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Vol. 10, No. 1, September 2009, pp. 18–33
issn 1532-0545 09 1001 0018
informs
®
doi 10.1287/ited.1090.0027
© 2009 INFORMS
I N F O R M S
Transactions on Education
A Spreadsheet Scenario Analysis Technique That
Integrates with Optimization and Simulation
Thomas A. Grossman
School of Business and Professional Studies, University of San Francisco, San Francisco, California 94117,
tagrossman@usfca.edu
Özgür Özlük
College of Business, San Francisco State University, San Francisco, California 94132, ozgur@sfsu.edu
S
cenario analysis is a widely used technique, and business students should be proficient in running scenarios
through a spreadsheet model. We propose 10 desirable properties for a scenario analysis technique, and
show that the Microsoft Excel Scenario Manager tool satisfies only one of them. We provide a tutorial for a
better technique that can be programmed into an existing spreadsheet in a matter of minutes. We show how to
integrate the technique with the Excel Solver to allow for rapid optimization of multiple scenarios and with the
Crystal Ball add-in for Monte Carlo simulation to enable simulation of multiple scenarios. Our undergraduate
and MBA students are able to learn the technique with little difficulty.
Key words: spreadsheets; scenarios; scenario analysis; optimization; simulation
History: Received: July 2008; accepted: January 2009.
1.
Introduction
analyst to compute key outputs by running multiple
scenarios through his model.
Ryan and Ryan (2002) report that 40% of the
financial analysts surveyed almost always use scenario analysis for capital budgeting. Weisel (2004)
presents scenario analysis in the context of managerial accounting. Other examples in the literature range
from wood paneling manufacturers (Buehlmann et al.
2000) to medical scientists (Postma et al. 2001).
Markham and Palocsay (2006) describe scenario
analysis, give a brief overview of scenario analysis
for problem solving that dates back to 1942, make
the case for placing scenario analysis in the business
school curriculum, and show how to use Excel’s builtin Scenario Manager tool. They point out that a shortcoming of the Scenario Manager tool is that it does
not support stochastic analysis.
Fortunately, it is easy for an analyst to program scenario analysis functionality in the spreadsheet. This
paper presents in detail an effective approach for
programming scenario analysis. We do not know
when this approach was first devised, and we speculate that it has been independently discovered by
many analysts. The earliest reference we can find is
Tennent and Friend (2001), who sketch an approach
in a section on “useful functions.” Powell and Baker
(2007, pp. 128–129) briefly present an equivalent technique. Minor programming distinctions among these
approaches are discussed in the appendix.
Spreadsheets are ubiquitous in business (Ragsdale
2001) and are used for critical business purposes
(Croll 2005, Grossman et al. 2007). They are one of the
major tools for managers in the decision-making process (Coles and Rowley 1996) and play an important
role in the practice of management science/operations
research (MS/OR) (LeBlanc and Grossman 2008).
Spreadsheets play a leading role in business school
management science courses, and essentially all business school management science textbooks rely heavily on spreadsheets.
Management science is concerned with advanced
analytical techniques such as optimization and simulation. Prior to studying these advanced techniques, the
student should have a foundation of basic techniques,
including how to establish a base case and perform
benchmarking (or change from base), sensitivity analysis, scenario analysis, and backsolving/goal seeking
(Powell and Baker 2007, Grossman 2008).
1.1. Scenario Analysis
This paper addresses “scenario analysis,” which is the
systematic investigation of the impact of different sets
of model inputs on key model outputs. A scenario is a
set of predefined input values, usually with a descriptive name. In forward-looking planning models, each
scenario can represent a coherent view of a possible
future state. Scenario analysis is the process used by the
18
Grossman and Özlük: A Spreadsheet Scenario Analysis Technique with Optimization and Simulation
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1.2. Contribution
We propose a set of 10 desirable properties that can
be used to evaluate a scenario analysis technique. We
explain why the Excel Scenario Manager tool fails to
satisfy most of these properties. We present a simple
and quick programming technique for scenario analysis (the “Scenario Engine”) that satisfies all 10 desirable properties. Based on our experience of teaching
the Scenario Engine to business students for many
years, we provide a tutorial on how to program it
into an existing model. Because it is a spreadsheet
programming technique rather than an Excel tool,
this approach is portable and can be used in any
spreadsheet, including Excel, Google’s spreadsheet,
and others.
Unlike the Excel Scenario Manager tool, the Scenario Engine can be combined with optimization and
Monte Carlo simulation. We show in §7 how to
integrate scenario analysis with optimization using
Solver. We show in §8 how to integrate scenario analysis with Monte Carlo simulation using Crystal Ball.
We believe that the Scenario Engine technique will
benefit business school students and should be taught
in or prior to a business school management science
course. The Scenario Engine technique is easy to learn
and integrates nicely with traditional management
science topics such as optimization and Monte Carlo
simulation.
2.
Desirable Properties of a Scenario
Analysis Technique
We propose 10 properties that can be used to evaluate
a scenario analysis technique. Ideally, a scenario analysis technique would satisfy all of these properties.
We group these properties into the following categories: spreadsheet engineering, analyst convenience,
and management science. This list of criteria is likely
not complete, but we believe it covers the most important issues.
2.1.
Desirable Properties for Spreadsheet
Engineering
Spreadsheet engineering is the effective software
engineering of a spreadsheet computer program
(Grossman and Özlük 2004). From the perspective
of spreadsheet engineering, a scenario analysis technique should be transparent, verifiable, and protected.
