simulation - 1 us army logistics management college part 1: simulation modeling w/ built in excel...

Simulation - 1

US Army Logistics Management CollegeUS Army Logistics Management College

Part 1: Simulation ModelingPart 1: Simulation Modelingw/ Built in Excel Toolsw/ Built in Excel Tools

Simulation - 2


Walton BookstoreWalton Bookstore• In August, Walton Bookstore must decide how many of next year’s

nature calendars to order.

• Each calendar costs the bookstore $7.50 and is sold for $10.

• After February 1 all unsold calendars are returned to the publisher for a refund of $2.50 per calendar.

• Walton believes that the number of calendars it can sell by February 1 follows this probability distribution.

CalendarsDemanded

100150200250300

Probability0.300.200.300.150.05

• Walton wants to simulate 1000 replications for order quantities 100, 125, 150, … , 300 to determine the quantity to order so as to

maximize the expected profit from calendar sales.

MyWalton1.xls

Simulation - 3


Step 1: Identify InputsStep 1: Identify Inputs Walton Bookstore 1Walton Bookstore 1

• Constant Inputs (No Uncertainty): Unit Cost (B4): $7.50 Unit Price (B5): $10.00 Unit Refund (B6): $2.50 Order Quantity (B9): 200

Note Named Cells

• Random Inputs (Probability Distribution): (D5): 0 (D6:D9): =D5+F5 Random # (B19): =Rand() Excel Math&Trig function Demand (C19): =VLOOKUP(B19,Lookup,2) Excel Lookup&Reference function

Simulation - 4


Step 2: Build Basic ModelStep 2: Build Basic Model Logic to Convert Inputs into OutputsLogic to Convert Inputs into Outputs

• Revenue (D19): =UnitPrice*MIN(C19,OrderQuan) Min is Excel Statistical function

• Cost (E19): =UnitCost*OrderQuan

• Refund (F19): =UnitRefund*MAX(OrderQuan-C19,0) Max is Excel Statistical function

• Profit (G19): =D19-E19+F19

• Copy (B19:G19) to (B19:G1018)

• Name (G19:G1018) “Profits”

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Step 3: Create Summary StatisticsStep 3: Create Summary Statistics Walton Bookstore 1Walton Bookstore 1

• Average Profit (B12): =AVERAGE(Profits)

• Stdev Profit (B13): =STDEV(Profits)

• Minimum Profit (B14): =MIN(Profits)

• Maximum Profit (B15): =MAX(Profits)

• 95% Confidence Interval

Lower limit (E12): =AvgProfit-NORMSINV(0.975) *StdevProfit/SQRT(1000)

Upper limit (E13): =AvgProfit+NORMSINV(0.975) *StdevProfit/SQRT(1000)

Simulation - 6


Step 4: Determine the “Best” Order QuantityStep 4: Determine the “Best” Order Quantity One-Way Data Table MethodOne-Way Data Table Method

Walton Bookstore 1Walton Bookstore 1

• Identify Table Output (B1022): =AvgProfit

• Select range (A1022:B1031)

•Select: Data + What If Analysis + DataTable

• Set the Column Input cell to B9

Order Quantity AvgProfit$197.38

100 $250.00125 $258.13150 $266.25175 $231.81200 $197.38225 $112.31250 $27.25275 ($88.38)300 ($204.00)

Data table for average profit versus order quantity

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Step 5: Graph the ResultsStep 5: Graph the Results Walton Bookstore 1Walton Bookstore 1

• Select Insert + Column Chart + Clustered Column

• Choose Select Data

• Add Series (Series Name: $B$1021, Series Values $B$1023:$B$1031)

• Edit Horizontal Category Axis Labels (Label Range $A$1023:$A$1031)

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Two-Way Data Table MethodTwo-Way Data Table MethodWalton3.xlsWalton3.xls

• Note the change in the basic model.

MyWalton3.xls

Demand (A19): =VLOOKUP(RAND(),Lookup,2).

