Question

A construction project consists of four activities. The duration, relationship, and cost parameters are given in the table. The indirect cost of the project is INR 5000 per week. If the project has to be completed by 12 weeks, the total project cost will be, INR _________ (Answer in integer)

 

Hint:

When crashing activities, focus on those that offer the most significant reduction in project duration relative to their crash cost.

Answer 1

Correct Answer: 164000

We are given the normal duration, crash duration, normal cost, and crash cost for each activity. We need to calculate the total cost of the project under the constraint that the project must be completed in 12 weeks. 
Step 1: Calculate the total project duration using the normal durations of the activities:
Activity P: Normal duration = 8 weeks
Activity Q: Normal duration = 5 weeks
Activity R: Normal duration = 6 weeks
Activity S: Normal duration = 4 weeks
From the table, we can see the relationships:
P and Q start at the beginning and do not have predecessors.
R depends on P (i.e., R starts after P).
S depends on Q (i.e., S starts after Q).
We first check the total normal project duration: \[ {Total Normal Duration} = \max({P} + {R}) \quad {and} \quad \max({Q} + {S}) = \max(8 + 6, 5 + 4) = 14 \, {weeks} \] Since the total normal duration is 14 weeks, which exceeds the required 12 weeks, we need to crash the activities to reduce the duration. 
Step 2: Identify the activities to crash:
Activity P: Can be crashed from 8 weeks to 5 weeks, reducing by 3 weeks. The cost increase is \( 26,000 - 20,000 = 6,000 \).
Activity Q: Can be crashed from 5 weeks to 2 weeks, reducing by 3 weeks. The cost increase is \( 33,000 - 30,000 = 3,000 \).
Activity R: Can be crashed from 6 weeks to 4 weeks, reducing by 2 weeks. The cost increase is \( 52,000 - 40,000 = 12,000 \).
Activity S: Can be crashed from 4 weeks to 3 weeks, reducing by 1 week. The cost increase is \( 13,000 - 10,000 = 3,000 \).
Step 3: Crash the activities to meet the required 12-week completion time:
We need to reduce the project duration by 2 weeks (from 14 weeks to 12 weeks). We can achieve this by crashing Activity P by 2 weeks (this will reduce the total duration by 3 weeks, but we'll crash it only for 2 weeks to meet the 12-week requirement). Crashing P by 2 weeks costs \( 2 \times 6,000 = 12,000 \).
Total cost for crashing P = \( 20,000 + 12,000 = 32,000 \).
Step 4: Calculate the indirect cost: The indirect cost is INR 5,000 per week. The project duration is reduced to 12 weeks, so the indirect cost is: \[ {Indirect cost} = 5,000 \times 12 = 60,000 \] Step 5: Calculate the total project cost: \[ {Total Cost} = {Normal Costs} + {Crash Costs} + {Indirect Costs} \] \[ {Total Cost} = (20,000 + 30,000 + 40,000 + 10,000) + 12,000 + 60,000 = 100,000 + 12,000 + 60,000 = 164,000 \] Conclusion: The total project cost is INR 164,000.