A scenario analysis technique is transparent when
the input values associated with each scenario are
readily available for inspection. (Transparency for scenario analysis is a special case of a more general concept of providing visibility of model inputs and model
logic.) Input values should not be buried in dialog boxes, VBA code, hidden cells, or hidden worksheets. A scenario technique that is transparent is less
19
likely to introduce errors due to faulty inputs in a
scenario.
A scenario analysis technique is verifiable when it is
easy to check the outputs to confirm they are accurate. This is of critical importance to any audit process (such as an audit process that can be required
for Sarbanes-Oxley compliance) or when transferring
a spreadsheet to another analyst. To be verifiable, it
must be possible to use cell formulas to trace output
values back to their corresponding input values and
inspect the intermediate cell formulas.
A scenario analysis technique is protected when it
is difficult to accidentally modify the scenario input
values, for example, by overtyping them unintentionally. Values that reside in a spreadsheet can easily
be protected through the use of Excel cell protection.
This can also be accomplished by accessing scenario
input values only through dialog boxes, VBA code,
hidden cells, or hidden worksheets, although such
approaches compromise transparency.
2.2. Desirable Properties for Analyst Convenience
An analyst is more likely to employ and use properly
a tool that is convenient. From the perspective of analyst convenience, a scenario analysis technique should
be dynamic, flexible, and efficient.
A scenario analysis technique is dynamic (or “live”;
see Wagner and Keisler 2006) when the outputs automatically update when the model changes (e.g., a cell
formula is modified) or an input not in the scenarios is changed (e.g., the scenarios contain only
data, and the analyst modifies a decision variable).
If the scenario analysis technique is “static” rather
than dynamic, then the scenario outputs become incorrect after even a minor change, and the analyst must
routinely perform extra work to rerun the scenario
analysis.
A scenario analysis technique is flexible when it is
easy to modify the scenario input values. In practice,
the input values used in scenarios can be negotiable
and subject to change and adjustment throughout
the analytical process. Such changes should be easy
to implement and are facilitated by having scenario
input values readily accessible in the spreadsheet and
by allowing the use of cell formulas in the input
values.
A scenario analysis technique is efficient when an
analyst can use it quickly once the managerial work
of defining the scenarios has been completed. Because
the input values for the scenarios are likely to be in
the rows of a spreadsheet, a scenario analysis technique that directly acts upon data in the spreadsheet
is advantageous.
2.3. Desirable Properties for Management Science
From the perspective of management science, a scenario analysis technique should be optimization ready,
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Grossman and Özlük: A Spreadsheet Scenario Analysis Technique with Optimization and Simulation
INFORMS Transactions on Education 10(1), pp. 18–33, © 2009 INFORMS
stochastic ready, and scalable, and it should use standard
terminology.
A scenario analysis technique is optimization ready
when it can easily be combined with optimization.
A scenario analysis technique is stochastic ready
when it can easily be combined with Monte Carlo
simulation. Markham and Palocsay (2006) raise this
as a desirable property in the context of the Excel Scenario Manager tool, which does not allow for stochastic analysis.
A scenario analysis technique is scalable when there
is no fixed upper bound on the number of inputs for
each scenario or on the number of scenarios.
A scenario analysis technique uses standard MS/OR
terminology. Markham and Palocsay (2006) raise this
as a desirable property in the context of the Excel Scenario Manager tool, which uses the term “changing
cell” in a nonstandard way.
3.
Excel’s Scenario Manager
Rates Poorly
Excel comes with a Scenario Manager tool that
is described thoroughly in Markham and Palocsay
(2006). Unfortunately, this tool rates poorly in terms
of the 10 desirable scenario analysis properties, satisfying only the property of being protected.
The Excel Scenario Manager tool is not transparent because the input values are buried in dialog
boxes and are not readily accessible. (This concern
was raised by Markham and Palocsay 2006.) It is
not verifiable because the output values are numbers
rather than formulas in a spreadsheet, so it is impossible to determine their origin after running the Scenario Manager tool. It is impossible to know whether
the values have been manually overwritten. It is protected because the scenario input values are stored in
a dialog box, and it is difficult to accidentally overwrite them.
The Excel Scenario Manager tool is not dynamic
because the outputs are static and do not contain any
formulas. The Scenario Manager must be rerun whenever a cell formula is changed or an input not in
the scenario list is changed. It is not flexible because
it is cumbersome to modify input values across scenarios as each scenario is buried in its own dialog
box. Markham and Palocsay (2006) point out that
the inputs do not accept cell formulas, so if one
input is to be changed across multiple scenarios, it
requires tedious dialog box navigation. It is not efficient because once the scenario input values have been
defined, each datum in each scenario must be manually entered into a dialog box.
The Excel Scenario Manager tool is not optimization ready because it cannot be combined with Solver.
As Markham and Palocsay (2006) point out, the Excel
Scenario Manager tool is not stochastic ready because
it does not support Monte Carlo simulation. It is not
scalable because it supports only 32 inputs. Markham
and Palocsay (2006) indicate that it does not use standard MS/OR terminology because of its unusual use of
the term “changing cell.”
Therefore, we conclude that Excel’s Scenario Manager has substantial shortcomings for serious analytical work. In §5, we present a better approach, called
the Scenario Engine, but we first present an example
model in §4.
4.