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Create the Two-Way Data TableCreate the Two-Way Data TableWalton3.xlsWalton3.xls

• Identify Table Output (A23): =Profit

• Select range A23:F1023 for the Data Table

•Select: Data + What If Analysis + DataTable

• For the Row input cell enter B9

• For the Column Input cell enter G23 or any other blank cell you choose.

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Part 2: Part 2: Intro to Simulation Modeling

with @Risk

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Walton Bookstore RevisitedWalton Bookstore RevisitedWalton4.xlsWalton4.xls

• Recall that Walton Bookstore buys calendars for $7.50, sells them at a regular price of $10, and gets a refund for all calendars that cannot be sold.

• The company does not know exactly how many calendars its customers will demand, but it does have historical data on demands for similar calendars in previous years. Walton wants to use these historical data to determine a reasonable probability distribution for next year’s demand for calendars.

• Walton wants to use this probability distribution, together with @Risk, to simulate the profit for any particular order quantity.

• Walton eventually wants to find the “best” order quantity.

MyWalton4.xls

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Solution ApproachSolution Approach Walton Bookstore 4Walton Bookstore 4

1. Use BestFit to identify demand probability distribution.

2. Use @Risk to Simulate 1000 runs for each potential order quantity.

3. Use @Risk RiskSimTable function to determine the “best” order quantity.

(does the work of the Data Table)

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Opening an Existing @Risk FileOpening an Existing @Risk File

1. Open @Risk for Excel

2. Open the file: MyWalton4.xls

3. Use File + Save As to save this file under a different name (such as Class MyWalton 4)

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Fitting a Probability DistributionFitting a Probability Distribution

• The historical demand data is on the Data tab of Walton4.

• The hard part is to find historic data that is appropriate for estimating the probability distribution of demand for next year’s calendars.

• To select a probability distribution to match the histogram well, we can use @Risk’s fitting ability.

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3. Copy and Paste Data into the 3. Copy and Paste Data into the FitFitTTabab

Fitting a Probability DistributionFitting a Probability Distribution

• Click on the “Show Excel Window” button

• Select the range A7:A121. • Click on the copy button.

• Click on the “Show @RISK-Model window” button.

• Select Edit + Paste from the Menu Bar

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4. Select Candidate Distributions4. Select Candidate Distributions Fitting a Probability DistributionFitting a Probability Distribution

To see the candidate probability distributions from which to choose, click on the Specify-Distributions-to-Fit button from the tool bar.

• You can check as many of the candidates as you like.

• Stick with familiar distributions such as the normal and triangular.

• Clicked on “OK” which accepts the defaults .

Simulation - 17


5. Do the Fitting5. Do the Fitting Fitting a Probability DistributionFitting a Probability Distribution

Click on the “Fit-Distributions-to-Input-Data” button in the tool bar .

• Note the distributions are ranked by the Chi-Sq test.• Change “Rank by” to K-S. The Weibull is better than the Normal.• Change “Rank by” to A-D. The Normal is better than the Weibull

For Normal: 168.1, 57.6

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Solution ApproachSolution Approach Walton Bookstore 4Walton Bookstore 4





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Step 1: Identify the Input Cell(s)Step 1: Identify the Input Cell(s) Creating the @Risk Simulation ModelCreating the @Risk Simulation Model

1. Enter the values for the mean and standard deviation estimated by BestFit! Mean = 168.1 in cells E4 StDev = 57.6 in cells E5.

2. In cell A13, use the @RISK Distribution function RiskNormal within the Excel Math & Trig function ROUND to enter the formula:=Round(RiskNormal

(MeanDem,StdevDem).

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Step 2: Build the Basic ModelStep 2: Build the Basic Model Creating the @Risk Simulation ModelCreating the @Risk Simulation Model

• Revenue (B13): =UnitPrice*MIN(OrderQuan,Demand).

• Cost (C13): =OrderQuan*UnitCost

• Refund (D13): =UnitRefund*MAX(OrderQuan-Demand,0)

Still the Hardest Partand the Heart of Simulation

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Step 3: Identify the Output Cell(s)Step 3: Identify the Output Cell(s) Creating the @Risk Simulation ModelCreating the @Risk Simulation Model

• In cell E13 enter the formula for Profit:=B13+D13-C13

• Designate cell E13 as an @Risk output cell by clicking on the the Add Output Cell button on the @Risk toolbar.

