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.

2

>with formulas

2

s)

Supplemental Instructor

*sqrt of

is the formula for the time between breakdowns

Week

r1

0

0 1 1

482957274

2.3105510566

1

0.20 2 2

3 3

11420962

0

4 4

																																																									Jet Copies Simulation Example (	5	Week	Jet Copies Simulation Set Up Suggestion by Professor Aungst, MAT5 Save Time On Research and Writing Hire a Pro to Write You a 100% Plagiarism-Free Paper. Get My Paper				4										0	Mat540
	Probability of Weekly Demand:	Note: x =	6		r							1
Note: z = 6r + 2 is the formula for copies lost
	Simulation:
	P(x)		Cumulative		Repair Time			r1		Time Between Breakdowns, x weeks	Cumulative Time Between Breakdowns		Repair Time y days	RN for Day1	RN for Day2	RN for Day				3	RN for Day4	Copies Lost Day1	Copies Lost Day2	Copies Lost Day3	Copies Lost Day4	Revenue Lost Day1	Revenue Lost Day2	Revenue Lost Day3	Revenue Lost Day4	Total Revenue Lost
			0.2		0.1		2.3105510566	0.1511624354
	0.45	0.2668388122	3.0993865908	5.4099376474
	0.25		0.65		0.22	2.8215448714	8.2314825188
0.10		0.9	0.4250803299	3.9118910871	12.1433736059
1.00
	Average Demand =
Average Lost Revenue =

fixed data

Probability of Weekly Demand: Simulation:
P(x) Cumulative Repair Time r1 Time Between Breakdowns, x weeks

r1 Repair Time y days r1

0.2 0 1

3.0707248147

1

0 0 0

0 0 0

758.7929269557

0.45 0.2 2
0.25 0.65 3
0.1 0.9 4

1
Average Demand =

Jet Copies Simulation Example (52 Weeks)
Sum of x	r2	r3	r4	Copies lost day 1 (thousands)	Copies lost day 2 (thousands)	Copies lost day 3 (thousands)	Copies lost day 4 (thousands)	Revenue Lost this breakdown	Cummulative lost revenue
0.2619264135		3.0707248147	0.148949842	0.9313215449	7.5879292696		758.7929269557
Average Lost Revenue =

Sheet3

0 0

1 0.055
2

3

4 0.22

5

6

If loss of revenue > $12,000 should purchase backup
Manual simulation for 1 year
Need time between breakdowns
At 6 week point there is a .33		0.055
0.11
0.165
First copier is $18,000
Smaller back up copier is $8000	0.275
.10 per copy	0.33
2000-8000 copies per day

Sheet1

MATH5

4

0Week

3

Assignment, Chapter

1

4, Jet Copies, Suggested Template for Word Document

Provided by Professor Supplemental Instruction

From Grading Rubric in Course Guide:

· 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).

· 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.

Information from Jet Copies Case Study (this part would be composed similarly to an Executive Summary in a Business Report … include the details and “story” about the project in your own words):

– Students bought an $18,000 copier to start their own copy business.

– Wanted to purchase a smaller copier for $8,000 as back-up

– Created a simulation to estimate the amount of revenue that would be lost if they did not have a backup

– Time between breakdowns is 0 weeks to 6 weeks (see probability function on page 679, and provided later in this set up

– Developed following probability distribution of repair times:

Repair Time (days)	Probability
	1	0.2 0
	2		0.45
	3		0.25
	4		0.10

– Estimated they would sell between 2,000 and 8,000 copies per day at 10 cents (0.10) per copy

– Used a uniform probability distribution between 2,000 and 8,000 to estimate how many copies they would sell per day

– If loss of revenue due to machine downtime during 1 year is greater than or equal to $12,000, then they should purchase the back-up copier

– Decided to conduct a manual simulation of this process for 1 year to see if the model was working correctly

– Our assignment is to perform this manual simulation for JET copies and determine the loss of revenue for 1 year.

Here’s some preliminary Set Up information:

The probability function for time between repairs, f(x), is,

f(x) = x/18, 0 <= x <= 6

and, r = x^2/36

x2 = 36r

x = 6*sqrt of r
(use this formula in the column you designate as time between repairs)

You could develop the cumulative distribution and random number ranges for the distribution of repair times for reference if you would like that for reference.

Repair Time

1

2

0.45

3

0.25

4

0.10

		Repair Time	Cumulative Probability	RN Ranges
y (days)	P(y)
0.2

Note: whether the Cumulative Probability is set up via the Textbook method (starting with 0) or the true Mathematical Method (adding previous probabilities to the current one), the results of the simulation are the same because of how Excel looks at the range of probabilities and connects them to the correct repair time days using the VLOOKUP Tool).

The probability function for daily demand is developed by determining the linear function

for the uniform distribution, which is,

f(z) = 1 / b – a which equals 1/6

Letting F(z) = r in the Integrated Function, and solving for z we get: z = 6r + 2 (this is the formula for copies lost)

There are various ways to set up the Monte Carlo simulation in Excel using the formulas we learned in Chapter 14 … namely Random Number Generation (which is =RAND) and VLOOKUP which allows us to “point back” to a probability table and insert a probability based on that Random Number and the Probability associated with it in the table.

Most students start with developing the probability table for Repair time to later be used as the VLOOKUP Table for Repair Time probability.

Repair Time

P(x)	Cumulative

The Simulation itself would be for 52 weeks (which would be when the cumulative “time between breakdowns” reached 52 weeks). You could begin with a Random Number (r1) which would be multiplied by column 2, the Time Between Breakdown (in weeks) formula of 6*square root of r1

You could then sum those variables in a cumulative list in column 3 (so you could tell when the simulation reached 52 weeks).

In column 4 you could generate another random number (say, r2) to calculate the column 5 Repair time in y days.

That r2 could be used in a column 5 for Repair Time in y days which could be calculated by using the =VLOOKUP function which would relate that r2 to probabilities in the Repair Time probability table originally set up.

You might then set up some random number columns and result columns for repairs taking 1 day, 2 days, 3 days and 4 days.

At some point, you would need to figure out how to calculate copies lost in a day in thousands and that would probably include the formula z = 6r + 2

Finally, you would want to equate the number of copies lost to the revenue lost at 10 cents per copy and then cumulate that for all 52 weeks to find the annual lost revenue.

Remember to: Answer the question posed in the case study (as in … should they buy the back up copier, why or why not).

How confident are you that this answer is a good one? What are the limits of the study? Write at least one paragraph.