Module CSimulationQNT 5160 Data Driven Decision MakingMo.docx

Module C
Simulation
QNT 5160
Data Driven Decision Making
Module PowerPoints (rev 1.2)
1
Explain the basic concept of computer simulation.
Describe the role computer simulation plays in many
management science studies.
Use RSPE to perform various basic computer simulations.
Interpret the results generated by RSPE when performing a
computer simulation.
Describe the characteristics of some of the probability
distributions that can be incorporated into a computer
simulation when using RSPE.
Use an RSPE procedure that identifies the continuous
distribution that best fits historical data.
Use RSPE to generate a parameter analysis report and a trend
chart as a aid to decision making.
Module Learning Objectives
Structure the Decision
(Define the Problem)
Select, Build and Run a Model (if applicable)
Gather Information,
Collect Data
Make the Decision

Data Driven Decision Making
Simulation Models
A simulation is an imitation of reality
Simulation models can represent complex and dynamic
situations
Many other models are static – they only represent a single
point in time
They can “speed up time” to show long-term effects
Stochastic Simulation
“Stochastic” = involving chance or probability
A stochastic simulation can model the uncertain aspects of a
decision – to show how uncertain events might affect outcomes
We’ll be using RSPE software to build simulation models
Once a simulation model is set up, we can run experiments to
see what might happen in the future … actually for thousands of
futures … “in the long run”
Decision
Uncertainty
Consequence

RSPE Input Variables
Simulation Experiments
RSPE Output Variables
Analyzing Risk With Simulation
Risk =~ Uncertainty x Consequence
6
The Essence of Computer Simulation
A stochastic system is a system that evolves over time
according to one or more probability distributions.
Computer simulation imitates the operation of such a system by
using the corresponding probability distributions to randomly
generate the various events that occur in the system.
Rather than literally operating a physical system, the computer
just records the occurrences of the simulated events and the
resulting performance of the system.
Computer simulation is typically used when the stochastic
system involved is too complex to be analyzed satisfactorily by
analytical models.
Outline of a Major Computer Simulation Study (1 of 3)
Step 1: Formulate the Problem and Plan the Study
What is the problem that management wants studied?
What are the overall objectives for the study?
What specific issues should be addressed?
What kinds of alternative system configurations should be
considered?

What measures of performance of the system are of interest to
management?
What are the time constraints for performing the study?
Step 2: Collect the Data and Formulate the Simulation Model
The probability distributions of the relevant quantities are
needed.
Generally it will only be possible to estimate these
distributions.
A simulation model often is formulated in terms of a flow
diagram.
Step 3: Check the Accuracy of the Simulation Model
Walk through the conceptual model before an audience of all
the key people.
Step 4: Select the Software and Construct a Computer Program
Classes of software
Spreadsheet software (e.g., Excel, Crystal Ball)
A general purpose programming language (e.g., C, FORTRAN,
Pascal, etc.)
A general purpose simulation language (e.g., GPSS,
SIMSCRIPT, SLAM, SIMAN)
Applications-oriented simulators
Step 5: Test the Validity of the Simulation Model
If the real system is currently in operation, performance data
should be compared with the corresponding output generated by
the simulation model.
Conduct a field test to collect data to compare to the simulation
model.
Have knowledgeable personnel check how the simulation results
change as the configuration of the simulated system is changed.
Watch animations of simulation runs.

Step 6: Plan the Simulations to Be Performed
Determine length of simulation runs.
Keep in mind that the simulation runs do no produce exact
values. Each simulation run can be viewed as a statistical
experiment that is generating statistical observations of the
performance of the system.
Step 7: Conduct the Simulation Runs and Analyze the Results
Obtain point estimates and confidence intervals to indicate the
range of likely values for the measures.
Step 8: Present Recommendations to Management
Building an RSPE Model
Build a spreadsheet model (e.g. a P&L statement)
Designate certain cells as “inputs” – these are the random
variables
For each input cell, define the appropriate probability
distribution for that random variable
Designate certain cells as “outputs” – these are the outcomes of
interest in the decision (e.g. Profit)
The model can then simulate thousands of futures by varying
the inputs according to their probability distributions and then
recording the outputs for each variation
Class 3 Videos
https://www.youtube.com/user/FrontlineSolvers (2:07)
http://www.solver.com/ribbon-and-task-pane-interface-
orientation (4:27)

Class 4 Video
http://www.solver.com/building-your-first-monte-carlo-
simulation-model-excel (5:52)
Tutorials
http://www.solver.com/risk-analysis-tutorial (printed version
provided by instructor)
http://www.solver.com/simulation-tutorial (more advanced
information which goes beyond class requirements)
RSPE Videos and Tutorials
Freddie the Newsboy
Freddie runs a newsstand in a prominent downtown location of a
major city.
Freddie sells a variety of newspapers and magazines. The most
expensive of the newspapers is the Financial Journal.
Cost data for the Financial Journal:
Freddie pays $1.50 per copy delivered.
Freddie charges $2.50 per copy.
Freddie’s refund is $0.50 per unsold copy.
Sales data for the Financial Journal:
Freddie sells anywhere between 40 and 70 copies a day.
The frequency of the numbers between 40 and 70 are roughly
equal.

13
Spreadsheet Model for Applying Simulation
14
Figure 13.1 A spreadsheet model for applying computer
simulation to the case study that involves Freddie the newsboy.
The uncertain variable cell is Demand (C12), the results cell is
Profit (C18), the statistic cell is MeanProfit (C20), and the
decision variable is Order Quantity (C9).
Application of Risk Solver Platform
Four steps must be taken to use Risk Solver Platform (RSPE) on
a spreadsheet model:
Define the uncertain variable cells.
Define the results cells to forecast.
Define any statistic cells as desired.
Set the simulation options.
Run the simulation.
15
Step 1: Define the Uncertain Variable Cells
A random input cell is an input cell that has a random value.
An assumed probability distribution must be entered into the
cell rather than a single number.
RSPE refers to each such random input cell as an uncertain
variable cell.
Procedure to define an uncertain variable cell:
Select the cell by clicking on it.
Select a probability distribution to enter into the cell by

choosing from the Distributions menu on the RSPE ribbon.
Use the distribution dialog box to enter parameters for the
distribution (preferably referring to cells on the spreadsheet that
contain these parameters).
Click on OK.
16
Distributions Menu on the RSPE Ribbon
17
Figure 13.2. The Distributions menu on the RSPE ribbon
showing the distributions available under the Discrete submenu.
In addition to the 8 distributions displayed here, 38 more
distributions are available in the other submenus.
Integer Uniform Distribution
18
Figure 13.3 The dialog box used to specify the parameters for
the integer uniform distribution in the uncertain variable cell,
Demand (C12), for the spreadsheet model in Figure 13.1. The
two parameters for the integer uniform distribution are lower
and upper, and are entered here as cell references to E12 (40)
and F12 (70), respectively.
Step 2: Define the Results Cell to Forecast
Each output cell that is being used to forecast a measure of
performance is referred to as a results cell.
Procedure for defining a results cell:

Select the cell.
Choose Output > In Cell from the Results menu on the RSPE
ribbon.
19
Step 3. Define any Desired Statistic Cells
Procedure for defining a statistic cell:
Click on the results cell for which you want a statistic.
Choose the statistic you want to show from the Results>Statistic
menu.
Click on the cell where you want to show the statistic.
20
Figure 13.4 The Results menu on the RSPE ribbon that shows
the statistics available under the Statistic submenu. Choosing a
statistic from this submenu will cause that statistic to be
calculated for the current simulation run. The value of this
statistic then will appear within a specified statistic cell.
Step 4: Set the Simulation Options
21
Figure 13.5. The RSPE Options dialog box after showing the
Simulation tab.
Step 5: Run the Simulation
If the Simulate button on the RSPE ribbon is lit (yellow
lightbulb) then RSPE is in interactive simulation mode (a
simulation is run automatically whenever any change is made to

the model).
If the lightbulb is not lit, clicking on it will turn on interactive
simulation mode and run the simulation.
Any statistic cell will show the results of the latest simulation
run.
For more extensive results, hover over a results cell to show a
small chart. Clicking on Click here to open full chart reveals
full results.
22
The Frequency Chart for Freddie’s Profit
23
Figure 13.6 The frequency chart and statistics table provided
by RSPE to summarize the results of running the simulation
model in Figure 13.1 for the case study that involves Freddie
the newsboy.
More Results for Freddie’s Profit
24
Figure 13.7 Two more ways (a cumulative frequency chart and
a percentiles table) RSPE can display the results of running the
simulation model in Figure 13.1 for the case study that involves
Freddy the newsboy.
Likelihood that Profit ≥ $40
Set Lower Cutoff value to see Likelihood of achieving a

minimum profit.
25
Figure 13.8 After setting a lower cutoff of $40 for desirable
profit values, the Likelihood box reveals that 64.5 percent of
the trials in Freddie’s simulation run provided a profit at least
this high.
How Accurate Are the Simulation Results?
An important number provided by the simulation is the mean
profit of $46.45.
This sample average provides an estimate of the true mean of
the distribution. The true mean might be somewhat different
than $46.45.
The standard error (on the Statistics Table) of $0.43 gives some
indication of how accurate the estimate might be. The true mean
will typically (approximately 68% of the time) be within the
mean standard error of the estimated value.
It is about 68% likely that the true mean profit is between
$46.02 and $46.88.
The standard error can be reduced by increasing the number of
trials. However, cutting the mean standard error in half
typically requires approximately ƒour times as many trials.
26
Optimizing with Interactive Simulation Mode
Adjusting the order quantity (in interactive simulation mode)
automatically reruns the simulation and recalculates the mean
profit.
Trial and error leads to a maximum mean profit of $47.26 at an
order quantity of 55.

