- 2073 Bhadra · 6 marks
TCTO numerical: optimal crashed result, Rs 300/week
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.
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 | - |
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.
| 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.)
✓ Answer checked by Claude Opus 5.5 (high effort)
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