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Submitted By LaNesha2012

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Words 1145

Pages 5

La Nesha H.Tyler

MTH 540:

Strayer University

Scientific management is based on the applying systematic approaches to solving problems and making decisions. This guide to decision making provides a number of mathematical techniques derived from varied sources such as natural science, mathematics, engineering and statistics (Taylor, 2010). One such technique used in scientific management is the Forecasting method. A Forecast provides a reasonable prediction for a future event. Being able to predict the future can provide a valuable asset for any organization. Predictions will not always be one hundred percent accurate, but they can be a reasonable guide to making decisions based on systematic data. Taylor, 2010, discusses two widely used forecasting methods; time series analysis and regression. This project will present information on forecasting in the form of a storyboard.

This project will provide an overview of forecast methods, how forecasts are measured, and identify different types of forecasting methods. According to author Bernard W. Taylor, 2010, “a variety of forecasting exist, and their applicability is dependent on the time frame of the forecast, the existence of patterns in the forecast, and the number of variables to which the forecast is related” (p.682). Time frame classifies forecast into three different categories, short –range, medium-range, and long-range forecast. Short-range forecast are forecast such as Weather forecast in that they predict daily, or weekly short-range outcomes. Medium-range forecast are typically a month to a year, and Long-range forecast are long-term patterns that are considered trends. These Forecasts are documented and observed from one to two years (Taylor, 2010). It is very important to make reliable predictions, and using forecasting, but the further out the prediction the less accurate the...

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...Assignment #1: JET Copies Case Problem For the first component of the case, I was asked to find the number of days needed to repair the copier. To begin, I used the RAND() function in Excel to produce random values for column B9:B22. Once the RAND() function produced values, I copied and pasted just the values in column B9:B22 (to ensure the values would stay frozen and not continue to change). Once I had the random probabilities, I used the table given with the case (entered in cells A1:C6) to find the number of days need to repair. To find this information I used Excel function VLOOKUP, which matched the random probability to the cumulative probability column and whichever column the random fit into, Excel used the corresponding repair time (days) from column C. The VLOOKUP function was used and the information was entered into cells C9:C22, giving the information of number of days needed to repair the copier. The second component, we were asked to find the interval between successive breakdowns. To solve for the time between breakdowns, I used the maximum number of 6 weeks. In cell D9, I used formula 6*SQRT(B9) to find the time between breakdowns in weeks. I copied and pasted this formula into cells D10:D22. Since the problem only wanted to find the cost of breakdowns over a year, I also included a cumulative breakdown time. In this column, cell E9 equals cell D9, cell E10 equals D9+D10, cell E11 equals E10+D11, and so on for cells E12:E22. The third......

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...JET Copies Case Problem Assignment #1 MAT540, Strayer University Assignment#1: JET Copies Case Problem According to the discrete distrubution, the number of days (y) needed to repair the copier is as follows (where “R2” is a random value in the excel sheet between and 0 and 1): 0 < R2 < .2, then it takes 1 day .2 < R2 < .65, then it takes 2 days .65 < R2 < .9, then it takes 3 days .9 < R2 < 1, then it takes 4 days James estimated that the time between break-downs was probably between 0 and 6 weeks, with the probability increasing the longer the copier went without breaking down. For simulating the interval between successive breakdowns: f(x) = x/18, 0 ≤ x ≤ 6 weeks where x= weeks between break-downs f(x) = x²/36, 0 ≤ x ≤ 6 weeks where x= weeks between break-downs f(x) = random number1 (R1) = x²/36 x = 6*sqrt(R1) 3. For simulating the lost revenue every day that the copier is out of service, select a random number (R3) between 2000 and 8000, since it is estimated that they would see between 2000 and 8000 copies a day. They will charge $0.10 per copy. Therefore, the lost revenue for each day the copier is out of service is equal to R3*.1*repair time. The amound of revunue lost is approxiamtely $12,934.80. Please see the attached excel sheet. In order to estimate the revenue lost for the one year of operations the simulation has been performed. The estimates indicated that the copies sales were between 2000 to 8000......