=RiskOutput() + B13+D13-C13

• Any number of cells can be designated in this way as output cells. They are typically “bottom line values of primary interest.”

• Click on the “Display List of Outputs &Inputs” button on the @Risk toolbar to check the list at any time.

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Step 4: Create Summary Statistics Step 4: Create Summary Statistics on the Output Cell(s)on the Output Cell(s)

Creating the @Risk Simulation ModelCreating the @Risk Simulation Model

1. In cell B16, use the @RISK Statistics function: =RiskMin(Profit)

2. In cell B17, enter: =RiskMax(Profit)3. In cell B18, enter: =RiskMean(Profit)4. In cell B19, enter: =RiskStdDev(Profit)

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Step 5: Specify the Simulation SettingsStep 5: Specify the Simulation Settings Creating the @Risk Simulation ModelCreating the @Risk Simulation Model

• Click on the “Simulations Settings” button.

• Click on the “Iterations” tab in the Simulation Settings dialog box. Set # Iterations to 1000. Set # Simulations to 1. Check Update Display.

• Click on the “Sampling” tab in the Simulation Settings dialog box. Set Sampling Type to Latin Hypercube . Set Standard Recalc to Monte Carlo . Set Random Generator Seed to Choose Randomly . Set Collect Distribution Samples to All .

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Step 6: Specify the Report SettingsStep 6: Specify the Report Settings Creating the @Risk Simulation ModelCreating the @Risk Simulation Model

• Click on the “Report Settings” button.

• For At the End of Each @RISK Simulation: Check Show Interactive @RISK

Results Window. Check Generate Excel Reports

Selected Below.

• For Excel Reports: Check Simulation Summary . Check Detailed Statistics.

• For Excel Reports: Check Active Workbook.

Simulation - 25


• To run the simulation, Click on the “Start Simulation” button.

• In the @Risk Results window To see Summary Statistics, use the “Summary Statistics

Window” button.

To see Detailed Statistics, use the “Detailed Statistics Window” button.

Step 6: Step 6: Run the @Risk SimulationRun the @Risk Simulation Creating the @Risk Simulation ModelCreating the @Risk Simulation Model

Simulation - 26


Analyzing the OutputAnalyzing the Output Walton Bookstore 4Walton Bookstore 4

@Risk generates a large number of output measures.

Summary Report. Assuming that the top box was checked in the @Risk Reports dialog box, we are immediately transferred to the @Risk Results window. This window contains the summary results shown here.

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Detailed Statistics Detailed Statistics Analyzing the OutputAnalyzing the Output

All of the information in the Summary Report is here, plus some.

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00

-1.2 -0.9 -0.6 -0.3 0 0.3 0.6

27.4% 67.6% 0 .5

Mean=182.3825

Distribution for Profit/E13

Va

lue

s in

10

^ -3

Values in Thousands

0.000

0.500

1.000

1.500

2.000

2.500

3.000

Mean=182.3825

-1.2 -0.9 -0.6 -0.3 0 0.3 0.6

Charts Charts Analyzing the OutputAnalyzing the Output

To create a histogram of the 1,000 profits:In the left pane of the Results window, click on ProfitsFrom the menu bar select: Insert+Graph+Histogram

Note the 27.4% chance of

losing money

Simulation - 29


Solution ApproachSolution Approach Walton BookstoreWalton Bookstore





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Using RISKSIMTABLEUsing RISKSIMTABLEWalton Bookstore 5Walton Bookstore 5

• Walton’s ultimate goal is to choose an order quantity that provides a large average profit.

• We could rerun the simulation model several times, each time with a different order quantity in the OrderQuan cell, and compare the results.

• The RISKSIMTABLE function in @Risk enables us to obtain a fair comparison quickly and easily.

• There are two modifications to the previous model.

– We will create a list of order quantities to test.

