A car repair shop has two hoists where cars can be lifted for repair work. Currently customers come in at the rate of 4 per hour and are processed at a similar rate. On average 8 cars are waiting to be processed, 4 needing routine repairs and 4 needing major repairs. People are served on a first come first serve basis.
(a) How long do customers wait on average before being processed?
(b) The repair shop owner feels that he is losing many customers needing routine repair because of the long wait. He dedicates one hoist for routine repair and one for major repairs. A study indicates that routine repairs are processed at the rate of 3 per hour and major repairs at the rate of 1 per hour. There are now 5 people waiting on average for routine repairs and 3 waiting on average for major repairs. How long does each type of customer now wait before being served?
(c) With the new system, what is the average waiting time over all customers?

Question

Quizplus · Accepted Answer

The Answer is (a) For the current process we have
Inventory, I = 8 cars,
Throughput, R = 4 cars per hour.
Thus,
Flow time, T = I/R = 8/4 = 2 hours.
Cars wait an average of 2 hours before being served.
(b) At the routine repair hoist, we have
Inventory, I = 5 cars,
Throughput, R = 3 cars per hour.
Thus,
Flow time, T = I/R = 5/3 = 1.67 hours.
Cars wait an average of 1.67 hours before being served at routine repairs.
At the major repairs hoist we have
Inventory, I = 3 cars,
Throughput, R = 1 car per hour.
Thus,
Flow time, T = I/R = 3/1 = 3 hours.
Cars wait an average of 3 hours before being served at major repairs.
(c) With the new system, we have
Inventory, I = 5 + 3 = 8 cars,
Throughput, R = 3 + 1 = 4 cars per hour.
Thus,
Flow time, T = I/R = 8/4 = 2 hours.
Cars wait an average of 2 hours before being served even in the new system.

A Car Repair Shop Has Two Hoists Where Cars Can