27
Figure 13.9 This figure illustrates what can happen when the
decision variable, OrderQuantity (C20), is changed by trial-and-
error and the statistic cell, MeanProfit (C20), is observed. When
the OrderQuantity is 55, the MeanProfit (C20) reaches its
maximum value of $47.26.
Group case
Bling Max Carwash
28
“Bling Max” Business Simulation Case
Profs. Yurovia, Griffin, Hoyte
Bling-Max
Touch–Free Carwash in Fort Lauderdale, Florida
Bling Max Car Wash
Bernard “Bernie” West stood under a tall palm admiring his new
business and the many vehicles entering it on a sunny Florida
day. Bernie’s Bling-Max Carwash had exceeded his
expectations as a small service business among many similar
enterprises in Fort Lauderdale. Owned and operated by 32 year
old Bernie, he had purchased the business outright about six
months ago, borrowing against his house and drawing down all
his savings. The carwash, about 8 years old with a single auto

wash bay, was not the newest equipment to be found in a
modern automated car wash, but it had been flawlessly
maintained and was the popular high pressure, touch free,
Pulse-Pro equipment with excellent reliability. Best yet, the
business was located in the perfect spot in Fort Lauderdale, near
a major intersection close to offices, popular clubs, restaurants,
and busy shopping areas. There were no nearby competitors
and Bernie wanted to keep it that way.
Bernie assessed the current business situation. Bling-Max offers
its customers three levels of wash service, “Economy”,
“Custom”, and “Deluxe”, which are priced at $8.00, $9.00, and
$10.00 respectively. Based on Bernie’s market research, the
prices are slightly high but still competitive, compared to other
automated washes. More important than pricing, he knew he
had to do something to reduce wait times to keep customers
from going elsewhere.
Bling-Max is open 7 days per week, 365 days per year from
8:00 AM to 6:00 PM. This 10 hour operating schedule provides
14 “off-hours” for the necessary cleaning, preventive
maintenance, and refill of wash chemicals. During operating
hours, arriving cars line up in a perimeter corral queue that
holds 14 or more cars, depending on their size. The first car
arriving on or after 8:00 AM can pay with a quick credit card
swipe and enter the wash. Successively arriving cars can swipe
and enter as soon as they reach the control panel at the wash
entrance, providing it is before 6:00 PM closure. At 6:00 PM
the control panel lights up the “CLOSED” sign and will not
accept new customers. The last car entering just before 6:00 PM
gets a complete wash cycle and exits normally. Any cars
remaining in line when the service ends at 6:00 PM are let out a
special gate by the maintenance technician who has arrived to
perform the standard daily maintenance.
To better understand customer complaints about the long lines
and wait time problem, Bernie gathered random sample data at

various times of day and on different days, recording timing of
customer arrivals entering the corral and what wash service they
ultimately picked. The wash process times (Service Times) for
the “Economy”, “Custom”, and “Deluxe” washes are 6, 7, and 8
minutes respectively, which includes credit card swipe, entry,
and drive-off times. Since these three times are predominantly
controlled by sophisticated electronic timers in the automated
wash itself, any driver-induced variance from the 6, 7, and 8
minutes is of no consequence (for example, there are no 6.2 or
7.9 minute wash cycles, only 6, 7, and 8 min.). The customer
Inter-Arrival Times (IAT) and selected wash services are shown
in the Excel file Q1 Raw Data Worksheet.xlsx.
Bling Max Car Wash (cont.)
With six months financials completed, Bernie is confident that
all-in costs (utilities, maintenance, chemicals, advertising, etc.)
are 35% of revenues. Since customers are balanced between
offices and shopping during the week, and restaurants, bars, and
shopping on weekends, there seems to be little variation from
day to day or within seasons. Demand is steady and strong all
day, every day, except for an estimated 6% rain periods when
the wash is idle.
The current car wash has the dryer blowers attached to the
robotic wash arm, so the vehicle stays put after the wash and
wax cycle and during the one minute drying cycle. Bernie has
found like-new blow-off equipment at an industrial distributor
and it is ready to install. He can purchase and install the blow-
off section at the car wash exit portal, instead of the wash arm,
for a total investment of $11,500, complete. This would de-
couple the one minute drying cycle from the wash cycle,
speeding up the service process by one minute per car, no
matter which wash they chose. As a car finished the wash
cycle it would move forward toward the exit to get dried off.

This investment would separate the wash and dry-off cycles,
reducing all wash cycles by 1 minute and allowing the next
customer to enter one minute earlier than before, thereby
improving throughput.
It makes sense to Bernie that his wait times could be improved
by a shorter cycle, but it is not obvious to what extent wait
times and lines would be improved, nor whether the investment
is financially justified. He could reduce average process time
just by selling more economy washes. He also knows that he is
not on the low side of competition with his pricing and is
concerned that long waits make it too easy for a competitor to
setup a nearby carwash and steal his market. Bernie is
pondering adding a fourth wash selection and related pricing
adjustments, as well the merits of investing in a new blow-off
section. Bernie knows that he can borrow the $11,500 for the
new blow-off from his commercial bank with a 3 year loan at
6.5% APR, but there is gnawing risk in taking out this loan and
pledging his carwash equity as collateral. He is thinking about
his wife, their two-year old son, and a new child on the way as
he considers his next steps. This business is everything to him
and his family. Can he afford to take this investment risk,
should he look for alternative improvements, or can he risk a
big loss of business if he does nothing?
Bernie’s brother Craig has an automated car wash in Georgia.
Craig’s wash has four wash selections, consisting of Bernie’s
three washes plus a higher-end “Elite” wash using Rain-X ™
brand glass treatment chemicals from a special dispenser that
costs $8,000 and adds 1 minute to the Deluxe cycle time.
Having run periodic specials Craig has given Bernie data on the
relative popularity of the four levels of washes based on price.
Bernie is considering further investment to add this fourth wash
selection and making pricing adjustments accordingly, but he
needs more clarity as he weighs reduction of wait times with
return on investment.

Bernie remembers some of Peter Drucker’s wisdom as he
ponders his next steps: “Efficiency is doing things right and
Effectiveness is doing the right things”, coupled with the key
question “What does the customer most value?”
Great Location, Convenient Hours
Bernie’s
Bling-Max
Carwash
For Your Convenience
8:00 AM to 6:00 PM
365 Days per Year!
Bling Max Case Assignment
Put yourself in the position of a management consultant helping
Bernie with his business improvement decision. Organize your
approach as follows:
Analysis of Raw Data: Fit and describe the distributions
represented by the IAT (inter-arrival times) and customer-
selected services data in the furnished Excel file titled “Q1 Raw
Data Worksheet”. Paste the RSPE histograms you develop for
the IAT and ST (service time) data on your Q1 Raw Data
Worksheet and into the Appendix of your report.
Current Situation: Open the furnished Excel file “Q2 Simulation
Worksheet” and build an RSPE simulation model for Bling-
Max, set the initial seed to 1234, run 10,000 iterations, and

enter “current situation” data into Table 1. The current situation
is long wash cycles with the integrated blow-off attached to the
wash arm.
New Blow-off Investment: Save-as your completed Q2
Simulation Worksheet using file name Q3 Simulation
Worksheet. Update the model to reflect the improved cycle
times from the new blow-off. Enter the Q3 output data into
Table 1.
Bling Max Case Assignment (cont’d)
New Blow-off + 4-washes with Pricing “a”: Save-as your
completed Q3 Simulation Worksheet using file name Q4
Simulation Worksheet. Update the model to reflect the
improved cycle times from the new blow-off plus the impact of
Q4 pricing (ref. Fig 3). Enter the Q4 output data into Table 1.
New Blow-off + 4-washes with Pricing “b”: Save-as your
completed Q4 Simulation Worksheet using file name Q5
Simulation Worksheet. Update the model to reflect the
improved cycle times from the new blow-off plus the impact of
Q5 pricing (ref. Fig 3). Enter the Q5 output data into Table 1.
Analyze the results from the Q2, Q3, Q4, and Q5 simulation
scenarios. What business decision would you make and why?
What are the implications from the standpoint of business
performance and from customer perception and retention?
Follow the guidelines found on BB in the Format of a
Management Report and the Grading Rubric when writing a 4-5
page (body) report. Place Table 1 and output charts in your
report Appendix section and use the model output to justify
your conclusions and recommendations.