Preliminaries: A Core Model and
a List of Scenarios
Before employing a scenario analysis technique, the
analyst requires a “core model” and a list of scenarios.
The core model is a spreadsheet computer program
that implements a mathematical model that is relevant to the business situation being considered. The
core model should be accurate and meaningful. This
core model should be designed so that the inputs are
clearly defined and documented. In this paper, we
present models where all of the inputs are contained
in a single module, but this is not a requirement.
Our core model was used by Markham and Palocsay (2006) and is from the direct mail example in
Chapter 2 in Winston and Albright (2001). A company
plans to print a catalog and mail it to customers who
might order by using a reply envelope. The base case
data are as follows. The fixed cost to print (the setup
cost) is $20,000, with a printing cost of $0.10 per catalog and mailing cost of $0.15 per catalog. The company incurs a $0.20 cost for each reply envelope that
is returned by a customer. The average size of a customer order is $40, and the company’s variable cost
per order averages around 80% of the order’s value.
The company plans to mail 100,000 catalogs, and they
expect a response rate of 8%.
Figure 1 presents a spreadsheet model for the direct
mail example, with cell formulas in Figure 2. The
original model consists of the INPUTS module and
the MODEL module. The INPUTS module contains
all the numeric values required by the model. The
MODEL module contains the cell formulas needed to
compute key outputs, which are net profit (Cell F16)
and breakeven response rate (Cell F20).
The list of scenarios is a well-organized set of
scenarios, where each scenario is a set of input values
with a descriptive name, and the data for all scenarios
are arranged in a consistent manner.
Markham and Palocsay (2006) consider three scenarios. To better illustrate the purpose of scenario
analysis, we use six scenarios.
Grossman and Özlük: A Spreadsheet Scenario Analysis Technique with Optimization and Simulation
21
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INFORMS Transactions on Education 10(1), pp. 18–33, © 2009 INFORMS
Figure 1
The Core Model and Scenario List for the Direct Mail Example
A
B
C
1 CORE MODEL FOR DIRECTMAIL CAMPAIGN
2
3
4
5
6
7
INPUTS
8
9
Mailing inputs
10
Fixed cost to print
11
$
20,000.00
Var. cost for printing $
12
0.10
Var. cost for mailing $
13
0.15
# of catalogs mailed
14
100,000
15
Order inputs
16
17
Average order
$
40.00
18
Var. % cost of order
80%
19
Var. envelope cost
$
0.20
Response rate
20
8%
21
22
23
24
25
Fixed cost to print
26
Cell C11
27
28
1 Current
29
2 Optimistic
SCENARIO
30
3 Pessimistic
LIST
31
4 High Average Order
32
5 Very High Response
33
6 Very Low Response
34
D
E
F
G
MODEL
Model of responses
# of responses
Model of profit
Total revenue
Costs
Fixed costs
Var. mailing costs
Var. order costs
Total cost
8,000
$
320,000.00
$
$
$
$
20,000.00
25,000.00
257,600.00
302,600.00
NET PROFIT $
17,400.00
Breakeven (BE) Model
BE point
BE response rate
$
$
$
$
$
$
Average order
Cell C17
20,000.00
18,000.00
22,000.00
20,000.00
20,000.00
20,000.00
Var % cost of order
Cell C18
$
40.00
$
45.00
$
35.00
$
65.00
$
40.00
$
40.00
5,769.20
5.77%
Response rate
Cell C20
80%
75%
85%
80%
80%
80%
8%
9%
7%
8%
15%
4%
Notes. The core model is in the INPUTS and MODEL modules. The scenarios are in Rows 28–33, with documentation in Rows 26 and 27.
Figure 2
Cell Formulas for the Direct Mail Spreadsheet Model
A
B
1
2
3
4
5
6
7
8
INPUTS
9
Mailing inputs
10
11
Fixed cost to print
12
Var. cost for printing
13
Var. cost for mailing
14
# of catalogs mailed
15
Order inputs
16
17
Average order
18
Var. % cost of order
19
Var. envelope cost
20
Response rate
21
22
23
24
25
26
27
28
1
29
2
30 SCENARIO 3
LIST
31
4
32
5
33
6
34
C
D
E
F
G
MODEL
Model of responses
# of responses
Model of profit
Total revenue
Costs
Fixed costs
Var. mailing costs
Var. order costs
Total cost
20,000
0.1
0.15
100,000
=C20*C14
=F6*C17
=C11
=(C12+C13)*C14
=(C19+C18*C17)*F6
=SUM(F11:F13)
NET PROFIT =F9-F14
40
0.8
0.2
0.08
Fixed cost to print
Cell C11
Current
Optimistic
Pessimistic
High Average Order
Very High Response
Very Low Response
Breakeven (BE) Model
BE point =(F11+F12)/(C17-C18*C17-C19)
BE response rate =F19/C14
Average order
Cell C17
20,000
18,000
22,000
20,000
20,000
20,000
Var % cost of order
Cell C18
40
45
35
65
40
40
Response rate
Cell C20
0.80
0.75
0.85
0.80
0.80
0.80
0.08
0.09
0.07
0.08
0.15
0.04
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22
Grossman and Özlük: A Spreadsheet Scenario Analysis Technique with Optimization and Simulation
INFORMS Transactions on Education 10(1), pp. 18–33, © 2009 INFORMS
• The “Current” scenario uses the base case data.
