The simulation of Jet Copies can be done by generating random numbers from given probability distributions. The different steps of this simulation and assumption made are explained below.
1. Simulation for the repair time.
It is given that the repair time follows
Repair Time (days) Probability
1 .20
2 .45
3 .25
4 .10
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1.00
To generate a random number from the above distribution, we use the following procedure.
Generate a random number denoted by r2 from between 0 and 1. If this generated random number is less than or equal to 0.2 take repair time = 1. If the generated random number is 0.2 to 0.65, we take repair time =2. If the generated random number is 0.65 to 0.90, we take repair time = 3 and take 4 otherwise.
2. Simulation for break-down Distribution
Given that the probability distributions of random variable X representing the time between break-downs varies from 0 to 6 weeks with probability increasing continuously, the copier went without breaking down can be approximated by the probability distribution f(x) =x/18 0 < x < 6
Hence the distribution function of x is F(x)=x2/36 0 < x < 6
If r1 is another random number generated between 0 and 1, then we can write r1= x2/36
Hence x=6
Therefore to simulate from the break down distribution, generate a random number r1 between 0 and 1 and make the transformation, x=6 .
3. Simulation for Lost Revenue.
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. To get the lost business due to this break down is obtained by multiplying r3 by repair time and lost revenue is obtained by multiplying r3* repair time*0.1.
4. Total time
We manually simulate the above problem by generating random numbers from break down distribution, repair time distribution and lost revenue distribution. Since the break down time is given in weeks, we stop the simulation when total number of weeks is greater than 52
5. Summary
Generate random number from the break down calculate breakdown time. Generate random number from the repair distribution and calculate repair time required to get the machine repaired. Generate random numbers between 2,000 to 8,000 and estimate lost revenue due to this particular break down. Calculate the lost revenue by multiplying this number with repair time and revenue from 1 copy ($0.1). Repeat this process until sum of all the break down time exceeds 52 weeks and calculate the total loss. The excel output under two different assumptions are attached.
6. Answer to the problem
From the attached table we can see that under this simulation the lost revenue for the first year (when total break down time exceeds 52 weeks) is $12,916.30, which is more than $12,000. Since the simulated loss of revenue due to machine downtime during 1 year is more than $12,000, the decision should be to purchase a backup copier. Since we have done the simulation only for one year the result of this study is not fully reliable. So we have to repeat the simulation for a large number of times to obtain proper results. This is because the time between break downs, repair time and revenue loss are probabilistic, the simulation results could exhibit significant variation. The only way to be sure of the accuracy of our results is to simulate each system many times and compute an average result.
When simulated for two additional years we receive the results of $13,260.90 and $15,973.90. When averaged over the 3 years, we receive an average of $14,050.37. This keeps in line with the decision to buy the backup copier.
Another limitation is the assumptions we have made. If any of the assumptions are violated, the result of this study may become different. For example, if there is change in the probability distribution any of the above three cases, the answer to the original question could be different.
I am confident this answer is a good answer because of the quantitative results generated from checking and double checking the work and numbers that are put into this assignment.
