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Session 7 Managerial Spreadsheet Modeling -- Prof. Juran1

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2 Outline Sensitivity Analysis Some fancy Excel functions and graphs

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Managerial Spreadsheet Modeling -- Prof. Juran3 Often our analysis depends on some number whose value is uncertain. –Inflation rate = 3%? Cost of lost goodwill = ? What if we aren’t able to reasonably defend our assumption? –SWAG (Simple Wild Guess) –Stratospheric Citation How critical is the accuracy of the estimated parameter to the business decision under consideration? –How much would our performance measure change? Would our decision change if we were off by 1%? By 10%? Or wouldn’t it matter? –Which estimates do we really need to pin down? E.g., for which parameters should we, as managers, devote additional time to estimate more precisely? Sensitivity Analysis

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Managerial Spreadsheet Modeling -- Prof. Juran4 Base Case: Your initial (best-guess) estimate Now estimate endpoints for a (non-statistical) confidence interval for your parameter. –Low & High / Pessimistic & Optimistic / Worst & Best Case estimates –What do you mean by “Best Case,” exactly? o What’s your Best Case for this evening? o What’s the worst that could have happened to British Petroleum? o However you define it, be consistent. o People generally are overconfident in their forecasting abilities, and make prediction intervals too small. Getting More Information

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Managerial Spreadsheet Modeling -- Prof. Juran5 Set all of the parameters to their worst (or best) case values. –But how representative are these results? Fit a probability distribution to the three (high / low / most likely) estimates Use Monte Carlo simulation to generate a distribution for the performance measures you’re interested in. Characterizing the Effects of Uncertainties

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Managerial Spreadsheet Modeling -- Prof. Juran6 One-at-a-time changes. –Set one parameter to its low and high values, respectively. –Keep all other parameters at the base case values. –Track the changes in the performance measure. Tornado Graph: Horizontal bar chart –Horizontal axis: performance measure –Vertical axis: Uncertain estimators –Sorted by magnitude of the effect (largest at the top) –Cross axis at base case value Characterizing the Effects of Uncertainties

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Managerial Spreadsheet Modeling -- Prof. Juran7 Base unit sales of kids’ breakfast cereal: 6,500,000 over the next two months Contribution margin: $1.48 / box Possible promotion: Add a trinket –Costs $0.10 –Will increase sales by 12% –Artwork cost of $125,000 Should we add the trinket or not? Example: Cereal Trinket

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Managerial Spreadsheet Modeling -- Prof. Juran8 Initial Calculations

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Managerial Spreadsheet Modeling -- Prof. Juran9 Base volume forecast could by off by ± 2%. Trinket cost could increase by $0.015 if our supplier can’t recover from his fire in time. It’s very difficult to forecast sales response to breakfast cereal: It could be anywhere between 8% and 14%. Artwork costs could be 5% lower, or 20% higher, than our initial estimate. Uncertainty?

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Managerial Spreadsheet Modeling -- Prof. Juran10 At this point we are able to calculate all the numbers that we’ll need: –Worst case: Set all 4 numbers to their “Pessimistic” values. (Similarly with the Best case.) –Tornado graph: Keeping the other three numbers at their base case values, set each of the four estimates to its pessimistic and optimistic values in turn. Pretty tedious, although straightforward. –We could just Copy, and Home | Paste | Paste Values for the Incremental Contribution ( H36 ) in each of the 4×2 cases. Sensitivity Analysis

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Managerial Spreadsheet Modeling -- Prof. Juran11 Index() function for easier changes Data tables: Automated “plug and chug” A couple of advanced Excel functions: Rank(), Match() Advanced chart features Admittedly “overkill” for a problem this small. Application of Advanced Excel

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Managerial Spreadsheet Modeling -- Prof. Juran12 Part 1: The Tornado Graph