• In the “Optimistic” scenario, the average order
is $45; the fixed cost to print is $18,000; the variable
order cost percentage is 75%; the response rate is 9%;
whereas other inputs are at base.
• In the “Pessimistic” scenario, the average order
is $35; the fixed cost to print is $22,000; the variable
order cost percentage is 85%; the response rate is 7%;
and other inputs are at base.
• The “High Average Order” scenario is the same
as the Current scenario, except that the average order
size is $65.
• The “Very High Response” scenario is the same
as the Current scenario, except that the response rate
is 15%.
• The “Very Low Response” scenario is the same
as the Current scenario, except that the response rate
is 4%.
The scenarios are in the SCENARIO LIST module
in Figure 1. Rows 26 and 27 contain documentation.
Each scenario row contains information for one scenario, including the scenario number (Cells B28:B33),
scenario name (Cells C28:C33), and a value for each
input (Cells D28:G33). Scenario numbers are sequential starting from 1. By convention, we use scenario
number 1 (Row 28) for the base case. Any number of
scenarios is possible; for illustration we use only six.
5.
The Scenario Engine Technique for
Scenario Analysis
Scenario analysis begins with a list of scenarios that
need to be run through the core model. The Scenario
Engine is programmed in three steps. First, we select
a scenario (§5.1) by writing the scenario number associated with the selected scenario in Cell B4. Second,
we create an IN USE module and write cell formulas
in Row 26 to display the input values for the selected
scenario (§5.2). Third, we “echo” the values from the
IN USE module to the INPUTS module by replacing appropriate input values in the INPUTS modules
with cell references (§5.3). The existing core model
logic then “sees” the input values for the selected scenarios, and the spreadsheet automatically computes
the key outputs.
5.1. Step 1: Select a Scenario
We type into Cell B4 the scenario number of the scenario we want to evaluate (Figure 3). The Scenario
Engine takes it from there, obtaining the appropriate
input values from the list of scenarios (§5.3) and feeding them to the core model (§5.4).
5.2.
Step 2: Display the Input Values for
the Selected Scenario
For convenience, we have (Figure 3) Cell B26 echo
the scenario number in Cell B4, using the cell formula
Cell B26: = B4. We now need to program Cells C26:G26
to display the input values from the scenario list
that correspond to the scenario number in Cell
B26. For example, Cell D26 will display the “Fixed
cost to print” for the selected scenario. We use the
INDEX function, Cell D26: = INDEX(D28:D33,$B$26)
(Figure 4). This use of INDEX instructs Excel to examine the range D28:D33 and return the value of the cell
in the row specified in Cell B26. For example, when the
scenario number in Cell B26 is 2, the INDEX function
examines the column range D28:D33, finds the second
row within the column range (Row 29), and returns
from Cell D29 the value 18,000.
We copy the formula in Cell D26 to Cells C26:G26.
(To facilitate this copy operation, Cell B26 is programmed in the INDEX function using an absolute
reference of $B$26.) Note that the scenario number in
Cells B28:B33 is a memory aid and is not directly referenced by the INDEX function.
5.3.
Step 3: Send the Input Values to
the Core Model
To complete the Scenario Engine, we need the core
model to “see” the input values from the selected scenario. In each core model input cell that appears in
the scenario list, we write a cell formula that echoes
(points to) the displayed scenario input value. For
example, the core model input “Fixed cost to print”
(Cell C11) is programmed to refer to the sales rep cost
value in Cell D25 (Figure 4), Cell C11: = D26. Similar changes are made for the other inputs. The input
“Average order” in Cell C17 is changed to refer to
the value in Cell E25; Cell C17: = E26. For the other
two scenario inputs, we enter similar formulas; Cell
C18: = F26, and Cell C20: = G26.
Typically, some core model inputs will not be
included in the scenarios. The cells for these core
model inputs are not modified when programming
the Scenario Engine; they remain numeric values.
This completes the programming of the Scenario
Engine. To use the Scenario Engine, simply enter the
selected scenario number into Cell B4, and the spreadsheet instantly computes the core model using the
inputs from the selected scenario.
5.4.
Step 4 (Optional): Improved Spreadsheet
Engineering
It is a wise spreadsheet engineering practice to separate data from formulas. For this reason, the INPUTS
module contains only numeric data. However, the
Scenario Engine approach places cell formulas into
some data cells to “echo” the values of the selected
scenario.
