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.
Going by my stimulation as seen above, the total revenue lost is $167,601. This amount is not 100% accurate due to the fact that the time frame for which it is calculated does not amount up to a year. It is important to do this stimulation as many times as possible and average out the total revenue lost for all the simulations to get a more accurate amount.
Interval between breakdowns:
To calculate the interval between breakdowns, I used the formula f(x) = 6*sqrt (random# 1) where” X” is equal to the number of weeks of breakdown. According to the case study, the length of time between breakdowns is from 0 and 6 weeks with the probability increasing the longer the copier went without breaking down. Random # 1 is a random computer generated number between 0 and 1 from a probability distribution to be used in the trial. Days to repair:
It is believed that the number of days needed to repair the copier is random; these numbers fall in the column random # 2 which are computer generated numbers between 0 and 1. Since the probabilities for days of repair are 0.20, 0.45, 0.25 and 0.10 for 1, 2, 3 and for days respectively. Random numbers less than or equal to 0.20 represent 1 day. Those random numbers less than 0.65 but greater than 0.20 represent 2 days to repair the copier. Those that are greater than 0.65 but less than 0.90 represent 3 days to repair the copier. Random numbers greater than 0.90 but less than 1 represent 4 days to repair the copier. As seen on the table in question one, 0.20, 0.65, 0.90 and 1 are cumulative numbers calculated from the various probabilities given in the case study. Lost Revenue:
To calculate the lost revenue for a day, Random #3 which is a computer generated random number between 2000 to 8000 is multiplied by the repair time and multiplied by $0.10 since it is the price to make a copy. Random #3 is between 2000 to 8000 because that is the estimated number of copies to be sold per day as given in the passage. The total revenue lost is a sum total of all the revenue lost. Putting it together:
The simulation has been put together as seen in the table above and the steps on how it was put together have been explained in the first three paragraphs of this answer. Computing the different models such as days between breakdowns, days to repair helped me compute the revenue lost per day of breakdown. The total revenue lost is computed by summing up all the estimated revenue lost in the various days of breakdown. The revenue lost can be calculated by estimating the number of customers per day and their various demands multiplied by the number of days of breakdown. The frequency of break will help determine the time between breakdowns. For example, breakdowns could occur every 7weekd or between 5 to 7 weeks. 6.
In my opinion, it will be wise for JET Copies to buy a backup copier since they are not certain how often their primary copier will breakdown and how long it will take them to repair it. According to the passage, it cost $8000 to buy a smaller backup copier which is less expensive as compared to the $167,601 they would be losing when their primary copier breaks down as shown by the simulation. The limitation to this stimulation is that it has been conducted only once. I cannot say the result is perfectly accurate. It is important for this simulation to be done several times and the amount gotten for the total revenue lost averaged out to get a close to accurate amount. This simulation is a great example of a real world situation because there are many limits and variances.
One limit could be expressed by the repair time in days for any breakdown. While this was introduced as a probability gathered from research information, it could also be a limitation. Depending on the type of breakdown it could be longer than four days and based on how busy the repair business is, business hours of the repair business, and so on; it is a dependent variable based on another independent variable. Another limit to the study was the variance of the revenue gained on a daily basis, which was two thousand to eight thousand copies being sold at ten cents a copy, and determining what the loss would be for each day the copier was broken down. In addition, the limit of twelve thousand as being the determining factor of whether another copier must be purchased or not could be seen as a limit of the study.