Table 1BLING MAX CAR WASH TABLE 1Performance
MeasureQ2: Current Situation (long cycle + 3 wash levels)Q3:
Invest in Exit Blow-off (3 wash levels)Q4:
Blow-off + 4-Wash Levels at Pricing "a"Q5: Blow-off + 4-Wash
Levels at Pricing "b"1Average number of cars washed per
day295% probability that cars washed in a day will
exceed3Average daily revenue4Average daily profit 5Average
annual revenue (adj for 6% rain days)6Average annual profit
(adj for 6% rain days)7Average wait time (min)8% chance that
avg wait time is 10 min or less9% chance that avg wait time is
10 to 20 min10% chance that avg wait time is more than 20
min11Q3 - change in annual profit vs. Q2 - current (as $)12Q3 -
change in average wait vs. Q2 - current (mins)13Q3 - simple
payback vs. Q2 (yrs to 2 decimals)14Q4 & Q5 incremental
annual profit vs. Q3 (as $)15Q4 & Q5 average wait vs. Q3
(mins)16Q4 & Q5 simple payback vs. Q3 (yrs)
Fig 1 - Financial Viability of a New Investment
What is the payback for installing a new blow-off section at the
exit portal?
$11,500 investment
Fig 2 – Current Services at Bling Max Carwash
Deluxe $10.00
Ultra-Wax & protect
Wheel clean
Undercarriage
Touchless wash
Spotless rinse
Super pre-wash

Auto dry
Custom $9.00
Wax
Wheel clean
Touchless wash
Spotless rinse
Auto dry
Economy $8.00
Touchless wash
Spotless rinse
Auto dry
Fig 3 - Wash Services Considered
4 Wash Selections
3 Wash SelectionsQ2: Current
SituationWASHMINUTESPRICEeconomy6$8.00 custom7$9.00
deluxe8$10.00 Q3: New Blow-
offWASHMINUTESPRICEeconomy5$8.00 custom6$9.00
deluxe7$10.00 Q4: New Blow-off + 4 wash
"a"WASHMINUTESPRICEPROBABILITYeconomy5$8.00
35%custom6$9.00 25%deluxe7$10.00 20%elite8$11.00 20%Q5:
New Blow-off + 4 wash
"b"WASHMINUTESPRICEPROBABILITYeconomy5$7.00
30%custom6$8.00 20%deluxe7$9.00 20%elite8$10.00 30%
Fig 4 - Business Challenge
How to improve the process to reduce waiting lines?
How to improve profitability of the carwash?

RETURN ON INVESTMENT
CUSTOMER RETENTION
Choosing the Right Distribution
A continuous distribution is used if any values are possible,
including both integer and fractional numbers, over the entire
range of possible values.
A discrete distribution is used if only certain specific values
(e.g., only some integer values) are possible.
However, if the only possible values are integer numbers over a
relatively broad range, a continuous distribution may be used as
an approximation by rounding any fractional value to the
nearest integer.
40
A Popular Central-Tendency Distribution: Normal
Some value most likely (the mean)
Values close to mean more likely
Symmetric (as likely above as below mean)
Extreme values possible, but rare
41
Figure 13.28 The characteristics and dialog box for a popular
central-tendency distribution: the normal distribution.
A Popular Central-Tendency Distribution: Triangular
Some value most likely
Values close to most likely value more common
Can be asymmetric
Fixed upper and lower bound

42
Figure 13.28 The characteristics and dialog box for a popular
central-tendency distribution: the triangular distribution.
The Uniform Distribution
Fixed minimum and maximum value
All values equally likely
43
Figure 13.29 The characteristics and dialog box for the uniform
distribution in RSPE’s Distribution menu.
A Distribution for Random Events: Exponential
Widely used to describe time between random events (e.g., time
between arrivals)
Events are independent
Rate = average number of events per unit time (e.g., arrivals per
hour)
44
Figure 13.30 The characteristics and dialog box for a
distribution that involves random events: the exponential
distribution.
A Distribution for Random Events: Poisson
Describes the number of times an event occurs during a given
period of time or space
Occurrences are independent
Any number of events is possible

Rate = average number of events per unit of time, assumed
constant over time
45
Figure 13.30 The characteristics and dialog box for a
distribution that involves random events: the Poisson
distribution.
Distribution for Number of Times an Event Occurs: Binomial
Describes number of times an event occurs in a fixed number of
trials (e.g., number of heads in 10 flips of a coin)
For each trial, only two outcomes are possible
Trials independent
Probability remains the same for each trial
46
Figure 13.31 The characteristics and dialog box for the
binomial distribution in RSPE’s Distribution menu.
Historical Demand Data for the Financial Times
47
Figure 13.35 Cells F4:F63 contain the historical demand data
that have been collected for the case study involving Freddie
the newsboy that was introduced in Section 13.1. Columns B
and C come from the simulation model for this case study in
Figure 13.1.
Procedure for Fitting the Best Distribution to Data
Gather the data needed to identify the best distribution to enter

into an uncertain variable cell.
Enter the data into the spreadsheet containing your simulation
model.
Select the cells containing the data.
Click the Fit button on the RSPE ribbon, which brings up the Fit
Distribution dialog box.
Make sure the Range box in this dialog box is correct for the
range of the historical data in your worksheet.
Specify which distributions are being considered for fitting
(continuous or discrete).
Select which ranking method should be used to evaluate how
well a distribution fits the data.
Click Fit.
48
The Fit Options Dialog Box
49
Figure 13.36 This Fit Options dialog box specifies (1) the
range of the data in Figure 13.35 for the case study, (2) only
continuous distributions will be considered, (3) shifted
distributions will be allowed, (4) a sample independence test
will be run, and (5) which ranking method will be used (the chi-
square test) to evaluate how well each of the distributions fit
the data.
The Fit Results
50

Figure 13.37 This Fit Results dialog box identifies the
continuous distributions that provide the best fit, ranked top-to-
bottom from best to worst on the left side. For the distribution
that provides the best fit (Uniform), the distribution is plotted
(the horizontal line at the top of the chart) so that it can be
compared with the frequency distribution of the historical
demand data. The value of the Fit Statistic (chi-square) is 4.4.
Decision Making with Parameter Analysis Reports
Many simulation models include at least one decision variable
Examples: Order quantity, Bid, Number of reservations to
accept
RSPE can be used to evaluate a particular value of the decision
variable by providing a wealth of output for the results cells.
However, this approach does not identify an optimal solution
for the decision variable(s).
Trial and error can be used to try different values of the
decision variable(s).
Run a simulation for each, and see which one provides the best
estimate of the chosen measure of performance.
RSPE provides a systematic way of doing this with parameter
cells.
51
Procedure for Defining a Parameter Cell
Select a cell containing the decision variable.
Choose Simulation from the Parameters menu on the RSPE
ribbon.
Enter the lower and upper limit of the range of values to be
simulated for the decision variable.
Click on OK.

52
Parameter Cell Dialog Box
53
Figure 13.38 This parameter cell dialog box specifies the
characteristics of the decision variable Order Quantity (C9) in
the simulation model in Figure 13.1 for the case study that
involves Freddie the newsboy.
Parameter Analysis Dialog Box
54
Figure 13.39 This Parameter Analysis dialog box allows you to
specify which parameter cells to vary and which results to show
after the simulation run. Here the OrderQuantity (C9) parameter
cell will be varied over seven different values and the value of
the mean will be displayed for each of the seven simulation
runs.
The Parameter Analysis Report for Freddie’s Order Quantity
55
Figure 13.40 The parameter analysis report for the case study
introduced in Section 13.1.
The Simulation Options Dialog Box to Run 7 Simulations

56
Figure 13.41 This Simulation Options dialog box allows you to
specify how many simulations to run before choosing a chart to
show the results of running simulations for that number of
different values of a parameter cell.
The Trend Chart Dialog Box
Choose Trend Chart from the Charts > Multiple Simulations
menu.
57
Figure 13.42 This trend chart dialog box is used to specify
which simulations should be used to show results. Clicking (>>)
causes the results from all of the simulations to appear in the
trend chart.
Trend Chart for Freddie’s Order Quantity
58
Figure 13.43 The trend chart that shows the trend in the mean
and in the range of the frequency distribution as the order
quantity increases for Freddie’s problem.
1
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5
6
7
8
9