Faculty who emphasize sound spreadsheet engineering may want to redesign the INPUTS module to
Grossman and Özlük: A Spreadsheet Scenario Analysis Technique with Optimization and Simulation
23
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Figure 3
The Scenario Engine Displaying Scenario 2
A
B
C
1 SCENARIO ANALYSIS FOR DIRECTMAIL CAMPAIGN
2
SCENARIO
3
SELECTED
4
2
5
6
7
8
INPUTS
9
Mailing inputs
10
11
Fixed cost to print
$
18,000.00
12
Var. cost for printing $
0.10
13
Var. cost for mailing $
0.15
14
100,000
# of catalogs mailed
15
Order inputs
16
17
Average order
$
45.00
18
Var. % cost of order
75%
19
Var. envelope cost
$
0.20
Response rate
20
9%
21
22
23
24
25
26
27
28
29
30
31
32
33
34
D
E
IN USE
1
2
3
4
5
6
SCENARIO
LIST
Current
Optimistic
Pessimistic
High Average Order
Very High Response
Very Low Response
G
MODEL
Model of responses
# of responses
Model of profit
Total revenue
Costs
Fixed costs
Var. mailing costs
Var. order costs
Total cost
9,000
$
405,000.00
$
$
$
$
18,000.00
25,000.00
305,550.00
348,550.00
NET PROFIT $
56,450.00
Breakeven (BE) Model
BE point
BE response rate
3,891.40
3.89%
Fixed cost to print
Scenario number
Scenario Name
2 Optimistic
F
Average order
$
Cell C11
18,000.00 $
$
$
$
$
$
$
20,000.00
18,000.00
22,000.00
20,000.00
20,000.00
20,000.00
Var % cost of order
Response rate
Cell C18
Cell C20
Cell C17
45.00
$
$
$
$
$
$
40.00
45.00
35.00
65.00
40.00
40.00
75%
9%
80%
75%
85%
80%
80%
80%
8%
9%
7%
8%
15%
4%
Notes. The Scenario Engine is controlled using Cell B4. The Scenario Engine is programmed in Cells C11, C17, C18, C20, and B26:G26. Cells F16 and F20
display the key outputs for Scenario 2.
Figure 4
Cell Formulas for the Scenario Engine
A
B
SCENARIO
2
3
SELECTED
4
2
5
6
7
8
INPUTS
9
10
Mailing inputs
11
Fixed cost to print
12
Var. cost for printing
13
Var. cost for mailing
14
# of catalogs mailed
15
16
Order inputs
17
Average order
18
Var. % cost of order
19
Var. envelope cost
20
Response rate
21
22
23
24
25
Scenario Number
26
IN USE =B4
27
28
1
29
2
30 SCENARIO 3
LIST 4
31
32
5
33
6
34
C
D
E
F
G
MODEL
Model of responses
# of responses
Model of profit
Total revenue
Costs
Fixed costs
Var. mailing costs
Var. order costs
Total cost
=D26
0.1
0.15
100,000
=C20*C14
=F6*C17
=C11
=(C12+C13)*C14
=(C19+C18*C17)*F6
=SUM(F11:F13)
NET PROFIT =F9-F14
=E26
=F26
0.2
=G26
Scenario Name
=INDEX(C28:C 30, $B$26)
Current
Optimistic
Pessimistic
High Average Order
Very High Response
Very Low Response
Breakeven (BE) Model
BE point =(F11+F12)/(C17-C18*C17-C19)
BE response rate =F19/C14
Fixed cost to print
Average order
Cell C11
Cell C17
=INDEX(D28:D30, $B$26) =INDEX(E28:E30, $B$26)
20,000
18,000
22,000
20,000
20,000
20,000
40
45
35
65
40
40
Notes. The programming required for the Scenario Engine is in Cells C11, C17, C18, C20, and B26:G26.
Var % cost of order
Cell C18
=INDEX(F28:F30, $B$26)
Response rate
Cell C20
=INDEX(G28:G30, $B$26)
0.80
0.75
0.85
0.80
0.80
0.80
0.08
0.09
0.07
0.08
0.15
0.04
Grossman and Özlük: A Spreadsheet Scenario Analysis Technique with Optimization and Simulation
Additional information, including supplemental material and rights and permission policies, is available at http://ite.pubs.informs.org.
24
Figure 5
INFORMS Transactions on Education 10(1), pp. 18–33, © 2009 INFORMS
The Direct Mail Spreadsheet Model (Redesigned)
A
B
C
1 SCENARIO ANALYSIS FOR DIRECTMAIL CAMPAIGN
2
SCENARIO
3
SELECTED
4
2
5
6
7
8
FIXED INPUTS
9
Var. cost for printing $
0.10
10
Var. cost for mailing $
0.15
11
# of catalogs mailed
100,000
12
Var. envelope cost
$
0.20
13
14
15
16
INPUTS FROM SELECTED SCENARIO
17
Fixed cost to print
$
18,000.00
18
Average order
$
45.00
19
Var. % cost of order
75%
20
Response rate
9%
21
22
23
24
25
26
27
28
29
30
31
32
33
34
D
E
IN USE
SCENARIO
LIST
1
2
3
4
5
6
Current
Optimistic
Pessimistic
High Average Order
Very High Response
Very Low Response
G
MODEL
Model of responses
# of responses
Model of profit
Total revenue
Costs
Fixed costs
Var. mailing costs
Var. order costs
Total cost
9,000
$
405,000.00
$
$
$
$
18,000.00
25,000.00
305,550.00
348,550.00
NET PROFIT $
56,450.00
Breakeven (BE) Model
BE point
BE response rate
3,891.40
3.89%
Fixed cost to print
Scenario Number
Scenario Name
2 Optimistic
F
Average order
$
Cell C17
18,000.00 $
$
$
$
$
$
$
20,000.00
18,000.00
22,000.00
20,000.00
20,000.00
20,000.00
$
$
$
$
$
$
Cell C18
45.00
40.00
45.00
35.00
65.00
40.00
40.00
Var % cost of order
Response rate
Cell C19
Cell C20
75%
9%
80%
75%
85%
80%
80%
80%
8%
9%
7%
8%
15%
4%
Notes. The INPUTS module of Figure 1 is divided into two modules: FIXED INPUTS, containing only numeric data, and INPUTS FROM SELECTED SCENARIO,
containing cell formulas that echo the values in the selected scenario.
distinguish between standard numeric input cells and
input cells controlled by the Scenario Engine.
