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                      DSS News
               D. J. Power, Editor
          July 30, 2006 -- Vol. 7, No. 16

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   "Decision Support for Global Enterprises" Conference
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Featured:

* Ask Dan! - How does sensitivity analysis differ from 
  "What If?" analysis?
* Dan Power Travel Plans
* What's New at DSSResources.COM
* DSS Conferences
* DSS News Releases 

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        Check the interview with Rob Armstrong 
"Driving usage versus gaining value from a data warehouse" 
               at DSSResources.com

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Ask Dan!

How does sensitivity analysis differ from "What If?" analysis?

by Dan Power
Editor, DSSResources.COM

In the early days of decision support systems, one of the major 
DSS "selling points" of vendors and academics was the
ability to do "What If?" analysis. In the 1970s, model-driven 
DSS for sales and production planning allowed a manager to 
change a decision variable like the number of units to produce 
and then immediately get a new result for an outcome variable 
like profit. As DSS have gotten more sophisticated and become 
more diverse, the use of "What If?" as a concept has broadened.  
We have also introduced more precise terminology from the 
mathematical modeling literature into our discussions like 
sensitivity analysis.

In most DSS, sensitivity and "What If?" analysis refer to quantitative 
analyses, the decision making and planning literature discusses 
"What-if analysis" as a qualitative, brainstorming approach that 
"uses broad, loosely structured questioning to investigate 
contingencies." In the context of business intelligence and 
data-driven DSS, "What If?" is a descriptor for ad hoc queries 
of a decision support data base. 

According to Applix.com, planners use models to address "What If" 
questions such as: 1) What profits can we anticipate next 
year if inflation is 7 percent and we continue current pricing 
policies? 2) If we open a new plant, what profits can we expect? 
3) What if we were to hire 55 people in Sales, 10 in Marketing 
and 35 in R&D? 4) What is the impact on manufacturing and shipping 
if the price of oil increases 15% during Q2? and 5) What would 
be needed for raw material and inventory if the demand of a 
product went up 20%?

In the DSS literature and in common discourse, we don't have 
agreement about the difference between "What If?" analysis and 
sensitivity analysis. The Microsoft Excel 2002 help document 
defines "What-if analysis" as a "process of changing the values 
in cells to see how those changes affect the outcome  of formulas 
on the worksheet. For example, varying the interest rate that is 
used in an amortization table to determine the amount of the 
payments." Four tools in Excel are commonly categorized as "What If?" 
or sensitivity analysis (Winston, 2004) tools: Data Tables, Goal 
Seek, Scenarios, and Solver. The simplest type of "What If?" 
analysis is manually changing a value in a cell that is used in 
a formula to see the result. Excel experts seem to use the terms 
sensitivity and "What If?" analysis interchangeably.

To get a better understanding of what is possible, let's briefly 
examine how one would implement "What If?" or sensitivity analysis 
using MS Excel tools. First, a data table is a range of cells that 
summarizes the results of changing certain values in formulas in 
a model. There are two types of data tables: one input variable 
tables and two input variable tables. "Two-variable data tables 
use only one formula with two lists of input values. The formula 
must refer to two different input cells." In Microsoft's Mortgage 
Loan Analysis example, a two-variable data table would show how 
different interest rates and loan terms would affect the mortgage 
payment amount. The table shows the decision maker how sensitive 
the payment amount is to the interest rate. The Goal Seek tool 
is helpful when you know the desired result from a model and want 
to find the appropriate input or decision variable levels. "What 
If?" involves incrementally changing an input until the goal is 
reached.  Goal Seek automates this trial and error process. Scenarios 
let an Excel user construct strategies where multiple decision 
variables are changed in each scenario.  For example, a decision 
maker may have best case, most likely, and worst case scenarios. 
Finally, Solver is an optimization tool that includes a sensitivity 
analysis capability. Monte Carlo simulation in Excel can also be 
used to assist in "What If?" or sensitivity analysis.  Spreadsheets 
models with probability distributions for inputs can simulate 
outcomes for a range of input parameters. 

According to Parnell (1997), "a decision variable is a variable 
over which the decision maker has control and wishes to 
select a level, whereas a strategy refers to a set of values for 
all the decision variables of a model. An optimal strategy 
is the strategy which maximises the value of the decision maker's 
objective function (e.g. profit, social welfare, expected 
utility)." In general, mathematical methods assess the sensitivity 
of a model's output to the range of variation of one or 
more inputs.  Sensitivity analysis is used to determine what inputs, 
parameters or decision variables contribute more to the 
variance in the output of a model and hence are the most important
and most "sensitive".

Let's check some definitions from Web sites. Wikipedia (wikipedia.org) 
notes "What-if analysis of a model considers the question: 'What 
happens to the result if we make a particular change to a parameter?'. 
If the change of a parameter is small this is also called sensitivity 
analysis: 'How sensitive is the result to a small change of a parameter?' 
Wikipedia also defines sensitivity analysis as "the study of how the 
variation in the output of a model (numerical or otherwise) can be 
apportioned, qualitatively or quantitatively, to different sources of 
variation." Wikipedia shows the differing usage of these terms across 
various disciplines. The sensitivity analysis entry notes that in a 
business context "sensitivity analysis can provide information to 
managers about which elements of the business require more concentration. 
For example if sales, variable costs, fixed costs or output were to 
increase or decrease by 10% which would have the most effect on profit?"