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13
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15
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AB CDEF
Freddie the Newsboy
Data
Unit Sale Price $2.50
Unit Purchase Cost $1.50
Unit Salvage Value $0.50
Decision Variable
Order Quantity 60
LowerUpper
Simulation
LimitLimit
Demand40Integer Uniform4070
Sales Revenue $100.00
Purchasing Cost $90.00
Salvage Value $10.00
Profit$20.00
Mean Profit$46.45

Group Case Using Simulation
QNT 5160
Bling Max Carwash
“Bling Max” Business Simulation Case
Bling-Max
Touch–Free Carwash in Fort Lauderdale, Florida
2
Bling Max Car Wash
Bernard “Bernie” West stood under a tall palm admiring his new
business and the many vehicles entering it on a
sunny Florida day. Bernie’s Bling‐Max Carwash had exceeded h
is expectations as a small service business among
many similar enterprises in Fort Lauderdale. Owned and operate
d by 32 year old Bernie, he had purchased the
business outright about six months ago, borrowing against his h
ouse and drawing down all his savings. The
carwash, about 8 years old with a single auto wash bay, was not
the newest equipment to be found in a modern
automated car wash, but it had been flawlessly maintained and
was the popular high pressure, touch free, Pulse‐
Pro equipment with excellent reliability. Best yet, the business
was located in the perfect spot in Fort Lauderdale,
near a major intersection close to offices, popular clubs, restaur
ants, and busy shopping areas. There were no

nearby competitors and Bernie wanted to keep it that way.
Bernie assessed the current business situation. Bling‐Max offers
its customers three levels of wash service,
“Economy”, “Custom”, and “Deluxe”, which are priced at $8.00
, $9.00, and $10.00 respectively. Based on Bernie’s
market research, the prices are slightly high but still competitiv
e, compared to other automated washes. More
important than pricing, he knew he had to do something to reduc
e wait times to keep customers from going
elsewhere.
Bling‐Max is open 7 days per week, 365 days per year from 8:0
0 AM to 6:00 PM. This 10 hour operating schedule
provides 14 “off‐hours” for the necessary cleaning, preventive
maintenance, and refill of wash chemicals. During
operating hours, arriving cars line up in a perimeter corral queu
e that holds 14 or more cars, depending on their
size. The first car arriving on or after 8:00 AM can pay with a
quick credit card swipe and enter the wash.
Successively arriving cars can swipe and enter as soon as they r
each the control panel at the wash entrance,
providing it is before 6:00 PM closure. At 6:00 PM the control
panel lights up the “CLOSED” sign and will not accept
new customers. The last car entering just before 6:00 PM gets a
complete wash cycle and exits normally. Any cars
remaining in line when the service ends at 6:00 PM are let out a
special gate by the maintenance technician who
has arrived to perform the standard daily maintenance.
To better understand customer complaints about the long lines a
nd wait time problem, Bernie gathered random
sample data at various times of day and on different days, recor
ding timing of customer arrivals entering the corral
and what wash service they ultimately picked. The wash proces
s times (Service Times) for the “Economy”,
“Custom”, and “Deluxe” washes are 6, 7, and 8 minutes respecti

vely, which includes credit card swipe, entry, and
drive‐off times. Since these three times are predominantly cont
rolled by sophisticated electronic timers in the
automated wash itself, any driver‐induced variance from the 6,
7, and 8 minutes is of no consequence (for
example, there are no 6.2 or 7.9 minute wash cycles, only 6, 7, a
nd 8 min.). The customer Inter‐Arrival Times (IAT)
and selected wash services are shown in the Excel file Q1 Raw
Data Worksheet.xlsx.
3
Bling Max Car Wash (cont.)
With six months financials completed, Bernie is confident that a
ll‐in costs (utilities, maintenance, chemicals, advertising, etc.) a
re 35%
of revenues. Since customers are balanced between offices and
shopping during the week, and restaurants, bars, and shopping o
n
weekends, there seems to be little variation from day to day or
within seasons. Demand is steady and strong all day, every day,
except
for an estimated 6% rain periods when the wash is idle.
The current car wash has the dryer blowers attached to the robot
ic wash arm, so the vehicle stays put after the wash and wax cyc
le
and during the one minute drying cycle. Bernie has found like‐
new blow‐off equipment at an industrial distributor and it is rea
dy to
install. He can purchase and install the blow‐off section at the
car wash exit portal, instead of the wash arm, for a total investm
ent of
$11,500, complete. This would de‐couple the one minute drying

cycle from the wash cycle, speeding up the service process by o
ne
minute per car, no matter which wash they chose. As a car fini
shed the wash cycle it would move forward toward the exit to ge
t
dried off. This investment would separate the wash and dry‐off
cycles, reducing all wash cycles by 1 minute and allowing the n
ext
customer to enter one minute earlier than before, thereby impro
ving throughput.
It makes sense to Bernie that his wait times could be improved
by a shorter cycle, but it is not obvious to what extent wait time
s and
lines would be improved, nor whether the investment is financia
lly justified. He could reduce average process time just by selli
ng
more economy washes. He also knows that he is not on the low
side of competition with his pricing and is concerned that long
waits
make it too easy for a competitor to setup a nearby carwash and
steal his market. Bernie is pondering adding a fourth wash sele
ction
and related pricing adjustments, as well the merits of investing i
n a new blow‐off section. Bernie knows that he can borrow the
$11,500 for the new blow‐off from his commercial bank with a
3 year loan at 6.5% APR, but there is gnawing risk in taking out
this loan
and pledging his carwash equity as collateral. He is thinking ab
out his wife, their two‐year old son, and a new child on the way
as he
considers his next steps. This business is everything to him and
his family. Can he afford to take this investment risk, should h
e look
for alternative improvements, or can he risk a big loss of busine
ss if he does nothing?

Bernie’s brother Craig has an automated car wash in Georgia. C
raig’s wash has four wash selections, consisting of Bernie’s thre
e
washes plus a higher‐end “Elite” wash using Rain‐X ™ brand gl
ass treatment chemicals from a special dispenser that costs $8,0
00 and
adds 1 minute to the Deluxe cycle time. Having run periodic sp
ecials Craig has given Bernie data on the relative popularity of t
he four
levels of washes based on price. Bernie is considering further i
nvestment to add this fourth wash selection and making pricing
adjustments accordingly, but he needs more clarity as he weighs
reduction of wait times with return on investment.
Bernie remembers some of Peter Drucker’s wisdom as he ponder
s his next steps: “Efficiency is doing things right and Effective
ness is
doing the right things”, coupled with the key question “What do
es the customer most value?”
4
Great Location, Convenient Hours
Bernie’s
Bling-Max
Carwash
For Your Convenience
8:00 AM to 6:00 PM
365 Days per Year!
5

Group Case
Understanding Bling Max
Scenarios Q2, Q3, Q4, and Q5
6
Bling Max Case Assignment
Put yourself in the position of a management consultant helping
Bernie with his
business improvement decision. Organize your approach as foll
ows:
1.
Analysis of Raw Data: Fit and describe the distributions represe
nted by the
IAT (inter‐arrival times) and customer‐selected services data in
the
furnished Excel file titled “Q1 Raw Data Worksheet”. Paste the
RSPE
histograms you develop for the IAT and ST (service time) data
on your Q1
Raw Data Worksheet and into the Appendix of your report.
2.
Current Situation: Open the furnished Excel file “Q2 Simulation
Worksheet” and build an RSPE simulation model for Bling‐Max
, set the
initial seed to 1234, run 10,000 iterations, and enter “current sit
uation”

data into Table 1. The current situation is long wash cycles with
the
integrated blow‐off attached to the wash arm.
3. New Blow‐off Investment: Save‐as
your completed Q2 Simulation
Worksheet using file name Q3 Simulation Worksheet. Update t
he model to
reflect the cycle times from the new blow‐off. Enter the Q3 out
put data
into Table 1. Calculate the loans and enter into the Raw Data fi
le.
7
Bling Max Case Assignment (cont’d)
4. New Blow‐off + 4‐washes with Pricing “a”: Save‐as
your completed Q3
Simulation Worksheet using file name Q4 Simulation Worksheet
. Update
the model to reflect the cycle times from the new blow‐off plus
the impact
of Q4 pricing (ref. Fig 3). Enter the Q4 output data into Table 1
.
5. New Blow‐off + 4‐washes with Pricing “b”: Save‐as
your completed Q4
Simulation Worksheet using file name Q5 Simulation Worksheet
. Update
the model to reflect the cycle times from the new blow‐off plus
the impact
of Q5 pricing (ref. Fig 3). Enter the Q5 output data into Table 1
.