Figure 5 presents such a redesign. The FIXED
INPUTS module (Cells C9:C12) contains numbers,
and the INPUTS FROM SELECTED SCENARIO module (Cells C17:C20) contains formulas.
5.5. Rapid Creation of a Scenario Summary Report
It is often desirable to create a “scenario summary
report” that presents the key outputs from each scenario, along with other information such as the scenario number, scenario name, and selected input and
output values for each scenario. This can be done
manually by entering different scenario numbers into
Cell B4 and recording the results.
It is less tedious and more reliable to create a scenario summary report by performing a one-parameter
sensitivity analysis on the scenario number. The analyst can perform the sensitivity analysis by using the
commercial add-in SensIt (2008), the Data Sensitivity
tool of the Sensitivity Toolkit (2007), the Data Table
feature of Excel, or by writing simple VBA code. The
Data Sensitivity tool is easy to use, but the results are
not dynamic. The Data Table is slightly harder to use,
but the results are dynamic (cf. Wagner and Keisler
2006). VBA code is difficult to write well, and we do
not use it in our courses.
We demonstrate in native Excel using the Data
Table feature. We create a scenario summary report
(using a process shown in Figure 6 with the results
in Figure 7) that shows for each scenario the corresponding scenario name (Cell C26), average order
(Cell C17), net profit (Cell F16), and the breakeven
response rate (Cell F20).
To set up the table in Figure 6, we enter documentation in Cells C36:F37 using text labels (Row 36) and
the corresponding cell addresses (Row 37). In Row
38, we enter a pointer to each cell documented in
the row above. Thus, Cell C38: = C26 (as documented
in Cell C37). We do the same in the next cell to the
right, Cell D38: = C17, and continue this process for
Cells E38:F38. We leave Cell B38 blank. We enter the
value 1 in Cell B38, continuing down to the value 6
in Cell B44.
To populate the data table (Figure 6), we select
Cells B38:F44 and perform Data\Table \, setting the
Grossman and Özlük: A Spreadsheet Scenario Analysis Technique with Optimization and Simulation
25
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INFORMS Transactions on Education 10(1), pp. 18–33, © 2009 INFORMS
Figure 6
Data Table to Create a Scenario Summary Report
Notes. Select Cells B38:F44, open the Data Table Dialog Box, enter $B$4 in “Column input cell,” and click “OK.”
“Column input cell” to be the scenario number in
Cell B4, and click “OK” as shown in Figure 6. The
results are shown in Figure 7 and the formula view
in Figure 8.
The scenario summary report allows for quick
comparison of model results for each scenario. The
scenario summary report is suitable for inclusion
in documents or presentations, and it can easily be
edited or formatted as desirable. Note that the analyst can include in the scenario summary report any
desirable inputs or outputs.
When created using Data Table, the scenario summary report is dynamic. Should there be a change to
the original model or to inputs not included in the
scenarios (for example, a change to the number of
catalogs mailed in Cell C14), the information in the
scenario summary report instantly updates. This powerful functionality is not available with the Excel Scenario Manager tool.
Figure 7
5.6.
The Scenario Engine Technique Satisfies the
Desirable Scenario Analysis Properties
The Scenario Engine technique satisfies all 10 of the
desirable scenario analysis properties defined in §2.
The Scenario Engine is transparent because the input
values are taken directly from the scenario list in
the spreadsheets. It is verifiable because the output
values displayed in the model and in the summary
report (§5.5) can be traced back using cell formulas to
the values in the scenario list. It is easily made protected by locking the scenario list values (using standard Excel protections), so they cannot be accidentally
overwritten.
The Scenario Engine is flexible because it is easy to
modify input values and to use cell formulas for input
values. It is dynamic because the outputs are live; if
a cell formula is changed, the outputs—including the
scenario summary table—automatically update without further effort by the analyst. It is efficient because
Completed Scenario Summary Report
A
B
C
D
E
Scenario Name
Average order
Net Profit
F
35
36
37
38
39
40
41
42
43
44
45
SCENARIO
OUTPUT
1
2
3
4
5
6
Cell C26
Optimistic
Current
Optimistic
Pessimistic
High Average Order
Very High Response
Very Low Response
$
$
$
$
$
$
$
Cell C17
45.00
40.00
45.00
35.00
65.00
40.00
40.00
$
$
$
$
$
$
$
Cell F16
56,450.00
17,400.00
56,450.00
(11,650.00)
57,400.00
72,000.00
(13,800.00)
Breakeven
Response Rate
Cell F20
3.89%
5.77%
3.89%
9.31%
3.52%
5.77%
5.77%
Grossman and Özlük: A Spreadsheet Scenario Analysis Technique with Optimization and Simulation
Additional information, including supplemental material and rights and permission policies, is available at http://ite.pubs.informs.org.
26
INFORMS Transactions on Education 10(1), pp. 18–33, © 2009 INFORMS
Figure 8
Completed Scenario Summary Report (Formula View)
A
B
C
D
E
F
Scenario Name
Average order
Net Profit
Breakeven Response Rate
Cell C25
Cell C17
Cell F16
35
36
37
38
39
SCENARIO
40
OUTPUT
41
42
43
44
45
1
2
3
4
5
6
=C26
=TABLE(,B4)
=TABLE(,B4)
=TABLE(,B4)
=TABLE(,B4)
=TABLE(,B4)
=TABLE(,B4)
=Average_order
=TABLE(,B4)
=TABLE(,B4)
=TABLE(,B4)
=TABLE(,B4)
=TABLE(,B4)
=TABLE(,B4)
once the scenario input values have been defined, the
programming is quick and easy, typically less than two
minutes.
