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# Unit 4: Project

Assignment 1: JET Copies Case Problem Pamela L. Williams Quantitative Methods MAT 540 Strayer University January 27, 2013

Unit 4: Project

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. First I created the cumulative distribution table of the probability distribution of repair times given and named it as Lookup. To simulate the breakdown situation lets assume that number of days needed to repair a copier is random and denoted by r1 between 0 and 1, thus: 0 < r1 < 0.2, then it takes 1 day 0.2 < r1< 0.65, then it takes 2 days 0.65 < r1< 0.90, then it takes 3 days 0.9 < r1< 1, then it takes 4 days. This was used along with a set of random numbers generated by Excel function RAND(). 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. In Excel, use a suitable method for simulating the interval between successive breakdowns, according to the continuous distribution shown. The interval of how many times it would breakdown between 0 and 6 weeks with the probability increasing as time goes on (Taylor, B. W. 2011). I used the probability distribution formula below to generate that function: F(x) = x/18, for 0x6 Where x= time between breakdowns When I substituted the information that was given in the text into this formula you get: F(x) = x/36 for 0x6 Or

Unit 4: Project

x= 6r2 (r2 is the random number used in the simulation) Therefore to simulate from the break down distribution, generate a random number r2 between 0 and 1 and make the transformation x = =6*SQRT(r2). In Excel, use a suitable method for simulating the lost revenue for each day the copier is out of service. It is given that the number of copies sold per day follows a uniform probability distribution between 2,000 and 8,000 copies. The revenue loss random number per day can be obtained by generating a uniform random number r3 between 2000 and 8000. The cost per copy is \$.10. The lost business on a specific day would be r3*repair time. The lost revenue would be equal to (\$0.1*) (r3*repair time). 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 the excel simulation model, A5 through C9 represents the cumulative distribution table. It contains the Lookup table from B6 through C9. E5 through L19 is the simulation. In the simulation Random r1 and r2 columns have been generated using Rand () function and Random r3 have been generated using RandomBetween(2000, 8000). Using simulation the estimated loss of revenue due to copier breakdown for one year is \$12,941.66. They should purchase a backup copier based on the result of simulation. In a word processing program, write a brief description/explanation of how you implemented each component of the model. The amount of revenue lost can be found by looking at how many days it takes to repair, and then multiplying by the amount of copies and the price per copy. The time between breakdowns will tell how often this occurs, and the sum in weeks is not to exceed 52. How confident are you that this answer is a good one? What are the limits of the study? Write at least one paragraph. Buying an extra copier would probably be a good choice,

Unit 4: Project

since the amount of revenue lost \$12,941.66 is about 70% more than \$8,000.00 the cost of smaller backup copy machine. Also from the case study we know that 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. The amount of revenue lost isn't entirely accurate since we would have to run a large number of trials and take the average to find exactly what revenue is lost per year.

References

Unit 4: Project

Taylor, B.M. (2010). Introduction to Management Science (11th Ed.). Upper Saddle River, NJ: Pearson/Prentice Hall. Pages 678-79
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