Analyze the results from the Q2, Q3, Q4, and Q5 simulation sce
narios. What
business decision would you make and why? What are the impli
cations from
the standpoint of business performance and from customer perce
ption and
retention?
Follow the guidelines found on BB in the Format of a Managem
ent Report and
the Grading Rubric when writing a 4‐6 page (body) report. Plac
e completed
Table 1, Raw Data Tab tables, and simulation output charts in y
our report
Appendix section and use the model output to justify your concl
usions and
recommendations.
8
Raw Data Worksheet File, Raw Data Tab
Students to complete
these tables for Q1 Q2
Checkpoint submission.
Include in Appendix for
final report upload.
9
Raw Data Worksheet File, Summary Tab

10
Q2 ‐ Car Wash Current State
Wash
Arm
Dry‐off blower on wash arm
Select Wash Option
NOTE: The 1 min blow off occurs in the final minute of the wa
sh cycle
11
Q3 Process Improvement
New dry‐off blower at exit
Select Wash Option Wash Arm
(no blower)
NOTE: The blow‐off is decoupled (removed) from the wash cyc
le by placing it
at the exit. The new blower is not an “extra” blower, it simply
replaces the
old one on the wash arm. This saves 1 min of process time, sinc
e the car in
the wash bay can now move out after washing to get dried.
No dry‐off blower on wash arm

12
Current Services at Bling Max Carwash
Deluxe $10.00
• Ultra-Wax & protect
• Wheel clean
• Undercarriage
• Touchless wash
• Spotless rinse
• Super pre-wash
• Auto dry
Custom $9.00
• Wax
• Wheel clean
• Touchless wash
• Spotless rinse
• Auto dry
Economy $8.00
• Touchless wash
• Spotless rinse
• Auto dry
13
Wash Services Considered
4 Wash Selections
3 Wash Selections
Q2: Current Situation

WASH MINUTES PRICE
economy 6 $8.00
custom 7 $9.00
deluxe 8 $10.00
Q3: New Blow‐off
WASH MINUTES PRICE
economy 5 $8.00
custom 6 $9.00
deluxe 7 $10.00
Q4: New Blow‐off + 4 washes at old prices (a)
WASH MINUTES PRICE PROBABILITY
economy 5 $8.00 35%
custom 6 $9.00 25%
deluxe 7 $10.00 20%
elite 8 $11.00 20%
Q5: New Blow‐off + 4 washes at lower prices (b)
WASH MINUTES PRICE PROBABILITY
economy 5 $7.00 30%
custom 6 $8.00 20%
deluxe 7 $9.00 20%
elite 8 $10.00 30%
14
Financial Viability of a New Investment
What is the payback for installing a new blow‐off section at the
exit portal?

$11,500
investment
15
Thoughts Regarding Business Challenge
How to improve the process
to reduce waiting lines?
How to improve profitability
of the carwash?
RETURN ON INVESTMENTCUSTOMER RETENTION
16
Q1‐Q2 Check Point
and Final Report
NEXT STEPS
17
Complete Q1 and Q2 spreadsheets:
1. Q1 & Q2 Checkpoint: Complete Q1 Raw Data tab tables for
distributions, investments, and loans. Complete the Q2 column
of Table 1. This is your basis for comparison. See slides 9‐10.

2.
Email to Prof your group’s completed Excel files for Q1 and Q2
,
by due date in order to make sure your paper is on track. DO
NOT TRY TO UPLOAD TO BB.
3.
When Q1 & Q2 are OK’d, you can build Q3, Q4, and Q5 models
with some degree of confidence. For the final submission, you
will have FIVE independent Excel files representing Q1 – Q5
Next Steps:
18
• 4‐6 pages of text, all charts & tables in Appendix
•
Follow APA guidelines for format (margins, page numbers, tabl
e of
contents, references, etc.)
• See “Format of a Mgmt Report” on BB.
•
Construct a concise & complete problem statement (single well‐
constructed sentence)
•
Your text book is not a research reference. Use library or intern
et
research. Consider implications of investment and other factors
impacting this small business (e.g. NPV of 10 year cash flows)

• Read & follow the Rubric to prevent losing points
• Proofread for punctuation, spelling, & grammar
•
Check your analysis calculations, and support your findings wit
h your
analysis
•
In addition to Q2‐Q5 scenario models, you may do a QX for “Xt
ra”
credit. Add a half page to describe at the end, and furnish a QX
Excel
model. Credit will be aligned with the quality of the submissio
n.
Tips Regarding Final Report
19
Grading Rubric
See Syllabus for Details
20
Group 5 Q1 BlingMax Raw Data Worksheet, Winter 2018 2.xlsx
Q1- Raw dataDrive up Inter-arrival times (IAT)Wash Service
Chosen by CustomerService Time (ST)All data in
minutes11.2economy7Q2 BASE: Situation NowQ3: New Blow-
offQ4: New Blow-off + 4 wash "a"Q5: New Blow-off + 4 wash
"b"7.4deluxe7WASHMINUTESPRICEWASHMINUTESPRICE
WASHMINUTESPRICEPROBABILITYWASHMINUTESPRICE

PROBABILITY28.0economy8economy6$8.00economy5$8.00ec
onomy5$8.0035%economy5$7.0030%13.6custom8custom7$9.00
custom6$9.00custom6$9.0025%custom6$8.0020%13.2economy
8deluxe8$10.00deluxe7$10.00deluxe7$10.0020%deluxe7$9.002
0%0.3economy6elite8$11.0020%elite8$10.0030%6.3deluxe8AN
ALYSIS OF SAMPLE VS FITTED
DISTRIBUTIONS4.3economy7INTERARRIVAL
TIMES:SERVICE TIMES:0.8deluxe8Descriptive StatisticsIAT
SampleIAT FittedDescriptive StatisticsST SampleST
Fitted1.8custom7Mean8.397.49Mean7.067.0022.7custom8Std
Dev8.277.49Std Dev0.840.822.3economy6Min0.01-
0Min6.006.002.1deluxe8Max38.15InfiniteMax8.008.003.3econo
my8Data Count147.00InifinityData Count147.00
Infinity6.4custom61.3economy6distributionExponential(7.49)di
stributionIntergerUnifrom(6,8)5.5deluxe62.3deluxe710.1custom
8LOAN CALCULATION4.0deluxe8Q3Q4, Q52.5deluxe6Q3
Blower Investment$ 11,500$ 11,50023.4deluxe6Q4, Q5
RainX Investmt$ 8,00011.4deluxe6TOTAL investment$
11,500$ 19,5005.1deluxe66.4custom6Loan principal$
11,500$ 19,50013.0economy8Annual interest
rate6.50%6.50%2.4economy8Monthly interest
rate0.54%0.54%5.7deluxe8Term years3.03.07.2deluxe7Term
months363621.8custom8Loan
payment/mo$352.46$597.661.3deluxe7Loan
payment/yr$4,229.56$7,171.874.9custom66.9deluxe815.5econo
my616.7custom87.1custom76.1economy613.6custom73.6deluxe
824.6deluxe71.1deluxe613.9custom84.1custom88.7custom83.2c
ustom634.4deluxe69.2economy63.3custom819.4economy85.5del
uxe70.6custom79.5economy70.5custom74.1deluxe89.9custom80
.1deluxe78.9custom64.1custom82.4deluxe80.1custom811.2custo
m60.5custom814.5economy64.6custom711.2custom710.5deluxe
61.9custom725.2custom82.6custom78.2custom70.5custom60.1e
conomy610.6economy82.6deluxe63.7economy77.2custom611.1d
eluxe83.2custom86.1deluxe87.5deluxe62.3deluxe610.4economy
84.2deluxe812.3custom86.8custom72.8custom816.6deluxe80.0e
conomy77.6deluxe638.2economy66.9deluxe62.1custom73.7delu

xe80.5custom60.0economy88.4deluxe62.7deluxe616.7custom71
1.7custom69.3deluxe613.5custom73.2custom73.7custom82.0eco
nomy813.0economy636.5deluxe73.6economy614.5economy810.
7deluxe70.1economy63.6deluxe60.1economy89.2custom737.2ec
onomy74.4deluxe60.7economy819.0economy79.5deluxe72.2del
uxe72.4economy62.1economy80.1custom83.0custom620.6econo
my82.7deluxe68.4economy81.7custom628.3deluxe734.5deluxe7
2.9economy85.5deluxe720.4economy710.2custom66.3economy8
10.4economy85.8custom80.5economy74.4deluxe83.4economy74
.7economy87.4custom78.0economy721.4custom82.8custom70.4
deluxe611.1custom621.1economy7
IAT (Continuous)
ST Discrete)
SummaryBLING MAX CAR WASH PERFORMANCE
METRICS TABLE 1Performance MeasureQ2: BASE
Situation now (long cycle + 3 wash levels)Q3: Improved
(New Exit Blow-off, same 3 wash levels)Q4: New Choices &
Prices (Q3 + 4 Wash Levels at Pricing "a")Q5: New Choices &
Prices ( Q3 + 4 Wash Levels at Pricing "b")1Average number of
cars washed per day77797978.0833295% probability of cars
washed per day exceeds666767673Average daily revenue$
689.28$ 711.04$ 738.00$ 663.694Average daily profit $
448.03$ 462.18$ 479.70$ 431.405Average annual revenue
(adj for 6% rain days)$ 236,491$ 243,959$ 249,451.00$
227,713.006Average annual profit (adj for 6% rain days)$
153,719$ 158,574$ 162,143.00$ 148,014.007Average wait
time (min)17.817.429.4211.7791001018% chance that
customers wait 10 min or less28%81%68%53%9% chance that
customers wait 10 to 20 min41%17%26%35%10% chance
customers wait more than 20 min31%2%6%12%11Improvement
in annual profit vs. BASE (Q2) as $$ 4,855.00$ 8,424.00$
(5,705.00)12Improvement in average wait vs. BASE (Q2) as
%60.70%47.13%33.86%13Simple payback vs. BASE (yrs @ 2
decimals)2.372.31-3.4214Annual loan repayment$ 4,229.56$
7,171.87$ 7,171.8715Profit Improvement (#11) less Loan

