JET Copies Case Problem - Assignment Example

Copier repair Copier repair The number of days needed to repair can be calculated through generating a random number between 0 and 1 denoted r2, if you assume that the number of days needed to repair a copier is random. 0 < random number < 0.2, then it takes 1 day 0.2 < random number < 0.65, then it takes 2 days 0.65 < random number < 0.90, then it takes 3 days 0.9 < random number < 1, then it takes 4 days 2. The interval between breakdowns can be obtained by the use of the function: F(x) = x/18, for 0≤x≤6, where x= weeks between machine breakdowns. Since the probability distribution of the random value varies between 0 to 6 weeks as the probability increases with time. The distribution function is: F(x) = x²/36 for 0≤x≤6 Setting this equal to another random number r1 between 0 and 1 then: r1 = x²/36 => x=6*sqrt (r1) 3. The following are the results from Excel simulation: R1 INTERVAL R3 R2 REPAIR TIME LOST REVENUE CUMULATIVE TIME 0.701956 5.026969649 2408 0.932503 4 $963.20 5.027 0.17021 2.47539156 5883 0.862385 3 $1,764.90 7.502 0.928673 5.782062103 4219 0.168984 1 $421.90 13.284 0.23227 2.891663586 7956 0.006808 1 $795.60 16.176 0.501451 4.248791398 5062 0.662814 3 $1,518.60 20.425 0.6136 4.699957656 4106 0.104352 1 $410.60 25.125 0.810078 5.400260602 7996 0.573274 2 $1,599.20 30.525 0.303253 3.304104176 2682 0.317832 2 $536.40 33.829 0.878418 5.623438256 4811 0.853539 3 $1,443.30 39.453 0.353656 3.568138331 4550 0.15716 1 $455.00 43.021 0.647412 4.827714798 4323 0.968717 4 $1,729.20 47.848 0.922426 5.76257919 3712 0.623942 2 $742.40 53.611 0.43762 3.969172592 4985 0.667187 3 $1,495.50 57.580 0.878465 5.623588243 7910 0.549703 2 $1,582.00 63.204 0.502996 4.255332677 3510 0.702209 3 $1,053.00 67.459   $16,510.80 Table 1: Results table The total revenue lost is about $16510.80, which is not completely accurate. Many trials should be done and the average taken in order to get what you lost exactly. Similarly, the duration does not add up to a year always, therefore you need to cater for that by adding up to the revenue that does not exceed a year. 4. The amount of revenue lost can be obtained through multiplying the number of days taken to repair the copier by the number of copies you may have sold that day (r3) which is a random number between 2000 and 8000 then multiplied by the amount used to sell a copy ($0.10). The interval of breakdowns tells you how frequent this happens, and the total number of weeks is not to surpass 52. 5. Days to repair: The number of days needed to repair the copier when it breaks down is assumed to be random. This random number is generated between 0 and 1, denoted as r2. If the random value generated lies between the range of 0 and 0.2, then the number of days taken to repair the copier is 1. If the random value generated lies between the range of 0.2 and 0.65, then the numbers of days taken to repair the copier are 2. If the random value generated lies between the range of 0.65 and 0.90 the numbers of days taken to repair the copier are 3. Finally, if the random value generated lies between the range of 0.90 and 1.0 then the numbers of days taken to repair the copier are 4. Interval between breakdowns: The time between breakdowns can be calculated through finding a random number between 0 and 1 (r1). The square root of r1 is then multiplied by 6 which is the maximum number of weeks of the interval. The probability distribution of the random value varies between 0 to 6 weeks as it increases the longer the copier functions without breaking down. The interval of breakdowns tells you how frequent the copier breaks down hence loss in total revenue. Lost revenue: The amount of revenue lost calculated through obtaining a random number (r3) between 2000 and 8000 since the number of copies sold per day is assumed to range between at least 2000 copies and at most 8000. The random number is then multiplied by the exact number of days used to repair the copier when it breaks down then finally multiplied by the amount used to sell a single copy which is $0.10. This should be done within 52 weeks only and not more. To obtain the average annual loss of revenue, this process should be done for several years. Putting together: According to table 1 (results table), R1 is the random number used to obtain the time between copier break down by multiplying its square root by 6. The interval is the number of weeks between 0 and 6 of copier break down obtained through multiplying the square root of R1 with 6. R3 is the random value between 2000 and 8000 which is the range of numbers of copies assumed to be sold in a given day. It helps in calculating the lost revenue in a day and yearly. R2 is a random number between 0 and 1 that is used to calculate the number of days used to repair the copier when it breaks down. Repair time is the total number of days used to repair the copier. Lost revenue is the amount of money lost when the copier breaks down. It is obtained through multiplying the number of copies that may have been sold in a given day by the number of days used to repair the copier and then by $0.10 the amount used to sell a single copy. 6. Purchasing another copier should be put into consideration because the total amount of revenue lost is practically double the amount of buying a new copier (US$16510.80 vs. US$8000.00). Though there are several limitations to it, I feel confident with my answer. The total number of weeks will not always add up to 1 year worth, hence it should be taken in to consideration. The simulation too should be run a number of times to obtain the average amount lost for the reflection of more accurate results of lost revenue in a year. Read More