GATE ME 2014 Set 2 — Question 60
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Question
A project has four activities P, Q, R and S as shown below.
The normal cost of the project is Rs. 10,000/- and the overhead cost is Rs. 200/- per day. If the project duration has to be crashed down to 9 days, the total cost (in Rupees) of the project is _______.
| Activity | Normal duration (days) | Predecessor | Cost slope (Rs./day) |
|---|---|---|---|
| P | 3 | - | 500 |
| Q | 7 | P | 100 |
| R | 4 | P | 400 |
| S | 5 | R | 200 |
Correct answer
12490 to 12510
Solution
1.Identify paths and durations:
- Path 1: P Q: days
- Path 2: P R S: days (Critical Path)
- Normal Cost = Rs. 10,000
- Overhead Cost (12 days) =
- To reduce Path 2 from 12 to 9 days (3 days reduction):
- Crash S (cheapest slope = 200) by 3 days. Cost = .
- Path 2 duration becomes 9 days.
- To reduce Path 1 from 10 to 9 days (1 day reduction):
- Crash Q (slope = 100) by 1 day. Cost = .
- Path 1 duration becomes 9 days.
- Total Crashing Cost = .
- Total Cost = Normal Cost + Crashing Cost + Overhead Cost (9 days)
- Total Cost = .
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