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Managerial Spreadsheet Modeling -- Prof. Juran13 Easy case: Pessimistic (and Optimistic) values are all positive: –Series 1: Pessimistic –Series 2: Optimistic – Pessimistic –Turn Series 1 invisible –Don’t delete it! –Set Fill to No Fill and Border Color to No Line Another easy case: All values are negative: –Series 1: Optimistic –Series 2: Pessimistic – Optimistic –Turn Series 1 invisible Stacked Bar Chart

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Managerial Spreadsheet Modeling -- Prof. Juran14 More generally, if the base value is positive but at least some pessimistic values are negative: –Series 1: min{Pessimistic, 0} –Series 2: max{Pessimistic, 0} ← and turn invisible –Series 3: Optimistic – Series 2 If the base value is negative but at lease some optimistic values are positive: –Series 1: max{Optimistic, 0} –Series 2: min{Optimistic, 0} ← and turn invisible –Series 3: Pessimistic – Series 2 Stacked Bar Chart

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Managerial Spreadsheet Modeling -- Prof. Juran15 Each of the four parameters needs to be set to its pessimistic and optimistic parameter values, while keeping the other three at their base values. Wouldn’t it be great if there were some way to automatically plug in all 4×2 different combinations of numbers, and record the incremental contribution for each combination? –Need to specify which parameter (1 – 4) is being changed. –Need to specify what value (2 or 3) it is being changed to. More generally, wouldn’t it be great if there were some way to automatically “plug and chug” different values for an input parameter (or two) and record the output performance in a table? Building the Tornado Graph

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Managerial Spreadsheet Modeling -- Prof. Juran16 Open and look at the range T16:V21. Notice that the three columns T, U, and V are in this form: Series 1 (column T): min{Pessimistic, 0} Series 2 (column U): max{Pessimistic, 0} Series 3 (column V): Optimistic – Series 2 Create a stacked bar chart using those three columns. Depending on your version of Excel, you may need to Switch Row/Column. Your chart should look like this:

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Managerial Spreadsheet Modeling -- Prof. Juran17 Eliminate legend, gridlines Right-Click | Format Axis (Vertical) Axis option | Categories in reverse order Axis option | Horizontal axis crosses at maximum category Axis option | Major tick mark type: None Axis option | Axis labels: High Line style | Width: 1.5 pt Line style | Dash type: Font size: 12 pt Right-Click | Format Axis (Horizontal) Axis options | Maximum Fixed Vertical axis crosses: Axis value: 301,400 Font size: 12 pt Number format: $???,??0; [Red]($???,??0)

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Managerial Spreadsheet Modeling -- Prof. Juran18 Make the middle data series invisible Format Data Series | Fill No fill Format Data Series | Border color No line Format the other two series Format Data Series | Series Options | Gap Width = 50% Format Data Series | Fill | Gradient Type = Linear; Angle = 90° Stop 1 (0%) and Stop 3 (100%): Same dark tone Stop 2 (50%): Light tone

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Managerial Spreadsheet Modeling -- Prof. Juran19 Volume Increase assumption has the biggest potential effect Widest range, and could lead to a negative outcome Decision maker would be wise to invest time and effort into refining this specific input value

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Managerial Spreadsheet Modeling -- Prof. Juran20 Part 2a: INDEX and OFFSET 1. OFFSET for the assumption labels 2. INDEX for optimistic and pessimistic 3. Formulas to create the series for the graph

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Managerial Spreadsheet Modeling -- Prof. Juran21 For the labels, use OFFSET: N18=OFFSET($D$11,V7,0) And copy down to rows 19:21. Looks to see what is 2 rows down and 0 columns to the right of D11 (because V7 is a 2) There’s nothing in D11; it’s just a reference point for the OFFSET

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Managerial Spreadsheet Modeling -- Prof. Juran22 Use INDEX to get the pessimistic and optimistic numbers: R18= INDEX(R$7:R$10, $V7) S18= INDEX(S$7:S$10, $V7) And copy down

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Managerial Spreadsheet Modeling -- Prof. Juran23 Now use these formulas to create the three series. T18= MIN(R18, 0) U18= MAX(R18, 0) V18= S18 - U18 And copy down

