A UPS employee has a 9 hour shift, where he has on average 1 container of packages containing a variety of basic, business, and oversized packages to process every 3 hours. As soon as he processes a package he passes to the next employee who loads it on a truck. The time is takes him to process:

Average # of minutes to label and package each unit-----Basic: 5 min, Business:4 min, Oversized: 6 min.

Average # of units per container: Basic: 10, Business: 10, Oversized: 5.

He processes packages as follows: first he processes all business packages in the container. The he randomly selects either basic packages or oversized packages for processing until the container is empty. His manager suggested that he for each container he should process all business packages first, second the basic packages, and last oversized packages.

1)IF he follows his supervisor's advice, what will happen to his utilization?
2)WHat will happen to the average time that a package spends in the container?

1) If the UPS employee follows his supervisor's advice and processes all business packages first, then basic packages, and lastly oversized packages, his utilization will likely increase. This is because business packages are processed faster compared to basic and oversized packages. By prioritizing the faster processing packages, the employee can complete more units in the given time, resulting in higher utilization.

2) If the employee follows his supervisor's advice, the average time that a package spends in the container may decrease. This is because business packages, which have a shorter processing time, will be processed first. By processing these packages quickly, the overall time the packages spend in the container will be reduced. However, the average time will still depend on the mix of packages in each container and the randomness of selection between basic and oversized packages.

To answer these questions, let's break down the process and compare the different scenarios.

1) If the UPS employee follows his supervisor's advice and processes the packages in the order of business packages first, basic packages second, and oversized packages last, here's what will happen to his utilization:

To calculate utilization, we need to determine the total time spent on processing packages and divide it by the total available time.

Total available time = 9 hours = 540 minutes

Total time spent on processing:
- Business packages take 4 minutes per unit, and there are 10 business units per container, so the total time spent on processing business packages per container is 10 units * 4 minutes/unit = 40 minutes.
- Basic packages take 5 minutes per unit, and there are 10 basic units per container, so the total time spent on processing basic packages per container is 10 units * 5 minutes/unit = 50 minutes.
- Oversized packages take 6 minutes per unit, and there are 5 oversized units per container, so the total time spent on processing oversized packages per container is 5 units * 6 minutes/unit = 30 minutes.

Total time spent processing packages per container = 40 minutes (business) + 50 minutes (basic) + 30 minutes (oversized) = 120 minutes

Utilization = Total time spent processing packages / Total available time = 120 minutes / 540 minutes ≈ 0.22 or 22%

So, if the UPS employee follows his supervisor's advice, his utilization will be approximately 22%.

2) To determine what will happen to the average time that a package spends in the container, we need to compare the different scenarios.

If the employee follows his supervisor's advice, the order of processing packages is business first, basic second, and oversized last. This means that business packages will be processed and passed on to truck loading first, followed by basic packages, and finally oversized packages. This reduces the time that any package spends waiting in the container.

In contrast, if the employee randomly selects either basic or oversized packages for processing, the order of processing may differ from container to container. This may result in more waiting time for certain packages as they may be processed last.

Therefore, if the employee follows his supervisor's advice, the average time that a package spends in the container will likely decrease compared to the scenario where packages are randomly processed.

It's important to note that these calculations are based on the given average times and quantities. The actual results may vary depending on specific circumstances and variations in processing times.