Question

In the production shop of a company, the breakdown of the machines is found to be Poisson distributed with an average rate of 3 machines per hour. Breakdown time at one machine cost 400 birr per hour to the company. There are two choices before the company for hiring the repairmen. One of the repairmen is slow but cheap, the other is fast but expensive. The slow cheap repairman demands 200 birr per hour and will repair the broken down machines exponentially at the rate of 5 per hour. The fast expensive man demands 300 birr per hour and will repair machines exponentially at an average rate of 6 per hour. Which repairman should be hired

Answer 1

The company should hire the slow repairman as the total cost of hiring him including the downtime of machines is 440 birr/hr which is lower than the total cost of hiring the fast repairman at 500 birr/hr.

Step-by-step explanation:

The company needs to decide which repairman to hire based on the total cost of machine breakdowns and repairman fees. The average breakdown rate is 3 machines per hour, and each breakdown costs the company 400 birr per hour. The slow, cheap repairman demands 200 birr per hour and repairs machines at a rate of 5 per hour, while the fast, expensive repairman demands 300 birr per hour and repairs at a rate of 6 per hour.

To calculate the total hourly cost for each repairman, we include the cost of machine downtime and their respective repair rates. For the slow repairman, the expected number of machines waiting to be repaired would be λ / μ1 = 3 / 5 machines. For the fast repairman, the expected number of machines waiting would be λ / μ2 = 3 / 6 machines. Multiplying the expected number of down machines by the cost of downtime per machine and adding the repairman's fee gives us the total cost.

For the slow repairman:
Expected cost of downtime = (3 / 5) × 400 birr/hr = 240 birr/hr
Plus repairman fee = 240 birr/hr + 200 birr/hr = 440 birr/hr

For the fast repairman:
Expected cost of downtime = (3 / 6) × 400 birr/hr = 200 birr/hr
Plus repairman fee = 200 birr/hr + 300 birr/hr = 500 birr/hr

The company should hire the slow repairman since the total cost (440 birr/hr) is lower than that of the fast repairman (500 birr/hr).