Payment (#14)$ 625.44$ 1,252.13$ (12,876.87)TOTAL
INVESTMENT$ 11,500$ 19,500$ 19,5003 year loan
monthly repayment$117.49$199.22$199.22
By looking at F15 we can already conclude that this option (Q5)
will not be profitable for the company and should be
disregarded.
Group 5 Q2 Simulation Worksheet, Winter 2018.xlsx
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.954TRUEFIT_EC81_D9D63Aircraft De-Icing Service Times
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0 0 0 1 23 BetaGeneral Binomial Expon
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1000 .954TRUEFIT_70E4D_F0CE3Aircraft Inter-arrival times
(IAT) 3ERROR:#REF!0F1 0 0 -1E+300 1E+300 1
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.954TRUEFIT_9A833_3040DDrive up Inter-arrival times
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1cnZlAAOMAQIAEwAMVW51c2VkIEN1cnZlAARMAQIAEw
AMVW51c2VkIEN1cnZlAAU5AQIAEwAMVW51c2VkIEN1cn
ZlAAZOAQIAEwAMVW51c2VkIEN1cnZlAAcjAQIAEwAMV
W51c2VkIEN1cnZlAAgpAQIAEwAMVW51c2VkIEN1cnZlAAl
gAQIArwG5AQEBAgGamZmZmZmpPwAAZmZmZmZm7j8AA
AUAAQEBAAEBAQA= 0 8
F1 0 1000
.954TRUEFIT_AEFAC_1A71DAuto Car Wash Service Times
(ST)ERROR:#REF!0F1 1 0 -1E+300 1E+300 1 0

-1 1 0 1 0 0
0GF1_rK0qDwEADgDCAQwjACYANACDAJcAmACmAL
QAnAG+AbgBKgD//wAAAAAAAQQAAAAAAAAAAAE2Rml
0IENvbXBhcmlzb24gZm9yIEF1dG8gQ2FyIFdhc2ggU2VydmljZ
SBUaW1lcyAgICAoU1QpARNSaXNrSW50VW5pZm9ybSg1LD
cpAQEQAAIAAQpTdGF0aXN0aWNzAwEBAP8BAQEBAQAB
AQEABAAAAAEBAQEBAAEBAQAEAAAACtMAAeEAAPQA
AAkBAB4BADMBAEgBAF0BAHIBAIcBAAwABUlucHV0AA
AlAQIAEQAKSW50VW5pZm9ybQABLwECABMADFVudXNl
ZCBDdXJ2ZQACTwECABMADFVudXNlZCBDdXJ2ZQADjAE
CABMADFVudXNlZCBDdXJ2ZQAETAECABMADFVudXNlZ
CBDdXJ2ZQAFOQECABMADFVudXNlZCBDdXJ2ZQAGTgEC
ABMADFVudXNlZCBDdXJ2ZQAHIwECABMADFVudXNlZC
BDdXJ2ZQAIKQECABMADFVudXNlZCBDdXJ2ZQAJYAECA
KQBrgEBAQIBmpmZmZmZqT8AAGZmZmZmZu4/AAAFAAE
BAQABAQEA 0 8 F1
0 1000 .954TRUEFIT_22514_2F7C3Auto Car
Wash Service Times (ST) 2ERROR:#REF!0F1 0 0 -
1E+300 1E+300 1 0 0 0 0 1 23
-1 1 0 1 0 0
IENvbXBhcmlzb24gZm9yIEF1dG8gQ2FyIFdhc2ggU2VydmljZS
BUaW1lcyAgICAoU1QpIDIBGlJpc2tVbmlmb3JtKDUuOTg2My
w4LjAxMzcpAQEQAAIAAQpTdGF0aXN0aWNzAwEBAP8BA
QEBAQABAQEABAAAAAEBAQEBAAEBAQAEAAAACtwAA
eoAAPoAAA8BACQBADkBAE4BAGMBAHgBAI0BAAwABUl

ucHV0AAAlAQIADgAHVW5pZm9ybQABLwECABMADFVud
XNlZCBDdXJ2ZQACTwECABMADFVudXNlZCBDdXJ2ZQAD
jAECABMADFVudXNlZCBDdXJ2ZQAETAECABMADFVudX
NlZCBDdXJ2ZQAFOQECABMADFVudXNlZCBDdXJ2ZQAGT
gECABMADFVudXNlZCBDdXJ2ZQAHIwECABMADFVudXNl
ZCBDdXJ2ZQAIKQECABMADFVudXNlZCBDdXJ2ZQAJYAE
CAKoBtAEBAQIBmpmZmZmZqT8AAGZmZmZmZu4/AAAFA
AEBAQABAQEA 0 8 F1
0 1000 .954TRUEFIT_3532A_CA87CAuto Car
1E+300 1E+300 1 0 0 0 0 1 23
-1 1 0 1 0 0
BUaW1lcyAgICAoU1QpIDMBGlJpc2tVbmlmb3JtKDYuOTg2M
yw5LjAxMzcpAQEQAAIAAQpTdGF0aXN0aWNzAwEBAP8BA
AEBAQABAQEA 0 8 F1
0 1000 .954TRUEFIT_E626C_16344Auto Car
1E+300 1E+300 1 0 0 0 0 1 23

-1 1 0 1 0 0
0GF1_rK0qDwEADgDEAQwjACYANACFAJkAmgCoALY
AngHAAboBKgD//wAAAAAAAQQAAAAAAAAAAAE4Rml0I
ENvbXBhcmlzb24gZm9yIEF1dG8gQ2FyIFdhc2ggU2VydmljZS
BUaW1lcyAgICAoU1QpIDQBE1Jpc2tJbnRVbmlmb3JtKDcsOS
kBARAAAgABClN0YXRpc3RpY3MDAQEA/wEBAQEBAAEB
AQAEAAAAAQEBAQEAAQEBAAQAAAAK1QAB4wAA9gAA
CwEAIAEANQEASgEAXwEAdAEAiQEADAAFSW5wdXQAA
CUBAgARAApJbnRVbmlmb3JtAAEvAQIAEwAMVW51c2VkI
EN1cnZlAAJPAQIAEwAMVW51c2VkIEN1cnZlAAOMAQIAE
wAMVW51c2VkIEN1cnZlAARMAQIAEwAMVW51c2VkIEN1c
nZlAAU5AQIAEwAMVW51c2VkIEN1cnZlAAZOAQIAEwAM
VW51c2VkIEN1cnZlAAcjAQIAEwAMVW51c2VkIEN1cnZlAA
gpAQIAEwAMVW51c2VkIEN1cnZlAAlgAQIApgGwAQEBAg
GamZmZmZmpPwAAZmZmZmZm7j8AAAUAAQEBAAEBAQ
A= 0 8 F1 0 1000
.954TRUEFIT_272DC_DF343Auto Car Wash Service
Times (ST) 5ERROR:#REF!0F1 1 0 -1E+300
1E+300 1 0 0 0 0 1 23 BetaGeneral
BUaW1lcyAgICAoU1QpIDUBE1Jpc2tJbnRVbmlmb3JtKDcsOS
kBARAAAgABClN0YXRpc3RpY3MDAQEA/wEBAQEBAAEB
AQAEAAAAAQEBAQEAAQEBAAQAAAAK1QAB4wAA9gAA
CwEAIAEANQEASgEAXwEAdAEAiQEADAAFSW5wdXQAA
CUBAgARAApJbnRVbmlmb3JtAAEvAQIAEwAMVW51c2VkI