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...probability range, r2 1 0.2 0.2 0.00 - 0.20 2 0.45 0.65 0.21- 0.65 3 0.25 0.9 0.66 - 0.90 4 0.1 1 0.91 - 1 2. Intervals between successive breakdowns: The probability distribution of the random variable varies between the times of 0 to 6 weeks, with the probability increasing as time goes on. This can be approximated by the function F(x) = x/18, for 0”x”6, where x= weeks between machine breakdowns Therefore the distribution function is: F(x) = x²/36 for 0”x”6 Lost revenue: Since the number of copies sold per day is a uniform probability distribution between 2000 to 8000 copies, r3 is a random number between 2000 and 8000. To get the amount of business lost on a particular day is r1, r2 and r3 are random number picked, as well as repair time, and the lost revenue is then calculated by their charging price of $0.10 per copy. Simulation Random Times between Cumulative S. Random Repair S. Random Z= 6r + 2 Lost Revenue Breakdowns r1 bkdowns X (weeks) time r2 time (y) r3 Z Copies # $ 1 45 4.02 4.02 61 2 19; 65 9.04 9040 904 2 90 5.7 9.72 11 1 51 5.06 5060 506 3 84 5.5 15.22 19 1 17 3.02 3020 302 4 17 2.47 17.69 58 3 63; 85; 37 17.1 17100 1710 5 74 5.16 22.85 30 2 89; 76 6.56 6560 656 6 94 5.82 28.67 95 4 71; 34; 11; 27 16.58 16580 1658 7 7 1.58 30.25 38 2 10; 59 8.14 8140 814 8 15 2.32 32.57 24 2 87; 08 9.7 9700 970 9 4 1.2 33.77 68 3 08; 89; 42 14.34 1434 43.4 10 31 3.34 37.11 41 2 79; 79 13.48 13480 1348 11 7 1.58 38.69 35 2 97;......

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...Explanation: I conducted a random simulation with the information provided based on 52 base week calendar. Author B. Taylor stated “simulation can be applied to a number of problems that are too difficult to model and solve analytically” (Taylor, 2009). In this case the results were based on the use of one copy machine, intervals of breakdown, requiring 1-4 days for repair at a loss, at $0.10 cents a copy. Day 1: 20%, Day 2: 45%, Day 3: 25%, Day 4: 10% a total probability of 100%. The point of this case study is to simulate the break-down and repair process for one year to obtain an average annual loss of revenue. In addition the amount of time between breakdowns increases the probability of needing more costly repairs. Should the anticipated lost revenue exceeds $12,000.00 annually a backup copier will be purchased. We must keep in mind the most important factors of customer satisfaction and convenience, which is what, prompted the owners of JET to start their business in the first place. The first part of creating the probability of breakdowns relied upon information supplied by Jet Copies and their estimated probability of distribution. The nearby college staff had prior knowledge of the service provider’s timelines for repair because they had the same copier in the campus office. JET used their own estimated repair time to recreate a random repair time probability table using a range of days. As a result the average repair time was 3 days at a cost of $691......

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...JET Copies Case Problem In analyzing the case, JET Copies Case Problem, the following categories will be addressed: Model number of days to repair 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. JET copies needs to know the number of days they need to repair, when the copy machine is out of service. Using the given table, there are three columns of probability, repair time and cumulative. I used the figures given in case problem for probability and repair time days but for the cumulative column we started at 0.00 cumulative, then added the 0.20 to that to get the cumulative for day 2. For each probability subsequent to the previous we added, so for the 0.45 probability we added the 0.20 to get 0.65. Then repeating the same for the rest of probabilities, after 0.65 the cumulative resulted in 0.90. Then we used the table with ten columns. In the first column starting at A5, the formula entered was the =RAND() function to create random number for the first cell. That function formula was then dragged down to the below cells and locked to have the values be fixed. In the next column, I use the numbers copied from my first column. Then in the G5 column, we entered the function VLOOKUP to find the number of days needed to repair =VLOOKUP(F5,Lookup,2) and dragged the cell to have the same formula for the below cells in the column. Look up, in......

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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......

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...to grade is within the Instructor Center. Click the link above to submit your assignment. 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: 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. There are two deliverables for this Case Problem, the Excel spreadsheet and the written description/explanation. Please submit both of them electronically......

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