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ABSTRACT

James, Ernie and Terri decided to open a copy center to fulfill a need for closer access to copy machines in their community. After buying their first copier, they learned some of the pitfalls associated including the breakdown of the machinery and the potential loss of revenue associated with the breakdown. Before borrowing the additional funds needed to purchase a backup copier, they wanted to get a reasonable estimate of what the potential loss of revenue would be to determine if buying the backup copier made sense. This paper will describe the steps necessary to run a simulation of weeks between one equipment failure and another, the downtime in days due to repair and the lost revenue over a year period of time due to the simulated equipment failure.

METHODOLOGY

The first step in this process is simulating the time between breakdowns. Without explicit information on frequency of breakdowns, some assumptions have to be made. In this case, the assumption is between 0 and 6 weeks with the probability of a breakdown increasing as time between breakdowns increases. I was given a probability distribution graph that showed time in weeks on the x axis from 0 to 6 with a y value of 0.33 where x = 6. The graph looked something like this:

From that information, I calculated that area under the line to ensure that this could be considered a continuous distribution function. For this to be true, the area under the curve must equal 1. The calculation looks like this ½bh = ½*1/3*6 =1/6*6/1 or 1. Since we determined this is a continuous probability distribution function (CDF), we can apply the calculation f(x) = x/18, 0<= x <=6 weeks to determine the weeks between equipment failures. The translation of that function for use in Excel was x=6*SQRT(r), where r is a random number between 0 and 1. I generated pseudorandom numbers for use

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...JET Copies Case Problem LaTonya Crutcher Dr. Emeka Dunu, MAT 540 6/3/13 In the JET Copies Case Problem the probability function of time between repairs is the one of the issues and the other is the loss of revenue if they do not purchase the new copier. We were asked to generate a random value for computation of times between breakdowns. Using these random numbers and the linear formula SQRT(R1)*6, which represents the slope and probability function for breakdown intervals, we were able to compute the interval between breakdowns. The amount of days in repair was one of the issues James, Ernie and Terry needed information. For each day the printer is down is equal to lost revenues and profits for their business. Using a probability look up chart based on assigned probabilities enabled us to randomly simulate the amount of time the printer would have been down or idle and losing print time. This is also another area that a broader random simulation may have helped us end at a more accurate and acceptable outcome. These values were cumulated and the total number of days in repair was calculated. A third set of random numbers were generated to use in our formula y=((6*R3)+2)*100 to calculate a dollar amount of lost revenues per day. These values were summed to get the number of annual lost revenues so that a decision could be made about purchasing a new copier. By formulating the range of random numbers to asses if there is a great need to purchase another copier...

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...The simulation of the jet copier is to help determine if a purchase of second copier is necessary now. In making the best decision, we need to create the best case scenario of potential future events relating to what could happen if the copier was out of commission. Some of what we do know is that the least to the most about of days the copier could be down. This plays a very important part, as we need to determine how much it would cost to not be able to supply the service of copying to the customers. Also, it is equally important to understand that in case of the copier being down, how long it would take to repair and the cost, in lost revenue that would respond to that. In this simulation we used the following information, to help determine the probability of days to repair. Probability (y) | Repair Time(days) | 0.2 | 1 | 0.45 | 2 | 0.25 | 3 | 0.1 | 4 | Secondly, we determined the average amount of time between breakdowns, in order to get this number we had to do a few things, first we had to determine the x value, for this formula ( 6*sqrt of r). The r in this equation was determined by using excel and generating random numbers samples. When substituting this number in for r, we found what we considered to be the time between breakdowns. Using this number to determine time between breakdowns helped up to generate the potential number of days that it took to repair the copier. After, getting all that information, we then used our final formula to help...