– Instead of entering a number in cell B9 (the Order Quantity), we will use the @RISK function RISKSIMTABLE( ).

MyWalton5.xls

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@Risk Simulation@Risk Simulation Walton Bookstore 5Walton Bookstore 5

Step 1: Identify Input Cell(s): (A13): =ROUND(RiskNormal(MeanDem,StdevDem),0)

Step 2: Build the Basic Model: (D9:L9): add 9 order quantities 100, 125, 150, …, 300

Step 3: Identify Output Cell(s): (E13): =B13-C13+D13

Click: =RiskOutput() + B13-C13+D13

Step 4: Instead of entering a number in cell B9, enter =RiskSimtable(OrderQuanList)Make sure cells D9:L9 are named OrderQuanList

Simulation - 32


Step 5: Specify the Simulation SettingsStep 5: Specify the Simulation Settings Walton Bookstore 5Walton Bookstore 5




9 Order Quantities

Simulation - 33


Step 6: Specify the Report SettingsStep 6: Specify the Report Settings Walton Bookstore 5Walton Bookstore 5




Selected Below.



Simulation - 34




Window” button.


Step 6: Step 6: Run the @Risk SimulationRun the @Risk Simulation Walton Bookstore 5Walton Bookstore 5

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Multiple Sources of UncertaintyMultiple Sources of UncertaintyWalton Bookstore 6Walton Bookstore 6

• As in previous examples, Walton needs to place an order for next year’s calendar. We continue to assume that the calendars will sell for $10 and customer demand for the calendars at this price is normally distributed with mean 168.1 and standard deviation 57.6. However, there are now two other sources of uncertainty.

• First, the maximum number of calendars Walton’s supplier can supply is uncertain and is modeled with a triangular distribution. It’s parameters are 125, 250, and 200. Once Walton places an order, the supplier will charge $7.50 per calendar if he can supply the entire Walton order. Otherwise, he will charge only $7.25 per calendar.

• Second, unsold calendars can no longer be returned to the supplier for a refund. Instead, Walton will put them on sale for $5 each after Feb 1. At that price, Walton believes the demand for leftover calendars is normally distributed with mean 50 and standard deviation 10. Any calendars still left over after March 1 will be thrown away.

• Walton plans to order 200 calendars and wants to use simulation to analyze the resulting profit.

MyWalton6.xls

Simulation - 36


Part 3:Part 3:@Risk Simulation Modeling

An Example

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Drug Production Model with Uncertain YieldsDrug Production Model with Uncertain YieldsTrying to Meet an Order Due Date at WozacTrying to Meet an Order Due Date at Wozac

• Wozac is a drug manufacturing company. It has recently accepted an order from its best customer for 8,000 ounces of a new miracle drug, and wants to plan its production schedule to meet the customer’s promised delivery date of December 1, 2000.

• There are three sources of uncertainty that make planning difficult.

Simulation - 38


• First, the drug must be produced in batches, and there is uncertainty about the time required to produce a batch, which could be anywhere from 5 to 11 days. This uncertainty is described by the discrete distribution of this table.

Sources of UncertaintySources of UncertaintyWozac Drug CompanyWozac Drug Company

Days56789

1011

Probability0.050.100.200.300.200.100.05

Distribution of Days to Complete a Batch

Simulation - 39


Sources of UncertaintySources of UncertaintyWozac Drug CompanyWozac Drug Company

ContinuedContinued

• Second, the yield (usable quantity) from any batch is uncertain. Based on historical data, Wozac believes the yield can be modeled by a triangular distribution with parameters 600, 1000, 1100.

• Third, all batches must go through a rigorous inspection once they are completed. The probability that a typical batch passes this inspection is only 0.8. Therefore, the probability is 0.2 that the batch fails inspection and none of it can be used to help fill the order.

Wozac wants to use simulation to help decide how many days prior to the due date it should begin production.

