1. Part 1: Simulation Modeling
w/ Built in Excel Tools

2. Walton 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.
Calendars
Demanded
100
150
200
250
300
Probability
0.30
0.20
0.15
0.05
MyWalton1.xls
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.

3. Step 1: Identify Inputs Walton 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):
(D6:D9): =D5+F5
Random # (B19): =Rand() Excel Math&Trig function
Demand (C19): =VLOOKUP(B19,Lookup,2)
Excel Lookup&Reference function

4. Step 2: Build Basic Model Logic 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”

5. Step 3: Create Summary Statistics Walton 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)

6. Step 4: Determine the “Best” Order Quantity One-Way Data Table Method Walton Bookstore 1
Identify Table Output (B1022):
=AvgProfit
Select range (A1022:B1031)
Select: Data + What If Analysis + DataTable
Set the Column Input cell to B9

7. Step 5: Graph the Results Walton 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)

8. Two-Way Data Table Method Walton3.xls
Note the change in the basic model.
MyWalton3.xls
Demand (A19): =VLOOKUP(RAND(),Lookup,2).

9. Create the Two-Way Data Table Walton3.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.

10. Part 2: Intro to
Simulation Modeling

11. Walton Bookstore Revisited Walton4.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 to simulate the profit for any particular order quantity.
Walton eventually wants to find the “best” order quantity.
MyWalton4.xls

12. Solution Approach Walton Bookstore 4
Use BestFit to identify demand probability distribution.
to Simulate 1000 runs for each potential order quantity.
RiskSimTable function to determine the “best” order quantity.
(does the work of the Data Table)

13. Opening an Existing @Risk File
for Excel
Open the file: MyWalton4.xls
Use File + Save As to save this file under a different name (such as Class MyWalton 4)

14. Fitting 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 fitting ability.

15. 3. Copy and Paste Data into the FitTab Fitting a Probability Distribution
Click on the “Show Excel Window” button
Select the range A7:A121.
Click on the copy button.
Click on the window” button.
Select Edit + Paste from the Menu Bar

16. 4. Select Candidate Distributions Fitting 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 .

17. 5. Do the Fitting Fitting 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

18. Solution Approach Walton Bookstore 4
Use BestFit to identify demand probability distribution.
to Simulate 1000 runs for each potential order quantity.
RiskSimTable function to determine the “best” order quantity.
(does the work of the Data Table)

19. Step 1: Identify the Input Cell(s) Creating the @Risk Simulation Model
Enter the values for the mean and standard deviation estimated by BestFit!
Mean = in cells E4
StDev = 57.6 in cells E5.
In cell A13, use
Distribution function
RiskNormal within the
Excel Math & Trig function
ROUND to enter
the formula:
=Round(RiskNormal
(MeanDem,StdevDem).

20. Step 2: Build the Basic Model Creating the @Risk Simulation Model
Revenue (B13):
=UnitPrice*MIN(OrderQuan,Demand).
Cost (C13):
=OrderQuan*UnitCost
Refund (D13):
=UnitRefund*MAX(OrderQuan-Demand,0)
Still the Hardest Part
and the Heart of Simulation

21. Step 3: Identify the Output Cell(s) Creating the @Risk Simulation Model
In cell E13 enter the formula for Profit:
=B13+D13-C13
Designate cell E13 as output cell by clicking on the
the Add Output Cell button on 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.

22. Step 4: Create Summary Statistics on the Output Cell(s) Creating the @Risk Simulation Model
In cell B16, use the @RISK Statistics function: =RiskMin(Profit)
In cell B17, enter:
=RiskMax(Profit)
In cell B18, enter:
=RiskMean(Profit)
In cell B19, enter:
=RiskStdDev(Profit)

23. Step 5: Specify the Simulation Settings Creating 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 .

24. Step 6: Specify the Report Settings Creating the @Risk Simulation Model
Click on the “Report Settings” button.
For At the End of Simulation:
Check Show
Results Window.
Check Generate Excel Reports
Selected Below.
For Excel Reports:
Check Simulation Summary .
Check Detailed Statistics.
Check Active Workbook.

25. Step 6: Run the @Risk Simulation Creating the @Risk Simulation Model
To run the simulation, Click on the “Start Simulation” button.
In Results window
To see Summary Statistics, use the “Summary Statistics Window” button.
To see Detailed Statistics, use the “Detailed Statistics Window” button.

