---
title: "TCTO numerical: optimal crashed result, Rs 300/week"
subject: "Construction Management"
chapter: 2
key: "semester_8/construction_management:tcto-2073-bhadra"
source: https://www.bctengineer.com/q/semester_8/construction_management/tcto-2073-bhadra
site: BCT Engineering
---

# TCTO numerical: optimal crashed result, Rs 300/week

Construction Management · Chapter 2: Construction Planning and Scheduling

- Asked in: 2073 Bhadra, 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-bhadra
- Whole chapter: https://www.bctengineer.com/md/semester_8/construction_management/chapter-2

## Question

The details of a project are shown below. If the indirect cost per week is Rs. 300, find the optimal crashed result of the project network.

| Activity | Immediate Predecessor(s) | Time (Weeks) Normal | Time (Weeks) Crash | Cost (Rs.) Normal | Cost (Rs.) Crash |
|---|---|---|---|---|---|
| A | - | 7 | 4 | 1800 | 2100 |
| B | - | 9 | 7 | 3500 | 3800 |
| C | B | 5 | 4 | 2500 | 2625 |
| D | A | 8 | 5 | 4000 | 4225 |
| E | C | 9 | 8 | 3000 | 3325 |
| F | B | 11 | 11 | 3000 | - |

## Short answer

Optimal crashed result: 20 weeks, total cost Rs 24,225. Crash B (2 weeks at Rs 150/wk) and C (1 week at Rs 125/wk). Crashing E (Rs 325/wk) is not economical because it exceeds the Rs 300/wk indirect saving.

## Answer

#### Given data and method
Indirect cost = 300 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.

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

| Activity | Normal dur | Crash dur | Normal cost | Crash cost | Slope |
|---|---|---|---|---|---|
| A | 7 | 4 | 1,800 | 2,100 | 100 |
| B | 9 | 7 | 3,500 | 3,800 | 150 |
| C | 5 | 4 | 2,500 | 2,625 | 125 |
| D | 8 | 5 | 4,000 | 4,225 | 75 |
| E | 9 | 8 | 3,000 | 3,325 | 325 |
| F | 11 | 11 | 3,000 | 3,000 | cannot crash |

#### Paths at normal duration
- A-D = 15 weeks
- B-C-E = 23 weeks
- B-F = 20 weeks

Critical activities (on the longest path or paths): B, C, E; normal duration = 23 weeks; normal direct cost = 17,800 Rs.

#### Crashing, step by step
| Step | Crash (by 1 unit) | Slope/cost | Duration | Direct | Indirect | Total |
|---|---|---|---|---|---|---|
| 0 | - | - | 23 | 17,800 | 6,900 | 24,700 |
| 1 | C | 125 | 22 | 17,925 | 6,600 | 24,525 |
| 2 | B | 150 | 21 | 18,075 | 6,300 | 24,375 |
| 3 | B | 150 | 20 | 18,225 | 6,000 | 24,225 |
| 4 | E | 325 | 19 | 18,550 | 5,700 | 24,250 |

#### Result
- **Optimum (minimum-cost) schedule:** duration 20 weeks, direct cost 18,225 + indirect 6,000 = **24,225 Rs**.
- Activities crashed at the optimum: B by 2, C by 1. Durations: A=7, B=7, C=4, D=8, E=9, F=11.
- **Minimum possible duration:** 19 weeks, with total cost 24,250 Rs (direct 18,550 + indirect 5,700).

**Answer: optimal crashed result = 20 weeks; minimum total cost = Rs 24,225.** (Crashing E to reach 19 weeks costs Rs 325 against a saving of Rs 300, so it is not worthwhile.)

## Check yourself

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

1. Why is crashing E to reach 19 weeks not worthwhile?
   A. E cannot be crashed
   B. Its slope Rs 325 exceeds the Rs 300 indirect saving per week
   C. Its slope is lower than Rs 300
   D. B-F becomes shorter
   Answer: B. Extra direct cost 325 is more than the 300 saved, so total cost rises from 24,225 to 24,250. (Key point: Why stop at 20 weeks)

2. Which activity is crashed first on the critical path B-C-E (slopes B 150, C 125, E 325)?
   A. B
   B. E
   C. C
   D. F
   Answer: C. C has the lowest slope (125) among the critical activities. (Key point: Cheapest first)

3. What are the optimum duration and total cost?
   A. 23 weeks, Rs 24,700
   B. 22 weeks, Rs 24,525
   C. 19 weeks, Rs 24,250
   D. 20 weeks, Rs 24,225
   Answer: D. Crashing C by 1 and B by 2 gives direct 18,225 + indirect 6,000 = Rs 24,225 at 20 weeks. (Key point: Optimum cost)

## Related in Construction Management

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