BLING MAX RAW DATA 1 PAGE AND QUESTIONS

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Module C

Simulation

QNT 5160 Data Driven Decision Making Module PowerPoints (rev 1.2)

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

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.

Outline of a Major Computer Simulation Study (2 of 3)

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.

Outline of a Major Computer Simulation Study (3 of 3)

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.

Spreadsheet Model for Applying Simulation

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.

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.

Distributions Menu on the RSPE Ribbon

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

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.

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.

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

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.

The Frequency Chart for Freddie’s Profit

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

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.

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.

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.

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

“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 1

	BLING MAX CAR WASH TABLE 1

	Performance Measure	Q2: 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"
1	Average number of cars washed per day
2	95% probability that cars washed in a day will exceed
3	Average daily revenue
4	Average daily profit
5	Average annual revenue (adj for 6% rain days)
6	Average annual profit (adj for 6% rain days)
7	Average wait time (min)
8	% chance that avg wait time is 10 min or less
9	% chance that avg wait time is 10 to 20 min
10	% chance that avg wait time is more than 20 min
11	Q3 - change in annual profit vs. Q2 - current (as $)
12	Q3 - change in average wait vs. Q2 - current (mins)
13	Q3 - simple payback vs. Q2 (yrs to 2 decimals)
14	Q4 & Q5 incremental annual profit vs. Q3 (as $)
15	Q4 & Q5 average wait vs. Q3 (mins)
16	Q4 & 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 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 wash "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 wash "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%

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.

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

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

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

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)

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

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

Figure 13.31 The characteristics and dialog box for the binomial distribution in RSPE’s Distribution menu.

Historical Demand Data for the Financial Times

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.

The Fit Options Dialog Box

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

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.

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.

Parameter Cell Dialog Box

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

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

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

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.

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

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.

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