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Managerial Spreadsheet Modeling -- Prof. Juran24 Part 2b: IF New template file: Built-in DataTable in Q6:S10 -- leave that range alone

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Managerial Spreadsheet Modeling -- Prof. Juran25 J12 = IF($J$17 = C12, $J$18, 1) and copy down to rows 13:15. Keeps all assumptions at their “base case” value by default Allows one assumption to be optimistic or pessimistic

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Managerial Spreadsheet Modeling -- Prof. Juran26 Note INDEX used in the table below. The four assumptions are linked to J12:J15, which are controlled by J17:J18. Try different combinations for J17:J18 and watch what happens in cell H36.

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Managerial Spreadsheet Modeling -- Prof. Juran27 Notice that the DataTable in Q6:S10 contains all of the combinations.

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Managerial Spreadsheet Modeling -- Prof. Juran28 Part 2c: DataTable New template file:

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Managerial Spreadsheet Modeling -- Prof. Juran29 Automated “plug and chug.” More generally, a slick way to automatically check the consequences of adjusting one or two input parameters. Data Tables: Enumerate, Don’t Optimize key output(s) key input parameters (1 or 2)

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Managerial Spreadsheet Modeling -- Prof. Juran30 Components of data tables –List(s) of values –Cell(s) which will assume these values –Performance measure to be tracked Two-input data table –Two input parameters change at once –Only one performance measure can be tracked One-input data table –Only one input parameter changes –Any number of performance measures can be tracked Data Tables

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Managerial Spreadsheet Modeling -- Prof. Juran31 Only one parameter to enumerate, but multiple performance measure recorded for each value. Tip: Make the performance measurement cells invisible across the top. Double secret tip: Use custom number formatting to replace these values with their labels. One-way Data Table Values for the Column input cell Formulas for multiple outputs Not used

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Managerial Spreadsheet Modeling -- Prof. Juran32 Start by building a table containing the values for the two variables you want to enumerate, across the top and down the left. Put the equation for the (one) performance measure in the top left corner. Two-way Data Table Values for the Column input cell Values for the Row input cell Formula for one output

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Managerial Spreadsheet Modeling -- Prof. Juran33 Q6=H36 Type Scenario numbers 2 and 3 in R6:S6. Type Parameter numbers 1, 2, 3, 4 in Q7:Q10 Now select the range Q6:S10, and select Data | What If Analysis | DataTable Fill in the dialog box as shown:

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Managerial Spreadsheet Modeling -- Prof. Juran34 Two-way Data Table

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Managerial Spreadsheet Modeling -- Prof. Juran35 Automatic Sorting T7 = S7 – R7 U7 = Rank(T7, $T$7:$T$10) U8 = Rank(T8, $T$7:$T$10) + CountIf($T$7:T7, T8 ) (Breaks ties in the rankings, otherwise use the formula for U7.) V7 = Match(Q7, $U$7:$U$10, 0) The #3 ranked parameter is in the 4 th row Parameter 1 is ranked #4

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Managerial Spreadsheet Modeling -- Prof. Juran36 The DataTable lists all $ contributions that would result from each assumption taking on its optimistic and pessimistic values – holding the other assumptions at base case values, which we then use to generate the data for the tornado graph.

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Managerial Spreadsheet Modeling -- Prof. Juran37 Sensitivity analysis (and tornado graphs) indicate which variables generate the largest effect on the performance measure. –Useful after prototyping, to see where to invest to get more accurate data. –Useful before Monte Carlo simulation. Some advanced Excel tools –The incredibly useful Index() function –Data tables –Rank() and Match() functions to automate sorting –Advanced chart settings Take-aways

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Managerial Spreadsheet Modeling -- Prof. Juran38 Index(array, num) –Returns the num item in a one-dimensional array –The array can be either horizontal or vertical. Index(range, row_num, col_num) –Returns the value from a two-dimension range. Appendix: The Index Function

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Managerial Spreadsheet Modeling -- Prof. Juran39 The Index Function: Example C3 = "Scenario: " & Index(C10:C12, B3)

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