndF = 3 - 0 - 3 = 0.

(Interfering float = TF - FF is the part of the total float that is shared with the successors; e.g. B: 5 - 0 = 5 days.)

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is total float?
   A. The time an activity can be delayed without delaying project completion
   B. Delay possible without affecting successors' earliest start
   C. Delay possible with predecessors at latest and successors at earliest
   D. The activity duration
   Answer: A. TF = LST - EST = LFT - EFT. (Key point: Total float)

2. What is the free float of D in the example?
   A. 0 days
   B. 3 days
   C. 5 days
   D. 2 days
   Answer: B. FF = min(EST of successors) - EFT = 9 - 6 = 3 days. (Key point: Free float)

3. How is independent float of D found?
   A. 9 - 6 = 3 using EFT only
   B. 7 - 4 = 3 using LST
   C. 9 - 4 - 2 = 3 days (successor EST - predecessor LFT - D)
   D. 4 + 2 = 6
   Answer: C. IndF = min(EST succ) - max(LFT pred) - D, floored at zero. (Key point: Independent float)

4. Why is TF of B equal to 5 days?
   A. EFT 3 minus EST 0 plus 2
   B. LST 5 plus duration 3
   C. EST of F minus 3
   D. LFT 8 minus EFT 3
   Answer: D. TF = LFT - EFT = 8 - 3 = 5; also LST - EST = 5 - 0. (Key point: Total float of B)

## Related in Project Engineering

- [Total float and independent float](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Atotal-float-independent-float) — Project Engineering, chapter 3
- [Dummy activity and its application](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Adummy-activity-application) — Project Engineering, chapter 3
- [Dummy activity; use of critical path in CPM](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Adummy-critical-path-use) — Project Engineering, chapter 3
- [Critical path and dummy activity significance](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Acritical-path-dummy-significance) — Project Engineering, chapter 3

## Related in other subjects

- [Definitions of psychrometric terms](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_thermodynamics%3Apsychrometric-terms-definitions) — Applied Thermodynamics, chapter 4
- [CPM schedule, critical path and float](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_engineering_and_management%3Acpm-network-critical-path-float) — Industrial Engineering and Management, chapter 3