Question

the process for renewing a drivers license at the archer county courthouse is as follows. first, the clerk fills out the application; then the clerk takes the drivers picture; and finally, a typist enters the information into the computer system and processes the new license. it takes an average of six minutes to fill out an application, one minute to take a picture, and nine minutes to process the new license. due to county and state budget cuts, archer county courthouse now has only three clerks and three typists and expects to process 45 drivers/hour. what is the current labor utilization of each labor type? do not round intermediate calculations. round your answers to the nearest whole number. labor utilization of clerks: % labor utilization of typists: % where is the bottleneck in this three - stage process? the ability of the system is limited to select. how might the job and process design be improved? the best way to help alleviate this bottleneck is by using select work practices and technology to select service rates.

Explanation:

Step1: Calculate total available time per hour for clerks

Each clerk has 60 minutes in an hour, and there are 3 clerks. So total available minutes for clerks per hour is $3\times60 = 180$ minutes.

Step2: Calculate total time required by clerks per hour

To process one driver, a clerk spends $6 + 1=7$ minutes. To process 45 drivers, total time required is $45\times7 = 315$ minutes.

Step3: Calculate clerk labor - utilization

Labor - utilization of clerks is $\frac{315}{180}\times100\approx175\%$ (but this is not possible in reality, there is a bottleneck). Let's calculate the maximum number of drivers clerks can handle in an hour. Each clerk can handle $\frac{60}{7}\approx8.57$ drivers per hour. 3 clerks can handle $3\times8.57 = 25.71$ drivers per hour. So the actual labor - utilization of clerks is $\frac{45}{25.71}\times100\approx175\%$ (rounding issues aside, conceptually this shows the bottleneck). In a more proper way, the time available for clerks is $3\times60 = 180$ minutes. The time required for 45 drivers is $45\times(6 + 1)=315$ minutes. Labor - utilization of clerks $=\frac{315}{180}\times100 = 175\%$. Since this is over 100%, the clerks are the bottleneck.

Step4: Calculate total available time per hour for typists

Each typist has 60 minutes in an hour, and there are 3 typists. So total available minutes for typists per hour is $3\times60=180$ minutes.

Step5: Calculate total time required by typists per hour

To process one driver, a typist spends 9 minutes. To process 45 drivers, total time required is $45\times9 = 405$ minutes.

Step6: Calculate typist labor - utilization

Labor - utilization of typists is $\frac{405}{180}\times100 = 225\%$. But considering the maximum number of drivers typists can handle, each typist can handle $\frac{60}{9}\approx6.67$ drivers per hour. 3 typists can handle $3\times6.67 = 20$ drivers per hour. The actual labor - utilization of typists is $\frac{45}{20}\times100 = 225\%$. In a more proper way, time available for typists is $3\times60 = 180$ minutes. Time required for 45 drivers is $45\times9=405$ minutes. Labor - utilization of typists $=\frac{405}{180}\times100 = 225\%$. Since the clerks are the bottleneck, the actual number of drivers processed is limited by the clerks. So the effective labor - utilization of typists is based on the number of drivers the clerks can handle. The clerks can handle $\frac{3\times60}{7}\approx25.71$ drivers. The time required for typists for these drivers is $25.71\times9 = 231.39$ minutes. Labor - utilization of typists is $\frac{231.39}{180}\times100\approx128.55\%\approx129\%$.

Answer:

Labor utilization of clerks: 175%
Labor utilization of typists: 129%
The bottleneck in this three - stage process is the clerks.
The best way to help alleviate this bottleneck is by using more efficient work practices and technology to increase service rates.