...Jet Copy Simulation Prepared by Joe Miller Prepared for February 7th 2013 TABLE OF CONTENTS INTRODUCTION SUMMARY JET COPY SIMILATION CONCLUSION AND RECOMMENDATIONS APPENDIX INTRODUCTION The purpose of this report is to examine the feasibility to for Jet Copy to purchase a second copy machine. Based on copies produced and lost with only the use of one copier. In this report I will use data from a simulation to assist in the determination of an additional copier for Jet Copy. As a reminder that this is a random simulation and the information in the simulation will only assist between when the test stop and 52 week will not have great affect on the outcome of the in the decision making. The simulation that was run was base on a 52 week scenario. The actual results are based on 51 week trial. The difference between the 51 week test and the actual 52 weeks will not have any great impact on the recommendation. ------------------------------------------------- SUMMARY This report creates a simulation that shows one possible outcome for Jet Copier when there one copier is out for repair for up to 4 days. It will also aid in the decision to ad d or not to add a second copier. This report will answer the following questions: 1. Using Excel to generate the number of days needed to repair the copier. 2. Using Excel to generate the interval between successive breakdowns according to continuous distribution. 3. Using Excel, use a suitable method to...
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...Quantitative Methods -MAT 540 JET Copies Case Problem Assignment #1 Days-to-repair Terri was able to gather data from the college which allowed them to develop a table for the probability distribution of the wait for repair services on JET’s copier. To model the probability of wait times in the JET Copies simulation, the JET partners generated a random number representing the probability of an occurrence of a breakdown. They then programmed a VLOOKUP function to match this breakdown probability to the corresponding “Repair Time in Days” column of the table. The result is the simulated time to get repair service for each breakdown occurrence. Interval between breakdowns The James, Ernie, and Terri purchased a copier just like the one used at their college office. When Ernie talked with someone in the dean’s office at State, he was told that the University’s copier broke down frequently often for 1 to 4 days. The partners became worried that their machine would also frequently break down. Although they could not get an exact probability distribution, James was able to determine that breakdowns occurred between 0 and 6 weeks apart. The probability of a breakdown increased as time passed. To model the time between breakdowns in their simulation, JET created a list of random numbers. Next, they applied the probability function f(x) = 2x/a2 0≤ x ≤ a. For this situation, the formula used is x = a √r. Since James estimated breakdowns occur zero to six weeks apart...
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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 Study 1. 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. 2. In Excel, use a suitable method for simulating the interval between successive breakdowns, according to the continuous distribution shown. 3. In Excel, use a suitable method for simulating the lost revenue for each day the copier is out of service. 4. 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. 5. 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). 6. 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. Answers 1. # of days P(x) Cumulative 1 0.2 0 2 0.45 0.2 3 0.25 0.65 4 0.1 0.9 Q: 2-4. Break Random times b/w Random Repair Random Lost cumulative down # 1 Break (weeks) # 2 Time #3 Revenue time 1 0.78468 5.314929 0.88991 3 2237 $6,711 5.314929 2 0.512227 4.294201 0.831365 2 3244 $6,488 9.60913 3 0.389251 3.743399 0.912647 2 5874 $11,748 13.35253 4 0.998082 5.994243 0.216353 1 3330 $3,330 19.34677 5 0.963834 5.890502 0.415313 4 5487 $21,948...
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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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...Jet Copies a Case Study Jet Copies is a small business that was started by three friends to provide copy services to students at State University. To accomplish this they borrowed from one of the partners parents to purchase a high end copy machine. But after purchasing the copy machine they found that it was not as reliable as they were led to believe. The partners wanted to find out how long and how often the copier would be out of service. They also wanted to know how much money they would lose when the copier was out of service. If the copier was out of service so long that they would lose more than 12,000 dollars they would purchase a backup unit. To accomplish this we will use Microsoft Excel to create a statistical analysis of a year of operation of the copier. Number of days to repair the copier probability days .45 1 .20 2 .25 3 .10 4 Based on the data provided above we see that the probability for a repair to the copier to take one day is 45%, two days is 20%, three days is 25%, and four days is 10%. To compute this in Excel we will use the random number feature and the lookup function. First we create a table to account for the probability of the duration of repairs based on the data provided. probability days 0 1 0.45 2 0.65 3 0.9 4 As you can see 0-.44 is a 1 day repair, .45-64 is a 2 day repair, .65-89 is a 3 day repair, and .9- 1 is a 4 day repair. We then use a random number generated by Excel by using the RAND () function. This will provide...
