- 2070 Bhadra · 5 marks
Time cost trade-off 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.
Discuss on time cost trade-off with examples and steps in planning.
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
- Draw the network and find the critical path and normal duration.
- Find the normal and crash time and cost of every activity.
- Compute the cost slope = (crash cost - normal cost)/(normal time - crash time).
- 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.
- Recompute project duration, direct cost, indirect cost and total cost.
- Repeat until the slope exceeds the indirect cost saved per unit time, or all critical activities are at crash limit.
- 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.
✓ Answer checked by Claude Opus 5.5 (high effort)
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