JET Copies assignment

Please review the material on continuous probability distributions on pages 643 – 645 prior to the
following discussion. The method of solution for this first assignment is very similar to the example
“Simulation of Machine Breakdown and Maintenance System” given in the textbook.
In the JET Copies assignment, you will be required to generate the probability function for the time
between repairs, the time to repair and for the number of copies expected to sell in a day. Let us first
consider the time between repairs (breakdowns). The function is shown on page 679. For such a graph,
the continuous probability function is given by
The derivation of this function is done through the techniques for defining a graph that all of us should
have learned in Basic Algebra.
For this assignment, a = 6, so we have
Taking the integral of the function yields the cumulative probability distribution function F(x):
Let F(x) = r (i.e., a random number) and solve for x.
By generating random numbers for r (between zero and one), and substituting those values into this
function, we determine a value for x, which is the time between repairs (breakdowns).
Please review the material on continuous probability distributions on pages 643 – 645 for … Page 1 of 3
. 1/18/2011
The probability distribution for the repair time is given by the distribution given on page 679 and shown
below:
Use of this table and the VLOOKUP function will generate the repair time in days.
Let us now consider the number of copies sold per day. The problem states that between 2,000 and
8,000 copies would be sold each day. For such a uniform distribution, the function would be given by
Taking the integral of this function yields the cumulative distribution function F(z):
Let F(z) = r (i.e., a random number) and solve for z.
By generating random numbers for r (between zero and one), and substituting those values into this
function, we determine a value for z, which is the number of copies sold per day (in thousands).
Therefore, the simulation goes as follows:
You will have 8 columns and depending on how many weeks you want to repeat the simulation, a
number of rows where the number of weeks sum to 52 (one year).
Generate r between 0 and 1 (first column) – use to find the time between breakdowns in weeks
(column 2) – calculate Σx (cumulative number of weeks)(column 3) – generate another random number
between 0 and 1 (column 4) – use VLOOKUP and the above table to match the corresponding repair
time y in days (column 5) – depending on the value in column 5, generate random numbers between 0
and 1. For example, if the number of repair days in column 5 is 2, you must generate 2 such random
numbers (one for each day) in this column (column 6) – for each r that you have generated in the
previous column, use the equation z = 6r + 2 to find the number of copies lost (in thousands). If you had
Use these two columns with the
VLOOKUP function
Repair time y
(days)
P(y) Cumulative
Probability
Probabilities Repair time y
(days)
1 0.20 0.20 0.00 1
2 0.45 0.65 0.20 2
3 0.25 0.90 0.65 3
4 0.10 1.00 0.90 4
Please review the material on continuous probability distributions on pages 643 – 645 for … Page 2 of 3
. 1/18/2011
to generate two r’s in the previous column,, you must use the above equation twice to find the two
values of z (one for each r) and add them up (column 7) – after finding the number of copies lost in the
previous column, find the revenue lost as a consequence (column 8).
Add up all of the entries in column 8 to estimate the total revenue cost during the given time period.
Based on that figure, you make a decision whether they need to purchase a back-up copier.
Please review the material on continuous probability distributions on pages 643 – 645 for … Page 3 of 3
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Week 3: Week 3 – Assignment #1
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. Please submit both of them electronically via the dropbox.
The assignment will be graded using the associated rubric.
Outcome Assessed:
· Create statistical analysis of
simulation results.
· Communicate issues in management science
Grading Rubric for JET Copies Case Problem
There are 12 possible points in each of the five criteria for a total of 60 points possible.
