Introduction to Management Science (10th Edition)

JET C OPIES

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 downspecifically, 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:

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.