26. Analyzing the Output Walton Bookstore 4
@Risk generates a large number of output measures.
Summary Report. Assuming that the top box was checked in Reports dialog box, we are immediately transferred to Results window. This window contains the summary results shown here.

27. Detailed Statistics Analyzing the Output
All of the information in the Summary Report is here, plus some.

28. Charts Analyzing the Output
To create a histogram of the 1,000 profits:
In the left pane of the Results window, click on Profits
From the menu bar select: Insert+Graph+Histogram
Note the 27.4% chance of losing money

29. Solution Approach Walton Bookstore
Use BestFit to identify demand probability distribution.
to Simulate 1000 runs for each potential order quantity.
RiskSimTable function to determine the “best” order quantity.
(does the work of the Data Table)

30. Using RISKSIMTABLE Walton 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 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 function RISKSIMTABLE( ).
MyWalton5.xls

31. @Risk Simulation Walton 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

32. Step 5: Specify the Simulation Settings Walton Bookstore 5
Click on the “Simulations Settings” button.
Click on the “Iterations” tab in the Simulation Settings dialog box.
Set # Iterations to 1000.
Set # Simulations to 9.
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 .
9 Order Quantities

33. Step 6: Specify the Report Settings Walton Bookstore 5
Click on the “Report Settings” button.
For At the End of Simulation:
Check Show
Results Window.
Check Generate Excel Reports
Selected Below.
For Excel Reports:
Check Simulation Summary .
Check Detailed Statistics.
Check Active Workbook.

34. Step 6: Run the @Risk Simulation Walton Bookstore 5
To run the simulation, Click on the “Start Simulation” button.
In Results window
To see Summary Statistics, use the “Summary Statistics Window” button.
To see Detailed Statistics, use the “Detailed Statistics Window” button.

35. Multiple Sources of Uncertainty Walton 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 and standard deviation 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 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

36. @Risk Simulation Modeling
Part 3:
@Risk Simulation Modeling
An Example

37. Drug Production Model with Uncertain Yields Trying 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.

38. Sources of Uncertainty Wozac Drug Company
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.
Days 5 6 7 8 9 10 11
Probability
0.05
0.10
0.20
0.30
Distribution of Days to Complete a Batch

39. Sources of Uncertainty Wozac Drug Company Continued
My Wozac Drugs.xls
(Incomplete)
Wozac Drugs.xls
(Complete)
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.

40. Building the Basic Model Wozac 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 0
Enough? = Yes or is blank IF
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 Distrib. functions

41. Is the Order Filled? Building the Basic Model
Col. E&F
CumYield (cumulative usable product) (E25:E48):
=IF(OR(F24=“Yes”,F24=“”),” “,IF(D25=“Yes”,C25+E24,E24))
THEN
Leave blank which acts as 0
Enough? = Yes or is blank IF
ELSE
IF this batch passed
Then Add this batch to sum
Else Use previous sum
Enough? (Is the order filled) (F25:F48):
=IF(OR(F24=“Yes”,F24=“”),” “,IF(E25>=AmtReqd,”Yes”,”Not yet”)) IF
Enough? = Yes or is blank
THEN
Leave blank which acts as 0
ELSE
IF CumYield>= cell B5
Then Yes the order is filled
Else No, we must do next row

42. Run Summary Measures Building 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 Output cells,
but we’ll handle that later

43. @Risk Summary Measures Wozac Drug Company
For 1,000 runs, we 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)
Prob of meeting any given due date (I37) :
=RiskTarget(DaysReqd,DueDate-H37)
RiskMax, RiskMean, etc., Statistics functions

44. Identify Output Cells Wozac Drug Company
Select “Batches required”, cell I23
Click on the “Add Output” button.
=RiskOutput()+COUNT(B24:B48)
Select “Days to complete”, cell I24
Click on the “Add Output” button.
=RiskOutput()+ SUM(B24:B48)

45. Specify the Simulation Settings Wozac Drug Company
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 .

46. Specify the Report Settings Wozac Drug Company
Click on the “Report Settings” button.
For At the End of Simulation:
Check Show
Results Window.
Check Generate Excel Reports
Selected Below.
For Excel Reports:
Check Simulation Summary .
Check Detailed Statistics.
Check Active Workbook.

47. Run the @Risk Simulation Wozac Drug Company
To run the simulation, Click on the “Start Simulation” button.
In Results window
To see Summary Statistics, use the “Summary Statistics Window” button.
To see Detailed Statistics, use the “Detailed Statistics Window” button.

