---
title: "TCTO numerical: optimal crashed time, Rs 3000/week"
subject: "Construction Management"
chapter: 2
key: "semester_8/construction_management:tcto-2073-magh"
source: https://www.bctengineer.com/q/semester_8/construction_management/tcto-2073-magh
site: BCT Engineering
---

# TCTO numerical: optimal crashed time, Rs 3000/week

Construction Management · Chapter 2: Construction Planning and Scheduling

- Asked in: 2073 Magh, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/construction_management/tcto-2073-magh
- Whole chapter: https://www.bctengineer.com/md/semester_8/construction_management/chapter-2

## Question

Consider the data of a project as shown in table below. If the indirect cost per week is Rs. 3000, find the optimal crashed project completion time and corresponding minimum cost.

| Activity | Immediate Predecessor | Normal time (Week) | Normal Cost (Rs.) | Crash Duration (Week) | Crash Cost (Rs.) |
|---|---|---|---|---|---|
| A | - | 8 | 2000 | 5 | 2300 |
| B | - | 10 | 4000 | 8 | 4300 |
| C | A | 6 | 3000 | 5 | 3125 |
| D | A | 9 | 5000 | 6 | 5225 |
| E | B | 10 | 2500 | 9 | 2700 |
| F | B | 13 | 5000 | 13 | - |
| G | D, E | 5 | 1000 | 3 | 1700 |

## Short answer

Optimal crashed completion time: 21 weeks, minimum total cost Rs 86,350. Achieved by crashing B (2 wks), E (1 wk), and G (1 wk) on the critical path B-E-G. Cost slopes: B Rs 150/wk, E Rs 200/wk, G Rs 350/wk.

## Answer

#### Given data and method
Indirect cost = 3,000 Rs/week. Time-cost trade-off (TCTO) crashes the activities on the critical path, one time-unit at a time, always choosing the cheapest cost slope, as long as the saving in indirect cost is more than the extra direct cost.

F cannot be crashed (crash duration equals normal duration).

$$
\text{Cost slope}=\frac{\text{Crash cost}-\text{Normal cost}}{\text{Normal duration}-\text{Crash duration}}
$$

| Activity | Normal dur | Crash dur | Normal cost | Crash cost | Slope |
|---|---|---|---|---|---|
| A | 8 | 5 | 2,000 | 2,300 | 100 |
| B | 10 | 8 | 4,000 | 4,300 | 150 |
| C | 6 | 5 | 3,000 | 3,125 | 125 |
| D | 9 | 6 | 5,000 | 5,225 | 75 |
| E | 10 | 9 | 2,500 | 2,700 | 200 |
| F | 13 | 13 | 5,000 | 5,000 | cannot crash |
| G | 5 | 3 | 1,000 | 1,700 | 350 |

#### Paths at normal duration
- A-C = 14 weeks
- A-D-G = 22 weeks
- B-E-G = 25 weeks
- B-F = 23 weeks

Critical activities (on the longest path or paths): B, E, G; normal duration = 25 weeks; normal direct cost = 22,500 Rs.

#### Crashing, step by step
| Step | Crash (by 1 unit) | Slope/cost | Duration | Direct | Indirect | Total |
|---|---|---|---|---|---|---|
| 0 | - | - | 25 | 22,500 | 75,000 | 97,500 |
| 1 | B | 150 | 24 | 22,650 | 72,000 | 94,650 |
| 2 | B | 150 | 23 | 22,800 | 69,000 | 91,800 |
| 3 | E | 200 | 22 | 23,000 | 66,000 | 89,000 |
| 4 | G | 350 | 21 | 23,350 | 63,000 | 86,350 |

#### Result
- **Optimum (minimum-cost) schedule:** duration 21 weeks, direct cost 23,350 + indirect 63,000 = **86,350 Rs**.
- Activities crashed at the optimum: B by 2, E by 1, G by 1. Durations: A=8, B=8, C=6, D=9, E=9, F=13, G=4.
- **Minimum possible duration:** 21 weeks, with total cost 86,350 Rs (direct 23,350 + indirect 63,000).

**Answer: optimal crashed project completion time = 21 weeks; minimum total cost = Rs 86,350.**

## Check yourself

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

1. Which path is critical at normal duration?
   A. A-D-G (22 weeks)
   B. B-F (23 weeks)
   C. A-C (14 weeks)
   D. B-E-G (25 weeks)
   Answer: D. B-E-G is the longest at 10+10+5 = 25 weeks. (Key point: Critical path)

2. What is the cost slope of G (normal 5 wk, Rs 1000; crash 3 wk, Rs 1700)?
   A. Rs 700/week
   B. Rs 350/week
   C. Rs 233/week
   D. Rs 1700/week
   Answer: B. (1700-1000)/(5-3) = 350 per week. (Key point: Slope calculation)

3. In which order are B-E-G activities crashed (slopes B 150, E 200, G 350)?
   A. G, E, B
   B. B, B, E, G, cheapest slope first
   C. E, G, B
   D. B once, then stop because slopes are above Rs 3000
   Answer: B. Lowest slope first: B twice (150), then E (200), then G (350). All are below the Rs 3000/week indirect cost, giving 21 weeks and Rs 86,350. (Key point: Crash order)

## Close variants set in other exams

- [TCTO numerical: optimal crashed time, Rs 2500/week](https://www.bctengineer.com/question.md?key=semester_8%2Fconstruction_management%3Atcto-2078-chaitra) — Construction Management, chapter 2, asked 2×

## Related in Construction Management

- [TCTO numerical: optimal crashed result, Rs 300/week](https://www.bctengineer.com/question.md?key=semester_8%2Fconstruction_management%3Atcto-2073-bhadra) — Construction Management, chapter 2
- [TCTO numerical: lowest cost schedule, Rs 400/week](https://www.bctengineer.com/question.md?key=semester_8%2Fconstruction_management%3Atcto-2075-bhadra) — Construction Management, chapter 2
- [TCTO numerical: least cost schedule, Rs 2000/week](https://www.bctengineer.com/question.md?key=semester_8%2Fconstruction_management%3Atcto-2068-bhadra) — Construction Management, chapter 2
- [TCTO numerical: seven activities, Rs 2000/day](https://www.bctengineer.com/question.md?key=semester_8%2Fconstruction_management%3Atcto-2079-shrawan) — Construction Management, chapter 2
- [TCTO numerical: seven activities, Rs 225/day](https://www.bctengineer.com/question.md?key=semester_8%2Fconstruction_management%3Atcto-2078-kartik) — Construction Management, chapter 2
- [TCTO numerical: seven activities, Rs 1000/day](https://www.bctengineer.com/question.md?key=semester_8%2Fconstruction_management%3Atcto-2070-magh) — Construction Management, chapter 2