A UPS employee, Davis, packs and labels three types of packages: basic packages, business packages, and oversized packages. Business packages take a priority over basic packages, and oversized packages because those customers paid a premium to have guaranteed two-day delivery. During his nine-month shift, he has, on average, one container of packages containing a variety of basic, business, and oversized packages to process every 3 hours. As soon as Davis processes a package, he passes it to the next employee, who loads it onto a truck. The times it takes him to process the three different types of packages and the average number of packages per customer are shown below.

Basic: 5 minutes – average number of minutes to label and package each unit 10 - average number of units per container
Business: 4 minutes – average number of minutes to label and package each unit 10 - average number of units per container
Oversized: 6 minutes – average number of minutes to label and package each unit 5 - average number of units per container
Davis currently processes packages from each container as follows. First, he processes all business packages in the container. Then he randomly selects either basic packages or oversized packages for processing until the container is empty. However, his manager suggested to Davis that, for each container, he should process all the business packages first, second the basic packages, and last the oversized packages.
a. If Davis follows his supervisor’s advice, what will happen to Davis’s utilization?

b. What will happen to the average time that a package spends in the container?

Would this be factoring the wait time for each type of package before and after he implements his manager's advice. If so, how is this done?

21

To answer these questions, we will consider Davis's current process and compare it to his manager's advice.

a. Davis's current process:
- Davis processes all business packages first, followed by randomly selecting either basic or oversized packages.
- This means that Davis spends 4 minutes per business package, regardless of the number of basic or oversized packages in the container.

Davis's manager's advice:
- Davis should process all the business packages first, then the basic packages, and lastly the oversized packages.
- This means that Davis will spend 4 minutes per business package, 5 minutes per basic package, and 6 minutes per oversized package.

Now let's analyze the impact of following his manager's advice:

1. Utilization:
Utilization refers to the amount of time a resource (in this case, Davis) is actively working on processing packages.

In Davis's current process, Davis spends 4 minutes per business package on average. With his manager's advice, Davis will still spend the same amount of time per business package. Therefore, his utilization will not change.

b. Average time a package spends in the container:
To calculate the average time a package spends in the container, we need to consider the time taken to process each type of package and the number of packages in the container. We'll assume that all packages are processed one by one, without any waiting time within the container.

In Davis's current process:
- The average time a business package spends in the container = 4 minutes (processing time per package) * 10 (average number of business packages per container) = 40 minutes
- The average time a basic package spends in the container = 5 minutes (processing time per package) * 10 (average number of basic packages per container) = 50 minutes
- The average time an oversized package spends in the container = 6 minutes (processing time per package) * 5 (average number of oversized packages per container) = 30 minutes

To calculate the overall average time a package spends in the container, we take the weighted average based on the proportion of each package type in the container:

Average time = (40 minutes + 50 minutes + 30 minutes) / (10 + 10 + 5) = 120 minutes / 25 = 4.8 minutes

If Davis follows his manager's advice:
- The average time a business package spends in the container = 4 minutes (processing time per package) * 10 (average number of business packages per container) = 40 minutes
- The average time a basic package spends in the container = 5 minutes (processing time per package) * 10 (average number of basic packages per container) = 50 minutes
- The average time an oversized package spends in the container = 6 minutes (processing time per package) * 5 (average number of oversized packages per container) = 30 minutes

Average time = (40 minutes + 50 minutes + 30 minutes) / (10 + 10 + 5) = 120 minutes / 25 = 4.8 minutes

The average time a package spends in the container remains the same, regardless of whether Davis follows his manager's advice or not.

It's important to note that we have only considered the processing time and the number of packages in the container. If you want to factor in waiting time for each type of package before and after implementing the manager's advice, you would need additional information on how packages are organized and handled within the container.