The local Department of Motor Vehicles issues new licenses and renews licenses.
ID: 3011622 • Letter: T
Question
The local Department of Motor Vehicles issues new licenses and renews licenses. The office receives 45 customers per hour. All customers first see a receptionist. It takes the receptionist 0.4 minutes to direct each of them in one of three directions. 75% go directly to Issue License (staffed by 9 workers) where a new photo and license are done. Each worker's processing time is 6 minutes per customer. 15% are required to take an eye test (staffed by one worker with processing time of 5 minutes per customer) and 10% must first take a 15-minute multiple-choice electronic written test (on one of three computers). Only 85% of people pass the eye test and the remaining 15% exit. The customers who pass the eye test proceed on to the Written Test. 10% of the people who take the written test fail it, while 90% pass the test and then proceed to Issue License. What is the implied utilization of the activity Issue License? (Please round your answer to two decimal places.)
Use excel to solve
The implied utilization of Issue License is _____%
(The professor said the answer is 47.74%, I just need to know how to get that/show my work)
Explanation / Answer
Suppose there are x customers for issuing license.
Then time spent on reception = 0.4x mins
0.75x customers proceed directly to Issue License taking time (9 workers) = 0.75x * 6 / 9 = 0.5x mins
0.1x customers take test for 15 mins each (on 3 computers) and 90% of them pass to go through Issue License
Total time taken = 0.1x * 15 / 3 + 0.9 * 0.1x * 6 / 9 = 0.56x mins
0.15 customers go for the eye test for 5 mins each (1 worker) and 85% of them go for written test before going to Issue License
Total time taken = 0.15x * 5 / 1 + 0.85 * 0.15x * 15 / 3 + 0.9 * 0.85 * 0.15x * 6 / 9 = 1.464x mins
Summation of all total time = 0.4x + 0.5x + 0.56x + 1.464x = 2.924x mins
Total time spent in Issue License = 0.75x * 6 / 9 + 0.9 * 0.1x * 6 / 9 + 0.9 * 0.85 * 0.15x * 6 / 9 = 0.6375x mins
Total number of customers Issue License can handle in an hour = 60 / 0.6375 = 94.12
Current number of customers= 45
Implied utilization = 45 / 94.12 = 47.8%
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