---
title: "Time cost trade-off and steps in planning"
subject: "Construction Management"
chapter: 2
key: "semester_8/construction_management:tcto-steps-planning"
source: https://www.bctengineer.com/q/semester_8/construction_management/tcto-steps-planning
site: BCT Engineering
---

# Time cost trade-off and steps in planning

Construction Management · Chapter 2: Construction Planning and Scheduling

- Asked in: 2070 Bhadra, 5 marks
- Video: [Time Cost Trade OFF](https://www.youtube.com/watch?v=8Ps5LzurAIE) — Sharma Design Studio
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/construction_management/tcto-steps-planning
- Whole chapter: https://www.bctengineer.com/md/semester_8/construction_management/chapter-2

## Question

Discuss on time cost trade-off with examples and steps in planning.

## Short answer

Steps: draw network, find critical path, compute each activity’s cost slope, crash critical activity with lowest slope one unit at a time, recompute duration and costs, repeat until slope exceeds indirect cost saved. In the example, crashing both P and Q fully (slopes Rs 400/day and Rs 300/day, below Rs 500/day indirect) gives optimum duration 4 days and total cost Rs 6,600.

## Answer

Time-cost trade-off is the study of the relation between project duration and cost, in order to find the duration with minimum total cost. Direct cost rises when activities are crashed; indirect cost falls when the project is shorter.

#### Steps in planning
1. Draw the network and find the critical path and normal duration.
2. Find the normal and crash time and cost of every activity.
3. Compute the cost slope = (crash cost - normal cost)/(normal time - crash time).
4. Crash the critical activity with the lowest slope by one unit (not below its crash time). If there are several critical paths, crash a combination that cuts all of them.
5. Recompute project duration, direct cost, indirect cost and total cost.
6. Repeat until the slope exceeds the indirect cost saved per unit time, or all critical activities are at crash limit.
7. Choose the duration with the lowest total cost as the optimum.

#### Example
Activities in series: P (normal 4 days, Rs 2,000; crash 2 days, Rs 2,800) and Q (normal 3 days, Rs 1,500; crash 2 days, Rs 1,800). Indirect cost Rs 500/day.

Slopes: P = (2800 - 2000)/2 = Rs 400/day; Q = 300/1 = Rs 300/day.

| Step | Crash | Duration | Direct | Indirect | Total |
|---|---|---|---|---|---|
| 0 | - | 7 | 3,500 | 3,500 | 7,000 |
| 1 | Q | 6 | 3,800 | 3,000 | 6,800 |
| 2 | P | 5 | 4,200 | 2,500 | 6,700 |
| 3 | P | 4 | 4,600 | 2,000 | 6,600 |

**Answer: all slopes are below the indirect cost of Rs 500/day, so the project is crashed fully: optimum duration 4 days, total cost Rs 6,600.**

## Check yourself

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

1. How is cost slope found?
   A. (crash cost - normal cost)/(normal time - crash time)
   B. Normal cost/normal time
   C. Crash time x crash cost
   D. (normal time - crash time)/cost
   Answer: A. Extra cost divided by time saved. (Key point: Slope)

2. Which activity is crashed first?
   A. Highest-slope non-critical
   B. Critical with lowest slope
   C. Longest activity
   D. Any with float
   Answer: B. Cheapest critical activity first. (Key point: Which to crash)

3. When to stop crashing?
   A. When slope exceeds indirect cost saved per unit time, or crash limits are reached
   B. After one step
   C. When duration is normal
   D. Never
   Answer: A. Beyond that point total cost rises. (Key point: Stop rule)

4. In the P/Q example (indirect Rs 500/day), the result is:
   A. 7 days, Rs 7,000
   B. 6 days, Rs 6,800
   C. 4 days, Rs 6,600 (full crashing)
   D. 5 days, Rs 6,700
   Answer: C. All slopes (400, 300) are below 500, so full crash gives 4 days at Rs 6,600. (Key point: Example result)

## Related in Construction Management

- [Time cost trade-off concept with example](https://www.bctengineer.com/question.md?key=semester_8%2Fconstruction_management%3Atcto-concept) — Construction Management, chapter 2, asked 5×
- [TCTO numerical with time-cost chart (five activities)](https://www.bctengineer.com/question.md?key=semester_8%2Fconstruction_management%3Atcto-2079-jestha) — Construction Management, chapter 2
- [Importance and steps of planning and scheduling](https://www.bctengineer.com/question.md?key=semester_8%2Fconstruction_management%3Aplanning-importance-steps) — Construction Management, chapter 2

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