The Scenario Engine is optimization ready because
it integrates with Solver as shown in §7 below. It is
stochastic ready because it supports Monte Carlo simulation, as shown in §8 below. It is scalable because it
supports any number of inputs and any number of
scenarios. It is consistent with standard MS/OR terminology because it introduces no new terms.
6.
Integrating Solver Optimization
with the Scenario Engine
An analyst performing optimization with Solver
might want to optimize multiple scenarios to see how
the optimal decisions are affected by different possible sets of future parameter values. Although this
can be done manually, it is preferable to automate
the optimization and reporting process. We show how
to do this by integrating Solver with the Scenario
Engine.
6.1. Example Model for Optimization
We show in Figure 9 an example model from Powell
and Baker (2007, §5.1). A product-marketing manager
Figure 9
Cell F20
=Net_profit
=TABLE(,B4)
=TABLE(,B4)
=TABLE(,B4)
=TABLE(,B4)
=TABLE(,B4)
=TABLE(,B4)
=Breakeven_response_rate
=TABLE(,B4)
=TABLE(,B4)
=TABLE(,B4)
=TABLE(,B4)
=TABLE(,B4)
=TABLE(,B4)
needs to decide how an advertising budget of $40,000
should be allocated to the upcoming four quarters.
The product sells for $40 and costs $25 to produce.
The overhead rate is 15%. Quarterly sales are adjusted
by a seasonal factor: 90% for Quarter 1, 110% for
Quarter 2, 80% for Quarter 3, and 120% for Quarter 4.
There is sales expense of $8,000 for Quarters 1 and 2
and $9,000 for Quarters 3 and 4. There are also quarterly ad expenditures (which are decision variables).
Consultants to the company assume the following
formula for the relationship between advertising and
quarterly unit sales:
unit sales = 35 × seasonal factor × 3000 + ad budget
6.2. Scenarios
We illustrate our approach using six scenarios
(Figure 10). In practice, one might use many more.
For each scenario, inputs that are not mentioned are
at their base case values.
• The “Current” scenario is the base case.
• The “Optimistic” scenario has a price of $41, cost
of $24, overhead rate of 12%, and an ad budget of
$45,000.
Core Model for Advertising Budget Example
A
B
C
1 CORE MODEL FOR ADVERTISING BUDGET
2
3
4
5
INPUTS
6
7
Price
8
$
40.00
Cost
$
25.00
9
Ad
Budget
$ 40,000
10
Overhead Rate
15%
11
Sales Parameters
35
12
13
Q1
14
Sales Expense
15
8,000
Seasonal
16
0.9
17
18
19
20
21
22
23
D
E
F
G
H
DECISIONS
I
Q1 Exp
$972
J
Q2 Exp
$2,919
K
Q3 Exp
$135
L
Q4 Exp
$4,063
M
Total
$8,089
MODEL
Quarter
Units Sold
Revenue
Cost of Goods
Gross Margin
$
$
$
Q1
Q2
Q3
Q4
Total
1,985
2,962
1,568
3,530
10,045
79,412 $ 118,475 $ 62,710 $ 141,192 $ 401,789
49,632 $ 74,047 $ 39,194 $ 88,245 $ 251,118
29,779 $ 44,428 $ 23,516 $ 52,947 $ 150,671
Sales Expense
Advertising
Overhead
Total Fixed Cost
$
$
$
$
8,000
972
11,912
20,884
Profit
Profit Margin
$
3,000
Q2
8,000
1.1
Q3
9,000
0.8
Q4
9,000
1.2
Note. The core model is in the INPUTS, DECISIONS, MODEL, and OUTPUTS modules.