Criteria 0
Unacceptable
(0 points)
1
Developing
(6 points)
2
Competent
(9 points)
3
Exemplary
(12 points)
1. Model
number of days
to repair
Did not submit or
did not model
this component
in an appropriate
manner
This component
was modeled,
but the method
and/or
implementation
had mistakes
that affected the
validity of the
model
Used a method
that is
recognizably
appropriate, but
the
implementation
had minor
mistakes
Used an
appropriate
method and
correctly
implemented it
2. Model
number of
weeks between
breakdowns
Did not submit or
did not model
this component
in an appropriate
manner
This component
was modeled,
but the method
and/or
implementation
had mistakes
that affected the
validity of the
model
Used a method
that is
recognizably
appropriate, but
the
implementation
had minor
mistakes
Used an
appropriate
method and
correctly
implemented it
Page 1 of 2
. 1/18/2011
3. Model lost
revenue due to
breakdowns
Did not submit or
did not model
this component
in an appropriate
manner
This component
was modeled,
but the method
and/or
implementation
had mistakes
that affected the
validity of the
model
Used a method
that is
recognizably
appropriate, but
the
implementation
had minor
mistakes
Used an
appropriate
method and
correctly
implemented it
4. Provide
written
description and
explanation of
the simulation
Did not submit or
described
insufficiently.
Omitted key
points.
Provided partially
developed
written
description that
matches the
method 70 –
79% accuracy.
Provided
sufficiently
developed
written
description that
matches the
method 80 –
89% accuracy.
Provided fully
developed
written
description that
is correct and
matches the
method used
with 90 – 100%
accuracy.
5. Combine
model
components to
produce a
coherent
answer to the
question posed
in the case
study. (a)
Answer the
question posed
in the case
study. (b) How
confident are
you that this
answer is a
good one? (c)
What are the
limits of the
study?
Did not submit or
result not
provided, and/or
discussed
insufficiently.
Provided partially
correct result.
Omitted
discussion of
confidence.
Discussed
limitations
partially with 70
– 79% accuracy,
logic, and clarity.
Provided
sufficiently
correct result.
Identified
confidence and
discussed
limitations
sufficiently with
80 – 89%
accuracy,
accuracy, logic,
and clarity.
Provided fully
correct result.
Identified
confidence and
discussed
limitations fully
with 90 – 100%
accuracy, logic,
and clarity.
Page 2 of 2
. 1/18/2011
678 Chapter 14 Simulation
36. In Chapter 8, Figure 8.6 shows a simplified project network for building a house, as follows:
There are four paths through this network:
Path A: 1–2–3–4–6–7
Path B: 1–2–3–4–5–6–7
Path C: 1–2–4–6–7
Path D: 1–2–4–5–6–7
The time parameters (in weeks) defining a triangular probability distribution for each activity
are provided as follows:
Time Parameters
Activity Minimum Likeliest Maximum
1–2 1 3 5
2–3 1 2 4
2–4 0.5 1 2
3–4 0 0 0
4–5 1 2 3
4–6 1 3 6
5–6 1 2 4
6–7 1 2 4
a. Using Crystal Ball, simulate each path in the network and identify the longest path (i.e., the
critical path).
b. Observing the simulation run frequency chart for path A, determine the probability that
this path will exceed the critical path time.What does this tell you about the simulation
results for a project network versus an analytical result?
1 2
3
5
4 6 7
3
Lay
foundation
Design
house and
obtain financing
Order
materials
Select
paint
Select
carpet
Build
house
Finish
work
Dummy
1
2 0
1 1
3 1
Case Problem
JET Copies
James Banks was standing in line next to Robin Cole at Klecko’s
Copy Center, waiting to use one of the copy machines. “Gee,
Robin, I hate this,” he said. “We have to drive all the way over here
from Southgate and then wait in line to use these copy machines.
I hate wasting time like this.”
“I know what you mean,” said Robin. “And look who’s here. A
lot of these students are from Southgate Apartments or one of the
other apartments near us. It seems as though it would be more
logical if Klecko’s would move its operation over to us, instead of
all of us coming over here.”
ISBN 0-558-55519-5
Introduction to Management Science, Tenth Edition, by Bernard W. Taylor III. Published by Prentice Hall. Copyright © 2010 by Pearson Education, Inc.
Case Problems 679
James looked around and noticed what Robin was talking
about. Robin and he were students at State University, and most
of the customers at Klecko’s were also students. As Robin
suggested, a lot of the people waiting were State students who
lived at Southgate Apartments, where James also lived with Ernie
Moore. This gave James an idea, which he shared with Ernie and
their friend Terri Jones when he got home later that evening.