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...JET Copies – Case Description University students James, Ernie and Terri are opening a new copy center business called JET Copies. They borrowed $18,000 from Terrie’s parents to purchase their main copy machine. After the copy machine was purchased Ernie found out from a friend that the copy machine had frequent breakdowns; a breakdown between 1 and 6 weeks and often took 1 – 4 days for repair. In order to keep the business running between repairs the business owners are evaluating whether to purchase an $8,000 back up copy machine. The owners decided that if revenue lost per year was greater than $12,000 the additional copier purchase would be made. JET Copies’ owners are putting together a simulation model to determine whether the purchase of another copy machine is necessary. They have the following information: • Time between breakdowns is 1- 6 weeks with probability of a breakdown increasing the longer the copier went without a breakdown • repair time probabilities Table 1: Probability of the days to repair copier Repair Time (days) Probability 1 0.20 2 0.45 3 0.25 4 0.10 • Loss of revenue during repair of the copier: approx. 2000 – 8000 copies/day at $0.10/copy Again, if revenue lost/year was greater than $12,000 then the purchase of a second copier would be warranted. A simulation model using MicroSoft Excel was run to determine lost revenue due to copier breakdowns. To compute the simulation analysis we will run 1000 random numbers (trials) in a MicroSoft...

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...closer to the end of the month. The number of breakdowns I based on the weeks, 52 weeks in a year. Using the same random function (=rand), I received the randomized number, within the 6 (=6*SQRT(I5); weeks intervals the square root gave me the time in between those breakdowns. My next step was to find the average of the square rooted number, lines J5- J56 of the weeks in between, which gave me that average. I also did an average of the days the repair time would take, lines G5-G34, which gave me that average. Of course these numbers can change from time to time. Upon gathering all of this info I need to find the loss of revenue for JET Copies. They estimated that they could produce 2,000 to 8,000 copies in a months’ time. That means possible revenue per day between $200 to $800. On the average of those copies we found that 5000 copies were or could be successful per day, which means the...

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...In the Jet Copies Case Study, we are introduced to three college students: James, Ernie, and Terri. They have discovered that they have a possible solution to two separate problems that they face: the need to make money and the lack of adequate copy services near the university that they attend. The three students decide to open their own copy service but soon discovered that they may have acted too soon in their decision. The first obstacle they had was the initial purchase of equipment. Without doing enough research, they purchased a copier for $18,000 that was obtained as a loan from Terri’s parents. After the purchase, they discovered that the particular brand they purchased had a history of frequently breakdowns. Although the copier manufacturer promised prompt repair service, the machine down time could range from one to four days. In order to hopefully alleviate too much lost revenue for the beginning company, the trio wanted to purchase a backup machine to use during the primary machine breakdowns. The cost of the second machine would be $8,000. Before they approached their parents for another loan, they wanted to determine if it would actually be a profitable move or an unnecessary purchase on a whim. To do this, they set up a simulation to determine how often the main copier could break down within a fifty-two week period. They decided that if the simulation showed that they lost more than $12,000 in revenue with just the one copier they would go ahead with...

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...Jet Copies DAYS TO REPAIR The days to repair component was calculated by using the probability distribution of repair times given. This was used along with a set of random numbers based on 100 breakdowns a year. Then, a vlookup was used and the probability distribution per day to come up with the days to repair, which varies based on the random number that excel generates. The random number represents the probability of how many days it would take to repair the copier. TIME BETWEEN BREAKDOWNS The time between breakdowns component was implemented by taking the formula for elapsed time between breakdowns as stated by Bernard Taylor III (2011). The formula is x=4√r1 where x equals the weeks between machine breakdowns and r1 equals the random number. Once the formula was entered into excel, the formula was calculated and based on the random number calculates the time between breakdowns. LOST REVENUE The lost revenue was calculated by taking the median revenue to be earned in a given day and multiplying this by the calculated days to repair. Once this number was calculated, it was then calculated annually by taking the sum of the lost revenue column and dividing it by the cumulative time divided by 52 for 52 weeks in a year. This calculates the annual loss of revenue. PUTTING IT ALL TOGETHER The lost revenue for one year is $52,518.04 based on calculations in the excel spreadsheet. Confidence in this answer is very high based on research. The limits of...

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