The Web Dictionary of Cybernetics and Systems defines sensitivity 
analysis as "a procedure to determine the sensitivity of 
the outcomes of an alternative to changes in its parameters (as 
opposed to changes in the environment; see contingency 
analysis, a fortiori analysis). If a small change in a parameter 
results in relatively large changes in the outcomes, the 
outcomes are said to be sensitive to that parameter. This may mean 
that the parameter has to be determined very accurately or 
that the alternative has to be redesigned for low sensitivity. (IIASA)"

Finally, the Michigan Department of Environmental Quality 
(www.michigan.gov) defines a sensitivity analysis as "the process 
of varying model input parameters over a reasonable range (range of 
uncertainty in values of model parameters) and observing 
the relative change in model response." 

Parnell (1997) identifies uses of sensitivity analysis in decision 
making, communication, understanding systems and in model development. 
Based on his discussion, a model-driven DSS with appropriate sensitivity 
analysis should help in 1) testing the robustness of an optimal 
solution, 2) identifying critical values, thresholds or break-even 
values where the optimal strategy changes, 3) identifying sensitive 
or important variables, 4) investigating sub-optimal solutions, 
5) developing flexible recommendations which depend on circumstances, 
6) comparing the values of simple and complex decision strategies, 
and 7) assessing the "riskiness" of a strategy or scenario. 

The most common "What If?" analysis in model-driven DSS is changing 
an input value in an ad hoc way and seeing the result. This type of 
analysis has severe limitations. The analysis is likely to be more 
complete if an input object like a spinner or a slider is used to 
change values.  Such an approach is much faster and easier than typing 
in individually new input values. A range sensitivity analysis evaluates 
the effect on outputs by systematically varying one of the model inputs 
across its entire range of plausible values. According to Frey and 
Patil "results of nominal range sensitivity are most valid when 
applied to a linear model."

What are the limitations of "What If?" analysis? If the analysis is 
ad hoc rather than systematic, the analysis is likely to miss potential 
problems and solutions. Managers may not understand the assumptions of 
the sensitivity analysis, e.g. assuming a linear relationship. Also, 
in general it is impossible to audit the thoroughness of sensitivity 
and "What If?" analyses and their impact on decision making.  My general 
sense is that systematic sensitivity analysis using a one or two-variable 
data table should be required in all model-driven DSS based upon algebraic
models. Relying on an ad hoc manipulation of single variables in a 
quantitative model is always problematic and limited.

So "What If?" analysis is used broadly for techniques that help 
decision makers assess the consequences of changes in models and 
situations. Sensitivity analysis is a more specific and technical 
term generally used for assessing the systematic results from changing 
input variables across a reasonable range in a model. The current 
frontier is animated sensitivity analysis where a visual display like 
a chart or graph is sytematically varied showing results of changing 
model parameters. Check the Planners Lab review (Power, 2006).

As always your comments and questions are welcome. 

References

Alexander, E.R. (1989). Sensitivity analysis in complex decision 
models, Journal of the American Planning Association 55: 323-333.

Frey, H. C. and S. R. Patil, "Identification and Review of Sensitivity
Analysis Method,"NCSU/USDA Workshop on Sensitivity Analysis Methods, 
http://www.ce.ncsu.edu/risk/abstracts/frey.html

Isukapalli, S.S., "Uncertainty Analysis of Transport-Transformation 
Models, "A dissertation submitted to the Graduate School--New 
Brunswick, Rutgers, The State University of New Jersey, URL 
http://www.ccl.rutgers.edu/~ssi/thesis/thesis-node14.html 

Microsoft help, http://office.microsoft.com/en-us/assistance/

Pannell, D.J. (1997). Sensitivity analysis of normative economic 
models: Theoretical framework and practical strategies. Agricultural 
Economics 16: 139-152, at URL
http://cyllene.uwa.edu.au/~dpannell/dpap971f.htm

Power, D., "What is Planners Lab?" DSS News, Vol. 7, No. 11, May 21, 
2006.

Sensitivity analysis, from Wikipedia, the free encyclopedia, URL
http://en.wikipedia.org/wiki/Sensitivity_analysis

Web Dictionary of Cybernetics and Systems at URL 
http://pespmc1.vub.ac.be/ASC/SENSIT_ANALY.html

What-if analysis, from Wikipedia, the free encyclopedia, URL
http://en.wikipedia.org/wiki/What-if_analysis

Winston, W. L., Microsoft Excel Data Analysis and Business 
Modeling, Microsoft Press, 2004.

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        Purchase Dan Power's DSS FAQ book 
  83 frequently asked questions about computerized DSS 
   http://dssresources.com/dssbookstore/power2005.html 

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Dan Power Travel Plans

Dan Power will be in Hong Kong August 12-24 teaching an MBA 
course about MIS and DSS for the University of Northern Iowa 
College of Business Administration Hong Kong degree program 
(http://www.mba.uni.edu.hk). Email him, power@uni.edu, if
you're in Hong Kong and want to meet to discuss DSS.

Dan Power will be attending Teradata Partners 2006 conference 
September 17-19 in Orlando, Florida (check 
http://www.teradata.com/teradata-partners).

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What's New at DSSResources.COM

07/28/2006 Posted an interview with Rob Armstrong "Driving 
usage versus gaining value from a data warehouse". Check 
the interviews page.

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DSS Conferences 

1. DEXA 2006, 17th International Conference on Database 
and Expert Systems Applications, September 4-8, 
2006, Krakow, Poland. Check http://www.dexa.org .

2. ICDSS 2007, 9th International Conference on DSS, Jan. 2-4, 2007, 
Calcutta, India. Theme: Decision Support for Global Enterprises.
Check http://www.ICDSS2007.org . 

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