---
title: "Forward and backward pass definition"
subject: "Project Engineering"
chapter: 3
key: "semester_7/project_engineering:forward-backward-pass"
source: https://www.bctengineer.com/q/semester_7/project_engineering/forward-backward-pass
site: BCT Engineering
---

# Forward and backward pass definition

Project Engineering · Chapter 3: Project Planning and Scheduling

- Asked in: 2067 Asar (old course), 4 marks
- Video: [Use forward and backward pass to determine project duration and critical path](https://www.youtube.com/watch?v=4oDLMs11Exs) — Engineer4Free
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/project_engineering/forward-backward-pass
- Whole chapter: https://www.bctengineer.com/md/semester_7/project_engineering/chapter-3

## Question

Define forward and backward pass in the network analysis.

## Short answer

The forward pass calculates earliest times from start to end, taking the largest predecessor EFT, with EFT=EST+duration; the final EFT is the project duration. The backward pass calculates latest times from end to start, taking the smallest successor LST, with LST=LFT-duration and the last LFT set to the project duration.

## Answer

#### Forward pass

The **forward pass** is the calculation carried out from the start event to the end event of the network to find the earliest start time (EST) and earliest finish time (EFT) of every activity, and the earliest event times $TE$.

$$
EST = \max(EFT\ \text{of all predecessors}), \quad EFT = EST + D
$$

At a merge point (several activities entering one event) the **largest** value is taken. The EFT of the last activity is the project duration.

#### Backward pass

The **backward pass** is the calculation carried out from the end event back to the start event to find the latest finish time (LFT) and latest start time (LST) of every activity, and the latest event times $TL$, without delaying the project.

$$
LFT = \min(LST\ \text{of all successors}), \quad LST = LFT - D
$$

At a burst point (several activities leaving one event) the **smallest** value is taken. For the last activity, LFT = project duration.

Example network (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.

- Forward: A 0-4; B 0-3; C 4-9; D 4-6; F 3-7; E: EST = max(9, 6) = 9, EFT = 12.
- Backward: E: LFT = 12, LST = 9; C: LFT = 9, LST = 4; D: LFT = 9, LST = 7; A: LFT = min(4, 7) = 4, LST = 0; F: LFT = 12, LST = 8; B: LFT = 8, LST = 5.

## Check yourself

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

1. What does the forward pass find?
   A. EST and EFT of activities and earliest event times
   B. LST and LFT only
   C. Float and cost
   D. Probability of completion
   Answer: A. It runs start to end computing earliest times. (Key point: Forward pass)

2. At a merge point in the forward pass, which value is taken?
   A. The smallest EFT
   B. The largest EFT of the predecessors
   C. The average
   D. The first predecessor
   Answer: B. EST = max(EFT of all predecessors). (Key point: Merge rule)

3. At a burst point in the backward pass, which value is taken?
   A. The largest LST
   B. The sum of LSTs
   C. The smallest LST of the successors
   D. The EST
   Answer: C. LFT = min(LST of all successors). (Key point: Backward rule)

4. In the example, what is EST of E?
   A. 9 days
   B. 6 days
   C. 7 days
   D. 12 days
   Answer: A. EST of E = max(EFT of C = 9, EFT of D = 6) = 9; EFT = 12. (Key point: Example)

## Related in Project Engineering

- [CPM network, 12 activities (A=10 to L=8)](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Acpm-network-twelve-act-as67) — Project Engineering, chapter 3
- [CPM network, 9 activities with successors](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Acpm-network-nine-act-a76) — Project Engineering, chapter 3
- [CPM network, building project (A to K)](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Acpm-network-eleven-act-s73) — Project Engineering, chapter 3

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