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...The purpose of this simulation was to create to determine if JET Copies needs to purchase a back up copier. To begin, information had to be gathered which was given based on research the founders of JET Copies did to determine the length of time between breakdowns, the probability of repair times, and the revenue they would take in daily. Because there is a variance amongst the days it would take to repair the copier as well as the revenue being lost, creating this simulation helps JET Copies make the best decisions considering all the possibilities through sampling and probability. While it would be more accuracy to follow the physical process to make the decision based on true, random occurrences, JET Copies wants to know the number of breakdowns and repair time for a year which calls for this simulation of random numbers. To begin this simulation the repair time table had to be computed because it would give an introduction overview of the probability of the repair time needed to fix any breakdowns; it would also be needed to fulfill some details in the next table as well. Based on this table the following information was gathered: the probability that it would take one to two days to repair a breakdown would be 65 percent whereas for it to take three days or more would be 90 percent. After this table was created it was time to focus on the main table of the simulation which would provide more detailed information from a probability basis. The first column of the second...
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...The purpose of the JET Copies Case Problem was to develop a simulation that would help identify the number of times that a copier machine would break down over a year’s time, the average repair time days, and lastly the estimated loss of revenue that occurred when the machine broke down each time. The owners of the company needed this information to make a decision on whether or not to purchase a backup copier. I decided to start with the table on page 679, which identified the probability of the days that it took the copier to get fixed each time that it broke down. I calculated the cumulative probability before beginning my simulation. I figured that in a year’s time with a max of six weeks between breakdowns according to the information given, that the copier would break down approximately 15 times. In Excel, I created fifteen random numbers (RN1) based upon my cumulative probability and probability distribution given. After which, I determined an average number of repair days for each break down which calculated to be about 2 days. The second step taken to begin this simulation was to determine the frequency of how often the copier would break down. The probability given was based upon speaking with staff members from the college of business and notating that the probability of the break downs increased the longer the copier went without breaking down. In looking at the visual provided on page 679, I was able to use the formula y=mx+b in order to find the probability...
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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...
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...Jet Copies Breakdown Cumulative Prob Time Between Breakdown Probability Cumulative Probability Repair Time (days) Probability (Uniform) Cumulative Probability Sales Vol. F(x) = .0275x2 x = 20*sqrt(r/11) 0.20 0 1 0.143 0 2000 0.45 0.20 2 0.143 0.143 3000 0.25 0.65 3 0.143 0.286 4000 0.10 0.90 4 0.143 0.429 5000 0.143 0.571 6000 0.143 0.714 7000 0.143 0.857 8000 Breakdowns "Random #, r1 ( rand() )" Time Between Breakdowns, x (weeks) Cumulative Time, x (weeks) Random #, r2 ( rand() ) Repair Time (days) "Random #, r3 ( rand() )" Number of Sales Per Day Revenue Lost Per Day, .10s Revenue Lost 1 0.87461092 5.639506491 5.639506491 0.812564485 3 0.618968125 6000 $600 $1,800 2 0.619910638 4.747863204 10.3873697 0.046586853 1 0.732973872 7000 $700 $700 3 0.648856412 4.857445687 15.24481538 0.149309122 1 0.415056638 4000 $400 $400 4 0.202647621 2.714591016 17.9594064 0.93071048 4 0.041572713 2000 $200 $800 5 0.035360553 1.133948101 19.0933545 0.985291726 4 0.84598125 7000 $700 $2,800 6 0.59729191 4.660440518 23.75379502 0.94815507 4 0.822362216 7000 $700 $2,800 7 0.538230976 4.424029326 28.17782434 0.14855159 1 0.120220407 2000 $200 $200 8 0.187726352 2.612740475 30.79056482 0.883373483 3 0.508932837 5000 $500 $1,500 9 0.661050419 4.902876406 35.69344123 0.069376826 1 0.265850047 3000 $300 $300 10 0.031228616 1.065638801...
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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 Shaneka Thompson Assignment 1 Math 540 Case Problem Finding the average days of repair in the simulation, first you click on the module at the top and scroll to simulation. Click simulation and open new file. There was a pop up box which you label. I labeled mine Average days of repair. Then I picked 4 categories and put in 100 trails and clicked Ok. When the spreadsheet came up I place in the value section 1, 2, 3, 4 and he frequency I placed 0.2, 0.45., 0.25, and 0.10 and clicked solved in the top. This gave me an average of 2.31 days. By hand I calculated the copies per day. I repeated the steps for getting the weeks between break down. I picked 4 categories and 100 trials. For the values I placed in 1, 2, 3, 4 symbolizing the weeks and 1,1,1,1 for the frequency. This simulation gave me the average of 2.68. By hand I calculated the estimated loss of revenue per year. The third simulation was to determine the loss of revenue per day. The values that were used were the estimated dollar amount and the frequency that I used was 1, 1, 1. This gave me an average of 521 days. I then by hand found the estimated revenue lost. Once the average numbers were tallied, I placed the numbers in the stimulation to gather the average cost per year which was by, simulation 23,633. 58 to 23,931.54 and by estimate was 23,100. The overall view the QM simulation if uses correctly and numbers are used correctly gives a correct simulation of loss or profit. I believe just using one...
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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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