“Look, you guys, I’ve got an idea to make some money,” James
started. “Let’s open a copy business! All we have to do is buy a
copier, put it in Terri’s duplex next door, and sell copies. I know
we can get customers because I’ve just seen them all at Klecko’s.
If we provide a copy service right here in the Southgate complex,
we’ll make a killing.”
Terri and Ernie liked the idea, so the three decided to go into
the copying business. They would call it JET Copies, named for
James, Ernie, and Terri. Their first step was to purchase a copier.
They bought one like the one used in the college of business office
at State for $18,000. (Terri’s parents provided a loan.) The company
that sold them the copier touted the copier’s reliability, but
after they bought it, Ernie talked with someone in the dean’s office
at State, who told him that the University’s copier broke down frequently
and when it did, it often took between 1 and 4 days to get
it repaired.When Ernie told this to Terri and James, they became
worried. If the copier broke down frequently and was not in use
for long periods while they waited for a repair person to come fix
it, they could lose a lot of revenue. As a result, James, Ernie, and
Terri thought they might need to purchase a smaller backup
copier for $8,000 to use when the main copier broke down.
However, before they approached Terri’s parents for another loan,
they wanted to have an estimate of just how much money they
might lose if they did not have a backup copier. To get this estimate,
they decided to develop a simulation model because they
were studying simulation in one of their classes at State.
To develop a simulation model, they first needed to know how
frequently the copier might break down—specifically, the time
between breakdowns. No one could provide them with an exact
probability distribution, but from talking to staff members in the
college of business, James estimated that the time between breakdowns
was probably between 0 and 6 weeks, with the probability
increasing the longer the copier went without breaking down.
Thus, the probability distribution of breakdowns generally looked
like the following:
Next, they needed to know how long it would take to get the
copier repaired when it broke down. They had a service contract
with the dealer that “guaranteed” prompt repair service. However,
Terri gathered some data from the college of business from which
she developed the following probability distribution of repair times:
Repair Time (days) Probability
1 .20
2 .45
3 .25
4 .10
1.00
Finally, they needed to estimate how much business they would
lose while the copier was waiting for repair. The three of them had
only a vague idea of how much business they would do but finally
estimated that they would sell between 2,000 and 8,000 copies per day
at $0.10 per copy. However, they had no idea about what kind of
probability distribution to use for this range of values. Therefore, they
decided to use a uniform probability distribution between 2,000 and
8,000 copies to estimate the number of copies they would sell per day.
James, Ernie, and Terri decided that if their loss of revenue due to
machine downtime during 1 year was $12,000 or more, they should
purchase a backup copier. Thus, they needed to simulate the breakdown
and repair process for a number of years to obtain an average
annual loss of revenue. However, before programming the simulation
model, they decided to conduct a manual simulation of this process for
1 year to see if the model was working correctly. Perform this manual
simulation for JET Copies and determine the loss of revenue for 1 year.
6 x, weeks
.33
f(x)
0
Case Problem
Benefit–Cost Analysis of the Spradlin Bluff
River Project
The U.S. Army Corps of Engineers has historically constructed
dams on various rivers in the southeastern United States. Its
primary instrument for evaluating and selecting among many
projects under consideration is benefit–cost analysis. The Corps
estimates both the annual benefits deriving from a project in
several different categories and the annual costs and then divides
the total benefits by the total costs to develop a benefit–cost ratio.
This ratio is then used by the Corps and Congress to compare
numerous projects under consideration and select those for funding.
A benefit–cost ratio greater than 1.0 indicates that the benefits
are greater than the costs; and the higher a project’s
benefit–cost ratio, the more likely it is to be selected over projects
with lower ratios.
The Corps is evaluating a project to construct a dam over the
Spradlin Bluff River in southwest Georgia. The Corps has identified
six traditional areas in which benefits will accrue: flood
ISBN 0-558-55519-5
Introduction to Management Science, Tenth Edition, by Bernard W. Taylor III. Published by Prentice Hall. Copyright © 2010 by Pearson Education, Inc.

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