GATE CE 2019 Set 1 — Question 47
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Structural Engineering → Construction Management → Crashing of Networks
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Question
The network of a small construction project awarded to a contractor is shown in the following figure. The normal duration, crash duration, normal cost, and crash cost of all the activities are shown in the table. The indirect cost incurred by the contractor is per day.
If the project is targeted for completion in 16 days, the total cost (in ) to be incurred by the contractor would be ______
| Activity | Normal Duration (days) | Crash Duration (days) | Normal Cost (INR) | Crash Cost (INR) |
|---|---|---|---|---|
| P | 6 | 4 | 15000 | 25000 |
| Q | 5 | 2 | 6000 | 12000 |
| R | 5 | 3 | 8000 | 9500 |
| S | 6 | 3 | 7000 | 10000 |
| T | 3 | 2 | 6000 | 9000 |
| U | 2 | 1 | 4000 | 6000 |
| V | 4 | 2 | 20000 | 28000 |
Correct answer
149500 to 149500
Solution
1.Calculate Cost Slopes for each activity:
Cost Slope = - /day
- /day
- /day
- /day
- /day
- /day
- /day
- Path 1: days
- Path 2: days
- Path 3: days (Critical Path)
3.Crash to 16 days:
- Step 1 (18 to 17 days): Crash critical path . Cheapest is (750/day). Crash by 1 day. Cost increase = 750. New durations: Path 1 = 17, Path 2 = 16, Path 3 = 17. Now Path 1 and Path 3 are critical.
- Step 2 (17 to 16 days): Crash both Path 1 and Path 3. Options: Crash (5000), (4000), or . Cheapest is or at . Crash by 1 more day (limit reached) and by 1 day. Cost increase = 2750. New durations: Path 1 = 16, Path 2 = 16, Path 3 = 16.
- Total Normal Direct Cost =
- Total Crash Cost =
- Total Indirect Cost for 16 days =
- Total Project Cost = .
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