My Wozac Drugs.xls(Incomplete)

Wozac Drugs.xls(Complete)

Simulation - 40


Building the Basic ModelBuilding the Basic Model Wozac Drug CompanyWozac Drug Company

• Batch Index: Limit of 25 by trial & error. Big enough.• Days (for this batch):(B25:B48): =IF(OR(F24=“Yes”,F24=“”),” “,RiskDiscrete(Day, Probs))

THEN Leave blank which acts as 0Enough? = Yes or is blankIF

The formula means:

ELSE RiskDiscrete(Day, Probs))

• Batch Yield: (C25:C48): =IF(OR(F24=“Yes”,F24=“”),” “,RiskTriang($D$19,$E$19,$F$19))

• Pass Inspection? (D25:D48):=IF(OR(F24=“Yes”,F24=“”),” “,IF(Rand()<PrPass,”Yes”,”No”))

RiskDiscrete & RiskTriang are @Risk Distrib. functions

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Is the Order Filled?Is the Order Filled? Building the Basic ModelBuilding the Basic Model

• CumYield (cumulative usable product) (E25:E48):=IF(OR(F24=“Yes”,F24=“”),” “,IF(D25=“Yes”,C25+E24,E24))


ELSE IF this batch passedThen Add this batch to sumElse Use previous sum

• Enough? (Is the order filled) (F25:F48):=IF(OR(F24=“Yes”,F24=“”),” “,IF(E25>=AmtReqd,”Yes”,”Not yet”))


ELSE IF CumYield>= cell B5Then Yes the order is filledElse No, we must do next row

Col. E&F

Simulation - 42


Run Summary MeasuresRun Summary Measures Building the Basic ModelBuilding the Basic Model

• Batches required (I23): =COUNT(B24:B48)(count the cells that are not blank)

• Days to complete (I24): =SUM(B24:B48)(blanks count as 0)

• Day to start (I25): =DueDate-DaysReqd Cell formatted for Date Assumes 7 day production week

I23 & I24 are @Risk Output cells, but we’ll handle that later

Simulation - 43


@Risk Summary Measures@Risk Summary MeasuresWozac Drug CompanyWozac Drug Company

For 1,000 runs, we want @Risk to Report:

• Max batches reqd (I28): =RiskMax(I23)

• How long does it take? Avg days reqd (I30): =Int(RiskMean(DaysReqd)) Min days reqd (I31): =RiskMin(DaysReqd) Max days reqd (I32): =RiskMax(DaysReqd) 5th perc days reqd (I33): =RiskPercentile(DaysReqd,0.05)95th perc days reqd (I34): =RiskPercentile(DaysReqd,0.95)

RiskMax, RiskMean, etc., are @Risk Statistics functions

• Prob of meeting any given due date (I37) :=RiskTarget(DaysReqd,DueDate-H37)

Simulation - 44


Identify Output CellsIdentify Output Cells Wozac Drug CompanyWozac Drug Company

1. Select “Batches required”, cell I23

2. Click on the “Add Output” button.

3. Select “Days to complete”, cell I24

4. Click on the “Add Output” button.

=RiskOutput()+COUNT(B24:B48)

=RiskOutput()+ SUM(B24:B48)

Simulation - 45


Specify the Simulation SettingsSpecify the Simulation Settings Wozac Drug CompanyWozac Drug Company




Simulation - 46


Specify the Report SettingsSpecify the Report Settings Wozac Drug CompanyWozac Drug Company




Selected Below.



Simulation - 47




Window” button.


Run the @Risk SimulationRun the @Risk Simulation Wozac Drug CompanyWozac Drug Company

Simulation - 48


Part 4:Part 4: Using TopRank with @Risk

for Powerful Modeling

Simulation - 49


New Product DevelopmentNew Product DevelopmentAt SIMTEXAt SIMTEX

• SimTex, a pharmaceutical company, is in the early stages of developing a new drug called Biathnon. As with most new drugs, the future of Biathnon is highly uncertain. For example, its introduction into the market could be delayed, pending tests by the FDA. Also, its market could be diminished by a potential rival product from SimTex’s competition.

