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Assignment 1 - Jet Case Problem

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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.
I calculated the cumulative distribution, random number ranges and average repair days below. Machine Repair time, y (days) | Probability of Repair time | Cumulative Probability | Random Number Range, r2 | | 1 | 0.20 | 0.20 | 0.00-0.20 | 0.2 | 2 | 0.45 | 0.65 | 0.21-0.65 | 0.9 | 3 | 0.25 | 0.90 | 0.66-0.90 | 0.75 | 4 | 0.10 | 1.00 | 0.91-1.00 | 0.4 | Average repair days | 2.25 | To find the repair time I used VLOOKUP /y days =VLOOKUP to probabilities in the Repair Time probability/ tool generating random number /which r2=RAND()/. If 0 < r2 < 0.2, then repair time is 1 day. If 0.02 < r2 < 0.65, then repair time is 2 days. If 0.65 < r2 < 0.90, then repair time is 3 days. If 0.9 < r2 < 1, then repair time is 4 days. r2 | Repair Time y days | 0.157479 | 1 | 0.319876 | 2 | 0.268242 | 2 | 0.616901 | 2 | 0.195559 | 1 | 0.563 | 2 | 0.886715 | 3 | 0.568449 | 2 | 0.758294 | 3 | 0.0156 | 1 | 0.020516 | 1 | 0.287682 | 2 | 0.988455 | 4 |

2. In Excel, use a suitable method for simulating the interval between successive breakdowns, according to the continuous distribution shown. r1 | Time Between Breakdowns, x weeks | Cumulative Time Between Breakdowns | 0.029508 | 1.030669 | 1.030669 | 0.987177 | 5.961406 | 6.992075 | 0.0002 | 0.08491 | 7.076985 | 0.525299 | 4.348651 | 11.42564 | 0.844252 | 5.51299 | 16.93863 | 0.925525 | 5.772252 | 22.71088 | 0.372143 | 3.660211 | 26.37109 | 0.781087 | 5.302747 | 31.67384 | 0.923197 | 5.764989 | 37.43883 | 0.95718 | 5.870136 | 43.30896 |

To find time between breakdowns, I generated random numbers /which is RAND()/ and then used formula of =6*SQRT(r1). Then found the cumulative time between breakdowns for 52 weeks.

3. In Excel, use a suitable method for simulating the lost revenue for each day the copier is out of service. Repair Time y days | RN for Day1 | RN for Day2 | RN for Day3 | RN for Day4 | Copies Lost Day1 | Copies Lost Day2 | Copies Lost Day3 | Copies Lost Day4 | 1 | 0.62031 | 0 | 0 | 0 | 5.7219 | 0 | 0 | 0 | 2 | 0.86132 | 0.5451 | 0 | 0 | 7.1679 | 5.2703 | 0 | 0 | 2 | 0.63029 | 0.0435 | 0 | 0 | 5.7818 | 2.2613 | 0 | 0 | 2 | 0.34373 | 0.0014 | 0 | 0 | 4.0624 | 2.0081 | 0 | 0 | 1 | 0.10382 | 0 | 0 | 0 | 2.6229 | 0 | 0 | 0 | 2 | 0.97802 | 0.3687 | 0 | 0 | 7.8681 | 4.2122 | 0 | 0 | 3 | 0.88966 | 0.8831 | 0.5947 | 0 | 7.3380 | 7.2989 | 5.5684 | 0 | 2 | 0.12888 | 0.1896 | 0 | 0 | 2.7733 | 3.1374 | 0 | 0 | 3 | 0.26107 | 0.8072 | 0.5978 | 0 | 3.5664 | 6.8430 | 5.5870 | 0 | 1 | 0.26641 | 0 | 0 | 0 | 3.5985 | 0 | 0 | 0 | 1 | 0.52892 | 0 | 0 | 0 | 5.1735 | 0 | 0 | 0 | 2 | 0.57064 | 0.3959 | 0 | 0 | 5.4238 | 4.3753 | 0 | 0 | 4 | 0.95449 | 0.9577 | 0.4594 | 0.7854 | 7.7269 | 7.7460 | 4.7564 | 6.7125 |

To find the lost revenue for each day, first I generated random number for each days based on the repair time using IF tool.
RN for Day1 is IF(y>=1,RAND(),0)
RN for Day2 is IF(y>=2,RAND(),0)
RN for Day3 is IF(y>=3,RAND(),0)
RN for Day4 is IF(y=4,RAND(),0)
Then I used formula of z=6r+2
Copies lost day1 is 6*RN for day1+2
Copies lost day2 is IF(y>=2,6*RN for day2,0)
Copies lost day3 is IF(y>=3,6*RN for day3,0)
Copies lost day4 is IF(y=4,6*RN for day4+2,0)

Revenue Lost Day1 | Revenue Lost Day2 | Revenue Lost Day3 | Revenue Lost Day4 | 572.19 | 0.00 | 0 | 0 | 716.79 | 527.03 | 0 | 0 | 578.18 | 226.13 | 0 | 0 | 406.24 | 200.81 | 0 | 0 | 262.29 | 0.00 | 0 | 0 | 786.81 | 421.22 | 0 | 0 | 733.80 | 729.89 | 556.836 | 0 | 277.33 | 313.74 | 0 | 0 | 356.64 | 684.30 | 558.6975 | 0 | 359.85 | 0.00 | 0 | 0 | 517.35 | 0.00 | 0 | 0 | 542.38 | 437.53 | 0 | 0 | 772.69 | 774.60 | 475.6403 | 671.2482 |

After finding the copies lost during the repair time, I calculated lost revenue from day1 to day4. Lost revenue for each copy is $0.10

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. Total Revenue Lost | 572.19 | 1243.82 | 804.30 | 607.05 | 262.29 | 1208.04 |
To find the annual lost revenue due to copier breakdowns over 1 year, I added lost revenues from day 1 to day 4 and then added all total lost revenues for 52 weeks. The annual lost revenue for 1 year is $58,008.27

5. I would say buying extra backup-copy machine would be good choice because lost revenue is very high than the cost of backup-copy machine. Instead of losing possible revenues, it is better to buy backup-copy machine at $12,000 and make more profit. 6. I am quite confident in my answer because I have run the simulation several times and annual lost revenue was 3 or 4 higher than the cost of copier (which is $12,000). However there are a few limits to the study. For instance, since we are generating random numbers each time it will give different annual lost revenue. Therefore, to be more accurate, the simulation must be run few times to find average annual lost revenue. Another limitation is, we don’t know whether the backup machine would break also or how much would it cost to fix the copy machine each time it breaks.

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