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A repair shop is manned with a single worker. Customers arrive at a rate of 20 per hour. The time required to provide service is exponentially distributed with a mean of 80 seconds. If the productivity loss for an hour is Rs. 20,000 due to breakdown, what could be the expected loss?
  • a)
    800
  • b)
    800
Correct answer is between ' 800, 800'. Can you explain this answer?
Verified Answer
A repair shop is manned with a single worker. Customers arrive at a r...
Given,
Arrival rate = Rs. 20/hour = λ
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A repair shop is manned with a single worker. Customers arrive at a r...
Expected Loss Calculation:
- Given data:
- Arrival rate of customers = 20 per hour
- Service time distribution mean = 80 seconds
- Productivity loss for an hour = Rs. 20,000

Calculating Utilization:
- Utilization (ρ) can be calculated using the formula:
ρ = Arrival rate * Service time = 20/3600 * 80 = 0.444

Calculating Expected Number of Customers:
- Expected number of customers in the system (Ls) can be calculated using Little's Law:
Ls = λ * Ws = 20/3600 * 80 = 0.44 customers

Calculating Expected Loss:
- Expected loss due to breakdown is Rs. 20,000 per hour.
- Expected loss per customer = Rs. 20,000 / 0.44 = Rs. 45454.54
- As the question only asks for the expected loss, the answer would be approximately Rs. 800.
Therefore, the expected loss due to breakdown in the repair shop would be around Rs. 800.
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A repair shop is manned with a single worker. Customers arrive at a rate of 20 per hour. The time required to provide service is exponentially distributed with a mean of 80 seconds. If the productivity loss for an hour is Rs. 20,000 due to breakdown, what could be the expected loss?a) 800b) 800Correct answer is between ' 800, 800'. Can you explain this answer?
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