• SimTex has identified a number of key inputs that will affect Biathnon’s future profitability:

Simulation - 50


Key Inputs Affecting ProfitabilityKey Inputs Affecting Profitability SIMTEX Product DevelopmentSIMTEX Product Development

1. Number of years after product is developed until it is produced (due to potential FDA delays).

2. Number of years for which the product sells.

3. Initial cost incurred in developing the product.

4. Salvage value obtained from equipment after production of the product has been discontinued.

5. Fixed production cost incurred during years in which the product is manufactured.

6. Unit cost of producing the product.

7. Unit price for the product.

8. Initial demand for the product during first year it is sold.

9. Annual percentage growth in demand for the product.

10.Percentage of demand for the product that is lost to the competition.

11.Discount rate used to discount cash flows from the product.

Simulation - 51


Key QuestionsKey Questions SIMTEX Product DevelopmentSIMTEX Product Development

• How do changes in the inputs affect the key output, the Net Present Value of Biathnon over its lifetime?

• Which inputs have a major affect on the Net Present Value of Biathnon over its lifetime?

• How can SimTex use TopRank and @Risk to analyze this problem?

SimTex1.xls

Simulation - 52


Understanding SIMTEX1:Understanding SIMTEX1: Cell B29 Cell B29

THEN “Yes” = Product IS being Produced this year

Year No. > Delay and <= Delay + LifeIF

The formula means:

ELSE “No” = Product is NOT being Produced this year

B29=IF(AND(B27>Delay,B27<=(Delay+Life)), “Yes”,”No”)

(Last Prod Yr)B13 B13+B14

The Key to understanding SIMTEX1 is the TIMING in Row 29

Simulation - 53


Financial Formulas (C30:C36)Financial Formulas (C30:C36) Understanding SIMTEX1Understanding SIMTEX1

C30: Fixed Cost=IF(C29=“Yes”, FixCost,0) If this is a production Year

Then Fixed cost (B17) is incurredElse Fixed Cost = 0

C31: Total Demand

=IF(AND(B29=“No”, C29=“Yes”),

If Last year was not a prod. year (B29=“No”)AND This year is a production Year (C29=“Yes”) Then this is 1st Prod year and Total Demand = InitDem (B20)

InitDem,

IF(C29=“Yes”, Else If this is a production Year (C29=“Yes”) (It cannot be the initial prod. year)

B31*(1+DemGrowth), Then Total Demand (C31) = Last years demand (B31) times 1 + DemGrowth (B21)

0)) Else this is not a prod yearAnd Total Demand = 0

Simulation - 54


Financial Formulas Financial Formulas (continued)(continued)C32: SimTex’s Demand=IF(C31=0,0, C31*(1-PctDemLost))

If Total Demand = 0, Then SimTex’s Demand =0Else SimTex’s Demand = Total Demand less part lost to competition

C33: Variable Cost=IF(C32=0,0, C31*(1-PctDemLost))

If SimTex’s Demand = 0, Then Variable Cost =0Else Var. Cost = SimTex’s Demand * Unit Cost (B18)

C34: Revenue=IF(C32=0,0, C31*(1-PctDemLost))

If SimTex’s Demand = 0, Then Revenue =0Else Revenue = SimTex’s Demand * Unit Price (B19)

C35: Salvage Value=IF(AND(C29=“Yes”,D29=“No”), If This is prod. yr & next yr is not

Then salvage val. incurred SalvVal,0) Else no salvage val. incurred

C36: Net Profit =-C28-C30-C33+C34+C35

Simulation - 55


Calculate the Net Present Calculate the Net Present ValueValue

B38=NPV(DiscRate,C36:AF36)+B36

B38=NPV(DiscRate,Profits)+B36

Profits = C36:AF36Where

Or

Simulation - 56


Evaluating ProfitabilityEvaluating Profitability SIMTEX Product DevelopmentSIMTEX Product Development

Now that the model is developed we can:

• Use trial and error to see how the NPV reacts to changes in the inputs.

• Use data tables to see how the NPV reacts to changes in the inputs.

• However, TopRank does this easily.