48. Using TopRank with @Risk for Powerful Modeling
Part 4:
Using TopRank for Powerful Modeling

49. New Product Development At 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:

50. Key Inputs Affecting Profitability SIMTEX Product Development
Number of years after product is developed until it is produced (due to potential FDA delays).
Number of years for which the product sells.
Initial cost incurred in developing the product.
Salvage value obtained from equipment after production of the product has been discontinued.
Fixed production cost incurred during years in which the product is manufactured.
Unit cost of producing the product.
Unit price for the product.
Initial demand for the product during first year it is sold.
Annual percentage growth in demand for the product.
Percentage of demand for the product that is lost to the competition.
Discount rate used to discount cash flows from the product.

51. Key Questions SIMTEX 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 to analyze this problem?
SimTex1.xls

52. Understanding SIMTEX1: Cell B29
The Key to understanding SIMTEX1 is the TIMING in Row 29
(Last Prod Yr)
B13
B13+B14
B29=IF(AND(B27>Delay,B27<=(Delay+Life)), “Yes”,”No”)
Year No. > Delay and <= Delay + Life IF
The formula means:
THEN
“Yes” = Product IS being Produced this year
ELSE
“No” = Product is NOT being Produced this year

53. Financial Formulas (C30:C36) Understanding SIMTEX1
C30: Fixed Cost
=IF(C29=“Yes”, FixCost,0)
If this is a production Year
Then Fixed cost (B17) is incurred
Else 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 year
And Total Demand = 0

54. Financial Formulas (continued)
C32: SimTex’s Demand
=IF(C31=0,0,
C31*(1-PctDemLost))
If Total Demand = 0, Then SimTex’s Demand =0
Else 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 =0
Else Var. Cost = SimTex’s Demand
* Unit Cost (B18)
C34: Revenue
=IF(C32=0,0,
C31*(1-PctDemLost))
If SimTex’s Demand = 0, Then Revenue =0
Else 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

55. Calculate the Net Present Value
B38=NPV(DiscRate,C36:AF36)+B36 Or
B38=NPV(DiscRate,Profits)+B36
Where
Profits = C36:AF36

56. Evaluating Profitability SIMTEX 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.

57. Evaluating Uncertainty SIMTEX Product Development
Change the input section to reflect uncertainty
SimTex2.xls

58. TopRank’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 input
Range 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:

59. Using TopRank
To use TopRank, we proceed in three steps very much like
use the Change Settings button
use the Add Output Cells button to select one or more output cells
use the Run What-if Analysis button to perform the calculations.

60. Using TopRank: Step 1 Avoid Lot’s of Results You Probably Don’t Want
Click on the Change Settings button
Click on the Input ID tab
Then UNCHECK the “Automatically Insert AutoVary Functions” box.
Click on OK

61. Using TopRank: Step 2 Identify Output Cells
Select the NPV cell (B38)
Click on the “Add Output Cells” button.

62. Using TopRank: Step 3 Run 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.

63. Tornado Charts Interpreting TopRank Results
Perhaps the best way to understand TopRank results is with a tornado chart.
To create a tornado chart:
Click on the Graph button in the TopRank screen.
Choose: tornado

64. @Risk Simulation SIMTEX Product Development
We will run 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.

65. Modify the TopRank Model @Risk Sim - SIMTEX Prod. Dev.
Adjust the data for the five key Inputs
SimTex3.xls
Enter 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 Output cell by clicking the “Add Output Cell” button.

66. Specify the Simulation Settings @Risk Sim - SIMTEX Prod. Dev.
Click on the “Simulations Settings” button.
Click on the “Iterations” tab in the Simulation Settings dialog box.
Set # Iterations to 500.
Set # Simulations to 4.
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 .

67. Specify the Report Settings @Risk Sim - SIMTEX Prod. Dev.
Click on the “Report Settings” button.
For At the End of Simulation:
Check Show
Results Window.
Check Generate Excel Reports
Selected Below.
For Excel Reports:
Check Simulation Summary .
Check Detailed Statistics.
Check Active Workbook.

68. Run the @Risk Simulation SIMTEX Product Development
To run the simulation, Click on the “Start Simulation” button.
In Results window
To see Summary Statistics, use the “Summary Statistics Window” button.
To see Detailed Statistics, use the “Detailed Statistics Window” button.

69. To Complete the Worksheet SIMTEX Product Development
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: =B *B43/SQRT(500)