EN1cnZlAAJPAQIAEwAMVW51c2VkIEN1cnZlAAOMAQIAE
wAMVW51c2VkIEN1cnZlAARMAQIAEwAMVW51c2VkIEN1c
nZlAAU5AQIAEwAMVW51c2VkIEN1cnZlAAZOAQIAEwAM
VW51c2VkIEN1cnZlAAcjAQIAEwAMVW51c2VkIEN1cnZlAA
gpAQIAEwAMVW51c2VkIEN1cnZlAAlgAQIApgGwAQEBAg
GamZmZmZmpPwAAZmZmZmZm7j8AAAUAAQEBAAEBAQ
A= 0 8 F1 0 1000
.954TRUEFIT_C0069_E1276Drive up Inter-arrival times
(IAT) 2ERROR:#REF!0F1 0 0 -1E+300 1E+300 1
0 0 0 0 1 23 BetaGeneral Binomial
Expon ExtValue ExtValueMin Gamma Geomet
IntUniform InvGauss Laplace Levy Logistic
LogLogistic Lognorm NegBin Normal Pareto
Pearson5 Pearson6 Poisson Triang Uniform
Weibull 0 1 -1 1 0 1 0 0
2YWwgdGltZXMgKElBVCkgMgEkUmlza0V4cG9uKDEwLjM2
MSxSaXNrU2hpZnQoMC45Mjk1MikpAQEQAAIAAQpTdGF0a
XN0aWNzAwEBAP8BAQEBAQABAQEABAAAAAEBAQEBA
AEBAQAEAAAACuUAAfMAAAEBABYBACsBAEABAFUBA
GoBAH8BAJQBAAwABUlucHV0AAAlAQIADAAFRXhwb24A
F1 0 1000
.954TRUEFIT_1A184_CD4B9Drive up Inter-arrival times (IAT)
3ERROR:#REF!0F1 0 0 -1E+300 1E+300 1 0 0

-1 1 0 1 0 0
2YWwgdGltZXMgKElBVCkgMwEkUmlza0V4cG9uKDQuNjM5
NSxSaXNrU2hpZnQoMC45Njg0NCkpAQEQAAIAAQpTdGF0a
XN0aWNzAwEBAP8BAQEBAQABAQEABAAAAAEBAQEBA
AEBAQAEAAAACuUAAfMAAAEBABYBACsBAEABAFUBA
GoBAH8BAJQBAAwABUlucHV0AAAlAQIADAAFRXhwb24A
F1 0 1000
.954TRUEFIT_E736D_F1D91Drive up Inter-arrival times (IAT)
4ERROR:#REF!0F1 0 0 -1E+300 1E+300 1 0 0
-1 1 0 1 0 0
2YWwgdGltZXMgKElBVCkgNAEkUmlza0V4cG9uKDYuNDg5
OCxSaXNrU2hpZnQoMC45NTU4NSkpAQEQAAIAAQpTdGF0

F1 0 1000
.954TRUEFIT_6B3AB_D0AB8Auto Car Wash Service Times
(ST) 6ERROR:#REF!0F1 0 0 -1E+300 1E+300 1 0
-1 1 0 1 0 0
BUaW1lcyAgICAoU1QpIDYBGlJpc2tVbmlmb3JtKDYuOTg2M
yw5LjAxMzcpAQEQAAIAAQpTdGF0aXN0aWNzAwEBAP8BA
AEBAQABAQEA 0 8 F1
0 1000 .954TRUEFIT_3042C_9CC0DAuto Car
1E+300 1E+300 1 0 0 0 0 1 23

-1 1 0 1 0 0
BUaW1lcyAgICAoU1QpIDcBE1Jpc2tJbnRVbmlmb3JtKDcsOSk
BARAAAgABClN0YXRpc3RpY3MDAQEA/wEBAQEBAAEBA
QAEAAAAAQEBAQEAAQEBAAQAAAAK1QAB4wAA9gAAC
wEAIAEANQEASgEAXwEAdAEAiQEADAAFSW5wdXQAAC
UBAgARAApJbnRVbmlmb3JtAAEvAQIAEwAMVW51c2VkIE
N1cnZlAAJPAQIAEwAMVW51c2VkIEN1cnZlAAOMAQIAEw
AMVW51c2VkIEN1cnZlAARMAQIAEwAMVW51c2VkIEN1cn
ZlAAU5AQIAEwAMVW51c2VkIEN1cnZlAAZOAQIAEwAMV
W51c2VkIEN1cnZlAAcjAQIAEwAMVW51c2VkIEN1cnZlAAg
pAQIAEwAMVW51c2VkIEN1cnZlAAlgAQIApgGwAQEBAgGa
mZmZmZmpPwAAZmZmZmZm7j8AAAUAAQEBAAEBAQA=
0 8 F1 0 1000
.954TRUEFIT_70B41_C1EAADrive up Inter-arrival times
(IAT) 5ERROR:#REF!0F1 0 0 -1E+300 1E+300 1
Weibull 0 1 -1 1 0 1 0 0
2YWwgdGltZXMgKElBVCkgNQEkUmlza0V4cG9uKDYuNDg5

F1 0 1000
.954TRUEFIT_4346B_EAE3DAuto Car Wash Service Times
(ST) 8ERROR:#REF!0F1 0 0 -1E+300 1E+300 1 0
-1 1 0 1 0 0
BUaW1lcyAgICAoU1QpIDgBGlJpc2tVbmlmb3JtKDYuOTg2My
AEBAQABAQEA 0 8 F1
0 1000 .954TRUEFIT_65D1F_390CFAuto Car
1E+300 1E+300 1 0 0 0 0 1 23

-1 1 0 1 0 0
BUaW1lcyAgICAoU1QpIDkBGlJpc2tVbmlmb3JtKDYuOTg2My
AEBAQABAQEA 0 8 F1
0 1000 .954TRUEFIT_9F703_8FA7BDrive up
Inter-arrival times (IAT) 6ERROR:#REF!0F1 0 0 -
1E+300 1E+300 1 0 0 0 0 1 23
-1 1 0 1 0 0
2YWwgdGltZXMgKElBVCkgNgEkUmlza0V4cG9uKDYuNDg5

F1 0 1000
.954TRUEFIT_1DFA0_7C990Drive up Inter-arrival times (IAT)
7ERROR:#REF!0F1 0 0 -1E+300 1E+300 1 0 0
-1 1 0 1 0 0
2YWwgdGltZXMgKElBVCkgNwEkUmlza0V4cG9uKDYuNDg5
F1 0 1000
.954TRUEFIT_11ACC_25E5DAuto Car Wash Service Times
(ST) 10ERROR:#REF!0F1 0 0 -1E+300 1E+300 1

Weibull 0 1 -1 1 0 1 0 0
0GF1_rK0qDwEADgDJAQwjACYANACNAKEAogCwAL
4AowHFAb8BKgD//wAAAAAAAQQAAAAAAAAAAAE5Rml0
BUaW1lcyAgICAoU1QpIDEwARpSaXNrVW5pZm9ybSg2Ljk4
NjMsOS4wMTM3KQEBEAACAAEKU3RhdGlzdGljcwMBAQD
/AQEBAQEAAQEBAAQAAAABAQEBAQABAQEABAAAAAr
dAAHrAAD7AAAQAQAlAQA6AQBPAQBkAQB5AQCOAQA
MAAVJbnB1dAAAJQECAA4AB1VuaWZvcm0AAS8BAgATAA
xVbnVzZWQgQ3VydmUAAk8BAgATAAxVbnVzZWQgQ3Vyd
mUAA4wBAgATAAxVbnVzZWQgQ3VydmUABEwBAgATAA
xVbnVzZWQgQ3VydmUABTkBAgATAAxVbnVzZWQgQ3Vyd
mUABk4BAgATAAxVbnVzZWQgQ3VydmUAByMBAgATAAx
VbnVzZWQgQ3VydmUACCkBAgATAAxVbnVzZWQgQ3Vydm
UACWABAgCrAbUBAQECAZqZmZmZmak/AABmZmZmZmbu
PwAABQABAQEAAQEBAA== 0 8
F1 0 1000
.954TRUEFIT_A2C52_8312Auto Car Wash Service Times
(ST) 11ERROR:#REF!0F1 1 0 -1E+300 1E+300 1
Weibull 0 1 -1 1 0 1 0 0
0GF1_rK0qDwEADgDFAQwjACYANACGAJoAmwCpALc
AnwHBAbsBKgD//wAAAAAAAQQAAAAAAAAAAAE5Rml0I
BUaW1lcyAgICAoU1QpIDExARNSaXNrSW50VW5pZm9ybSg
3LDkpAQEQAAIAAQpTdGF0aXN0aWNzAwEBAP8BAQEBAQ
ABAQEABAAAAAEBAQEBAAEBAQAEAAAACtYAAeQAAP
cAAAwBACEBADYBAEsBAGABAHUBAIoBAAwABUlucHV0
AAAlAQIAEQAKSW50VW5pZm9ybQABLwECABMADFVudX
NlZCBDdXJ2ZQACTwECABMADFVudXNlZCBDdXJ2ZQADj
AECABMADFVudXNlZCBDdXJ2ZQAETAECABMADFVudXN

lZCBDdXJ2ZQAFOQECABMADFVudXNlZCBDdXJ2ZQAGTg
ECABMADFVudXNlZCBDdXJ2ZQAHIwECABMADFVudXNl
CAKcBsQEBAQIBmpmZmZmZqT8AAGZmZmZmZu4/AAAFA
AEBAQABAQEA 0 8 F1
0 1000 .954TRUEFIT_E4752_517EFDrive up
Inter-arrival times (IAT) 8ERROR:#REF!0F1 0 0 -
1E+300 1E+300 1 0 0 0 0 1 23
-1 1 0 1 0 0
2YWwgdGltZXMgKElBVCkgOAEkUmlza0V4cG9uKDYuNDg5
F1 0 1000
.954TRUE
Q2 SimulationQ2 Simulation WorksheetOpen 8:00
am8.0hrs480minRain days idle (no biz)6%evrNOTE: FOR
PERSONAL AND TEAM USE ONLYClose 6:00
pm18.0hrs1080minDO NOT REPRODUCE OR DISTRIBUTE
EXCEPT AS PART OF YOUR TEAM SUBMISSIONProfit