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Evaluating UncertaintyEvaluating Uncertainty SIMTEX Product DevelopmentSIMTEX Product Development

• Change the input section to reflect uncertainty

SimTex2.xls

Simulation - 58


TopRank’s RISKVARY functionTopRank’s RISKVARY function

Modify the range B13:B23 to use:=RISKVARY(Expected value, low range, high range,

Range type, #Steps)where :

Expected value is the base case Low range is the smallest possible value for the input

High range is the largest possible value for the inputRange type is 0,1, or 2 and determines the way minimum and maximum should be entered#Steps is the number of values from minimum to maximum to use for this input

=RiskVary(D13,C13*D13,E13*D13,2,8)For B13:

Simulation - 59


Using TopRankUsing TopRankTo use TopRank, we proceed in three steps

very much like in @Risk:

1. use the Change Settings button

2. use the Add Output Cells button to select one or more output cells

3. use the Run What-if Analysis button to perform the calculations.

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Using TopRank: Step 1Using TopRank: Step 1Avoid Lot’s of Results You Probably Avoid Lot’s of Results You Probably

Don’t WantDon’t Want

2. Click on the Input ID tab

1. Click on the Change Settings button

Then UNCHECK the “Automatically Insert AutoVary Functions” box.

3. Click on OK

Simulation - 61


Using TopRank: Step 2Using TopRank: Step 2Identify Output CellsIdentify Output Cells

1. Select the NPV cell (B38)

2. Click on the “Add Output Cells” button.

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Using TopRank: Step 3Using TopRank: Step 3Run the ProgramRun the Program

Finally, run the analysis by clicking on the “Run What-if Analysis” button.

TopRank then varies each input cell from its minimum to maximum, using the number of steps you specified and keeping the other inputs at their base levels, and

keeps track of all the NPVs.

Simulation - 63


Tornado ChartsTornado Charts Interpreting TopRank ResultsInterpreting TopRank Results

• Perhaps the best way to understand TopRank results is with a tornado chart.

• To create a tornado chart:

1. Click on the Graph button in the TopRank screen.

2. Choose: tornado

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@Risk Simulation@Risk Simulation SIMTEX Product DevelopmentSIMTEX Product Development

• We will run an @Risk simulation to estimate the distribution of NPV earned by Biathnon.

• We will keep all inputs other than the five key inputs fixed at their base values.

• We will use a triangular distribution for each of the random inputs: product lifetime, unit price, unit cost and initial demand

• We will vary the discount rate systematically with the RISKSIMTABLE function.

Simulation - 65


Modify the TopRank ModelModify the TopRank Model @Risk Sim -@Risk Sim - SIMTEX Prod. Dev.SIMTEX Prod. Dev.

• Adjust the data for the five key Inputs

• Enter the @Risk formulas in random input cells. B14 is:=RiskTriang(E14,F14,G14)

• In cell B23 use the RISKSIMTABLE function: =RiskSimTable(DiscRateList)

• Select cell B38. Designate it the @Risk Output cell by clicking the “Add Output Cell” button.

SimTex3.xls

Simulation - 66


Specify the Simulation SettingsSpecify the Simulation Settings @Risk Sim -@Risk Sim - SIMTEX Prod. Dev.SIMTEX Prod. Dev.




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Specify the Report SettingsSpecify the Report Settings @Risk Sim -@Risk Sim - SIMTEX Prod. Dev.SIMTEX Prod. Dev.




Selected Below.



Simulation - 68




Window” button.


Run the @Risk SimulationRun the @Risk Simulation SIMTEX Product DevelopmentSIMTEX Product Development

Simulation - 69


• View the “Detailed Statistics Window”

• Select and copy the mean and standard deviations for the four simulations.

• Paste it into range B42:E43

• In cell B46 enter formula: =B42-1.96*B43/SQRT(500)

To Complete the WorksheetTo Complete the Worksheet SIMTEX Product DevelopmentSIMTEX Product Development

simulation - 1 us army logistics management college part 1: simulation modeling w/ built in excel...

Documents

b9 slide

inputs walton bookstore

stdevprofitsqrt1000

results walton bookstore

excel tools slide

twoway data table

simulation modeling

g1018 profits slide