quantitative statistic assignment
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Assignment #1: JET Copies Case Problem
Read the “JET Copies” Case Problem on pages 678-679 of the text. Using simulation estimate the loss of revenue due to copier breakdown for one year, as follows:
- In Excel, use a suitable method for generating the number of days needed to repair the copier, when it is out of service, according to the discrete distribution shown.
- In Excel, use a suitable method for simulating the interval between successive breakdowns, according to the continuous distribution shown.
- In Excel, use a suitable method for simulating the lost revenue for each day the copier is out of service.
- Put all of this together to simulate the lost revenue due to copier breakdowns over 1 year to answer the question asked in the case study.
- In a word processing program, write a brief description/explanation of how you implemented each component of the model. Write 1-2 paragraphs for each component of the model (days-to-repair; interval between breakdowns; lost revenue; putting it together).
- Answer the question posed in the case study. How confident are you that this answer is a good one? What are the limits of the study? Write at least one paragraph.
There are two deliverables for this Case Problem, the Excel spreadsheet and the written description/explanation. Please submit both of them electronically via the dropbox.
The assignment will be graded using the associated rubric.
| Outcome Assessed: |
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| Grading Rubric for JET Copies Case Problem There are 12 possible points in each of the five criteria for a total of 60 points possible. |
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| Criteria | 0Unacceptable(0 points) | 1Developing(6 points) | 2Competent(9 points) | 3Exemplary(12 points) |
| 1. Model number of days to repair | Did not submit or did not model this component in an appropriate manner | This component was modeled, but the method and/or implementation had mistakes that affected the validity of the model | Used a method that is recognizably appropriate, but the implementation had minor mistakes | Used an appropriate method and correctly implemented it |
| 2. Model number of weeks between breakdowns | Did not submit or did not model this component in an appropriate manner | This component was modeled, but the method and/or implementation had mistakes that affected the validity of the model | Used a method that is recognizably appropriate, but the implementation had minor mistakes | Used an appropriate method and correctly implemented it |
| 3. Model lost revenue due to breakdowns | Did not submit or did not model this component in an appropriate manner | This component was modeled, but the method and/or implementation had mistakes that affected the validity of the model | Used a method that is recognizably appropriate, but the implementation had minor mistakes | Used an appropriate method and correctly implemented it |
| 4. Provide written description and explanation of the simulation | Did not submit or described insufficiently. Omitted key points. | Provided partially developed written description that matches the method 70 – 79% accuracy. | Provided sufficiently developed written description that matches the method 80 – 89% accuracy. | Provided fully developed written description that is correct and matches the method used with 90 – 100% accuracy. |
| 5. Combine model components to produce a coherent answer to the question posed in the case study. (a) Answer the question posed in the case study. (b) How confident are you that this answer is a good one? (c) What are the limits of the study? | Did not submit or result not provided, and/or discussed insufficiently. | Provided partially correct result. Omitted discussion of confidence. Discussed limitations partially with 70 – 79% accuracy, logic, and clarity. | Provided sufficiently correct result. Identified confidence and discussed limitations sufficiently with 80 – 89% accuracy, accuracy, logic, and clarity. | Provided fully correct result. Identified confidence and discussed limitations fully with 90 – 100% accuracy, logic, and clarity. |
James Banks was standing in line next to Robin Cole at Klecko’s
Copy Center, waiting to use one of the copy machines. “Gee,
Robin, I hate this,” he said. “We have to drive all the way over here
from Southgate and then wait in line to use these copy machines.
I hate wasting time like this.”
“I know what you mean,” said Robin. “And look who’s here. A
lot of these students are from Southgate Apartments or one of the
other apartments near us. It seems as though it would be more
logical if Klecko’s would move its operation over to us, instead of
all of us coming over here.”
James looked around and noticed what Robin was talking
about. Robin and he were students at State University, and most
of the customers at Klecko’s were also students. As Robin
suggested, a lot of the people waiting were State students who
lived at Southgate Apartments, where James also lived with Ernie
Moore. This gave James an idea, which he shared with Ernie and
their friend Terri Jones when he got home later that evening.
“Look, you guys, I’ve got an idea to make some money,” James
started. “Let’s open a copy business! All we have to do is buy a
copier, put it in Terri’s duplex next door, and sell copies. I know
we can get customers because I’ve just seen them all at Klecko’s.
If we provide a copy service right here in the Southgate complex,
we’ll make a killing.”
Terri and Ernie liked the idea, so the three decided to go into
the copying business. They would call it JET Copies, named for
James, Ernie, and Terri. Their first step was to purchase a copier.
They bought one like the one used in the college of business office
at State for $18,000. (Terri’s parents provided a loan.) The company
that sold them the copier touted the copier’s reliability, but
after they bought it, Ernie talked with someone in the dean’s office
at State, who told him that the University’s copier broke down frequently
and when it did, it often took between 1 and 4 days to get
it repaired.When Ernie told this to Terri and James, they became
worried. If the copier broke down frequently and was not in use
for long periods while they waited for a repair person to come fix
it, they could lose a lot of revenue. As a result, James, Ernie, and
Terri thought they might need to purchase a smaller backup
copier for $8,000 to use when the main copier broke down.
However, before they approached Terri’s parents for another loan,
they wanted to have an estimate of just how much money they
might lose if they did not have a backup copier. To get this estimate,
they decided to develop a simulation model because they
were studying simulation in one of their classes at State.
To develop a simulation model, they first needed to know how
frequently the copier might break down—specifically, the time
between breakdowns. No one could provide them with an exact
probability distribution, but from talking to staff members in the
college of business, James estimated that the time between breakdowns
was probably between 0 and 6 weeks, with the probability
increasing the longer the copier went without breaking down.
Thus, the probability distribution of breakdowns generally looked
like the following:
Next, they needed to know how long it would take to get the
copier repaired when it broke down. They had a service contract
with the dealer that “guaranteed” prompt repair service. However,
Terri gathered some data from the college of business from which
she developed the following probability distribution of repair times:
Repair Time (days) Probability
1 .20
2 .45
3 .25
4 .10
1.00
Finally, they needed to estimate how much business they would
lose while the copier was waiting for repair. The three of them had
only a vague idea of how much business they would do but finally
estimated that they would sell between 2,000 and 8,000 copies per day
at $0.10 per copy. However, they had no idea about what kind of
probability distribution to use for this range of values. Therefore, they
decided to use a uniform probability distribution between 2,000 and
8,000 copies to estimate the number of copies they would sell per day.
James, Ernie, and Terri decided that if their loss of revenue due to
machine downtime during 1 year was $12,000 or more, they should
purchase a backup copier. Thus, they needed to simulate the breakdown
and repair process for a number of years to obtain an average
annual loss of revenue. However, before programming the simulation
model, they decided to conduct a manual simulation of this process for
1 year to see if the model was working correctly. Perform this manual
simulation for JET Copies and determine the loss of revenue for 1 year.