Margin65%Customer CountCar Inter-arrival times (IAT)Clock
Arrival TimeAfter Hours = 0Start Wash ServiceService time
(ST)End Wash ServiceWait timeWash idle timeNo Rain
RevenueNo Rain ProfitRESULTSOUTPUTRISK Mean
(Daily)RISK Mean (Annual)004800048000$ - 0$ - 0Car
Count8076.626,27711.0304855282481.0301481.03058489.0305
0.00001.0305$ 10.00$ 6.50Revenue$ 717.00$ 689.28$
236,49123.7557219119484.7861489.03057496.03054.24430.000
0$ 9.00$ 5.85Profit$ 466.05$ 448.03$
153,71938.5900695883493.3761496.03057503.03052.65420.000
0$ 9.00$
5.85417.9694685984511.3461511.34576517.34570.00008.3153$
8.00$
5.2051.4135991916512.7591517.34576523.34574.58640.0000$
8.00$ 5.20Average wait
time24.817.8168.6821321924521.4411523.34577530.34571.904
30.0000$ 9.00$ 5.85Max wait
time59.346.2275.8316481822527.2731530.34576536.34573.072
60.0000$ 8.00$
5.2081.0851852084528.3581536.34576542.34577.98740.0000$
8.00$
5.2096.1703555505534.5291542.34578550.34577.81710.0000$
10.00$ 6.50Average Idle
Time0.60.94101.0578665669535.5871550.34577557.345714.75
920.0000$ 9.00$ 5.85Max idle
time17.718.441115.9426916002551.5291557.34576563.34575.8
1650.0000$ 8.00$
5.20127.1269754731558.6561563.34577570.34574.68950.0000$
9.00$
5.85135.913570779564.5701570.34578578.34575.77600.0000$
10.00$
6.50WASHMINUTESPRICEPROBABILITY144.2370351433568
.8071578.34578586.34579.53890.0000$ 10.00$
6.50economy6$8.0033.33333%154.715091267573.5221586.345
76592.345712.82380.0000$ 8.00$
5.20custom7$9.0033.33333%1610.5475488353584.0691592.345

77599.34578.27630.0000$ 9.00$
5.85deluxe8$10.0033.33333%178.465556106592.5351599.3457
6605.34576.81070.0000$ 8.00$
5.20188.2765714573600.8121605.34576611.34574.53420.0000$
8.00$
5.20192.2298321192603.0411611.34577618.34578.30430.0000$
9.00$
5.85201.9888606083605.0301618.34577625.345713.31550.0000
$ 9.00$
5.85214.5077927663609.5381625.34576631.345715.80770.0000
$ 8.00$
5.20222.5596415885612.0981631.34578639.345719.24800.0000
$ 10.00$
6.50237.751050857619.8491639.34576645.345719.49700.0000$
8.00$
5.20247.5691088867627.4181645.34578653.345717.92790.0000
$ 10.00$
6.50254.1887305946631.6071653.34578661.345721.73920.0000
$ 10.00$
6.50261.4266641366633.0331661.34576667.345728.31250.0000
$ 8.00$
5.20279.4754412659642.5091667.34576673.345724.83700.0000
$ 8.00$
5.20289.853156526652.3621673.34576679.345720.98390.0000$
8.00$
5.20292.8238881746655.1861679.34578687.345724.16000.0000
$ 10.00$
6.50309.5482234687664.7341687.34578695.345722.61180.0000
$ 10.00$
6.50312.0645626747666.7991695.34577702.345728.54720.0000
$ 9.00$
5.853210.4269560918677.2251702.34577709.345725.12030.000
0$ 9.00$
5.853310.128501831687.3541709.34578717.345721.99180.0000
$ 10.00$
6.50343.062596238690.4171717.34576723.345726.92920.0000$

8.00$
5.20352.7350361975693.1521723.34578731.345730.19410.0000
$ 10.00$
6.50361.5567533067694.7081731.34577738.345736.63740.0000
$ 9.00$
5.85373.6125423819698.3211738.34578746.345740.02480.0000
$ 10.00$
6.50383.0702885568701.3911746.34576752.345744.95450.0000
$ 8.00$
5.20397.2231253802708.6141752.34576758.345743.73140.0000
$ 8.00$
5.204011.9823867559720.5971758.34577765.345737.74900.000
0$ 9.00$
5.85417.5040392171728.1011765.34577772.345737.24500.0000
$ 9.00$
5.85427.2964505632735.3971772.34578780.345736.94850.0000
$ 10.00$
6.50433.242773982738.6401780.34576786.345741.70580.0000$
8.00$
5.20449.7151169761748.3551786.34578794.345737.99070.0000
$ 10.00$
6.50455.722489367754.0781794.34576800.345740.26820.0000$
8.00$
5.20464.9056105406758.9831800.34576806.345741.36260.0000
$ 8.00$
5.20471.5790057492760.5621806.34576812.345745.78350.0000
$ 8.00$
5.20482.8492840183763.4111812.34577819.345748.93430.0000
$ 9.00$
5.854913.374760934776.7861819.34577826.345742.55950.0000
$ 9.00$
5.855024.6778048195801.4641826.34578834.345724.88170.000
0$ 10.00$
6.505110.1783310508811.6421834.34577841.345722.70340.000
0$ 9.00$
5.85527.0660767712818.7081841.34578849.345722.63730.0000

$ 10.00$
6.50531.0659141444819.7741849.34576855.345729.57140.0000
$ 8.00$
5.20542.0330968463821.8071855.34578863.345733.53830.0000
$ 10.00$
6.505513.3345406408835.1421863.34576869.345728.20370.000
0$ 8.00$
5.20563.5382592658838.6801869.34577876.345730.66550.0000
$ 9.00$
5.85571.1924785343839.8731876.34577883.345736.47300.0000
$ 9.00$
5.85584.2693229215844.1421883.34576889.345739.20370.0000
$ 8.00$
5.20594.4384945144848.5811889.34576895.345740.76520.0000
$ 8.00$
5.20605.9117757724854.4921895.34578903.345740.85340.0000
$ 10.00$
6.50611.223762204855.7161903.34577910.345747.62960.0000$
9.00$
5.85625.0491169606860.7651910.34578918.345749.58050.0000
$ 10.00$
6.50638.6576228433869.4231918.34577925.345748.92290.0000
$ 9.00$
5.85641.1499999778870.5731925.34577932.345754.77290.0000
$ 9.00$
5.85652.5016277251873.0741932.34578940.345759.27130.0000
$ 10.00$
6.506629.2473650543902.3221940.34576946.345738.02390.000
0$ 8.00$
5.20674.4903606943906.8121946.34576952.345739.53350.0000
$ 8.00$
5.20688.5164393045915.3291952.34576958.345737.01710.0000
$ 8.00$
5.20692.85209317918.1811958.34577965.345740.16500.0000$
9.00$
5.857010.3568749321928.5381965.34578973.345736.80810.000

0$ 10.00$
6.50711.7735430283930.3111973.34578981.345743.03460.0000
$ 10.00$
6.507220.2250782369950.5361981.34577988.345730.80950.000
0$ 9.00$
5.85735.4654062221956.0021988.34578996.345732.34410.0000
$ 10.00$
6.507419.8504166903975.8521996.345771003.345720.49370.00
00$ 9.00$
5.857530.8345345271006.68711006.686681014.68660.00003.34
08$ 10.00$
6.50765.10592682991011.79311014.686671021.68662.89410.00
00$ 9.00$
5.857712.91537210291024.70811024.707961030.70790.00003.0
213$ 8.00$
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Group 5 Q3 Simulation Worksheet, Winter 2018.xlsx
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