$
$
$
$
8,000
2,919
17,771
28,690
$ 9,000
$
135
$ 9,407
$ 18,542
8,895 $ 15,738 $
11.20%
13.28%
$
$
$
$
9,000
4,063
21,179
34,242
$ 34,000
$ 8,089
$ 60,268
$ 102,357
4,975 $ 18,705 $ 48,314
7.93%
13.25%
12.02%
OUTPUTS
Profit
$48,314
Grossman and Özlük: A Spreadsheet Scenario Analysis Technique with Optimization and Simulation
27
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INFORMS Transactions on Education 10(1), pp. 18–33, © 2009 INFORMS
Figure 10
Core Model with Scenario Engine Displaying Scenario 2
A
B
C
D
1 SCENARIO ANALYSIS FOR ADVERTISING BUDGET
2
SCENARIO SELECTED
3
2
4
5
6
FIXED INPUTS
7
Sales Parameters
35
3,000
8
9
Q1
Q2
10
Sales Expense
8,000
8,000
11
Seasonal
0.9
1.1
12
13
INPUTS
FROM
SELECTED
SCENARIO
14
41.00
Price
$
15
Cost
$
24.00
16
$
45,000
Ad Budget
17
12%
Overhead Rate
18
19
20
21
22
24
25
26
27
28
29 SCENARIO
30
LIST
31
32
33
1
2
3
4
5
6
Q3
9,000
0.8
Cost
Scenario
Name
Optimistic
Cell C8
$
41.00
Cell C9
$
24.00
Current
Optimistic
Pessimistic
High Price
High Cost
High Budget
$
$
$
$
$
$
40.00
41.00
37.00
45.00
40.00
40.00
F
G
H
I
DECISIONS
Price
23
Scenario Number
IN USE
2
E
$
$
$
$
$
$
25.00
24.00
26.00
25.00
30.00
25.00
Q4
9,000
1.2
Overhead
Rate
J
Q1 Exp
$8,261
Q2 Exp
$13,822
K
L
Q3 Exp
$5,898
Q4 Exp
$17,019
M
Total
$45,000
MODEL
Quarter
Units Sold
Revenue
Cost of Goods
Gross Margin
Q1
Q2
Q3
3,343
4,993
2,641
$ 137,051 $ 204,731 $ 108,287
$ 80,225 $ 119,842 $ 63,388
$ 56,826 $ 84,888 $ 44,900
Q4
Total
5,943
16,920
$ 243,646 $ 693,715
$ 142,622 $ 406,077
$ 101,024 $ 287,638
Sales Expense
Advertising
Overhead
Total Fixed Cost
$
$
$
$
$ 9,000
$ 5,898
$ 12,994
$ 27,892
$
$
$
$
Profit
Profit Margin
$
24,119 $ 38,499 $ 17,008
17.60%
18.80%
15.71%
$
8,000
8,261
16,446
32,707
$
$
$
$
8,000
13,822
24,568
46,390
9,000
17,019
29,238
55,257
$ 34,000
$ 45,000
$ 83,246
$ 162,246
45,767 $ 125,392
18.78%
18.08%
OUTPUTS
$125,392
Profit
Ad Budget
Cell C11
Cell C10
12% $ 45,000
15%
12%
18%
15%
15%
15%
$
$
$
$
$
$
40,000
45,000
35,000
40,000
40,000
55,000
Notes. The INPUTS module is divided into the FIXED INPUTS and INPUTS FROM SELECTED SCENARIO modules. The Scenario Engine is programmed in Cells
B25:G25 and D15:D18. The scenarios are presented in Rows 27–32, with documentation in Rows 23–24. The Scenario Engine is controlled using Cell B4.
• The “Pessimistic” scenario has a price of $37, cost
of $26, overhead rate of 18%, and an ad budget of
$35,000.
• The “High Price” scenario has a price of $45.
• The “High Cost” scenario has a cost of $30.
• The “High Budget” scenario has an ad budget of
$55,000.
6.3. Scenario Engine
We program a Scenario Engine as described in §5. In
Figure 10, the cells related to the Scenario Engine cells
are colored a shade of green. The scenarios themselves
are in Rows 27–32. The IN USE scenario values are
in Row 25. The selected scenario is in Cell B4. We
split the INPUTS module (of Figure 9) into two modules with the inputs controlled by the Scenario Engine
placed in the INPUTS FROM SELECTED SCENARIO
module and the remaining inputs placed in the FIXED
INPUTS module.
6.4. Combining Solver with the Scenario Engine
We program Solver with the ad expenditures (Cells
I4:L4) as the changing cells, the profit (Cell M22)
as the target cell, and the constraint that the total
ad expenditures ⇐ ad budget (M4 ⇐ C17), plus
nonnegativity.
To manually connect optimization to the Scenario
Engine, we simply set the scenario selected (Cell B4)
to the desired scenario number and invoke Solver. To
optimize multiple scenarios, we repeat this process
using different values in Cell B4. The manual process of running Solver and summarizing optimization
results for all the scenarios in a well-organized table
is tedious and error prone, especially with a sizable
number of scenarios. It should be automated.
Automation can be achieved using a parametric
optimization add-in such as Solver Table (2003) or the
Solver Sensitivity tool of Sensitivity Toolkit (2007), or
by writing VBA code. Solver Table and the Solver
Sensitivity tools are easy to use. We used the Solver
Sensitivity tool (Figure 11), which allows us to include
any outputs as long as they are in cells adjacent to one
another, to generate the results shown in Figure 12.
This section showed how to perform optimization on any number of scenarios. This approach is
quick and easy. The prerequisites are a fully specified Solver model and a set of scenarios. The analyst
must program a Scenario Engine and then run Solver
Sensitivity. For an analyst who is comfortable implementing the Scenario Engine technique and using the
Solver Sensitivity tool, this requires only a few minutes of effort. More importantly, using the Scenario
Engine, the analyst can change any number of model
inputs, as opposed to at most two inputs that can be
changed using either Solver Table or the Solver Sensitivity tool.
Solver returns static output, so any approach
that uses Solver will also have static output. Hence,
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INFORMS Transactions on Education 10(1), pp. 18–33, © 2009 INFORMS
Figure 11
Solver Sensitivity Dialog Boxes
Note. Note that the worksheet name is “AdvertisingBudget.”
the Solver scenario analysis is not dynamic. Note that
Solver does not function on worksheets that have
Excel’s “protect sheet” feature enabled, so whenever
Solver is used, cells on the worksheet cannot be
protected.
7.
Integrating Crystal Ball Simulation
with the Scenario Engine
Markham and Palocsay (2006) point out that the
Excel Scenario Manager tool does not allow stochastic
analysis. This is a serious shortcoming for the management scientist. In this section, we show how to
combine stochastic analysis with scenario analysis by
integrating the Scenario Engine with the Crystal Ball
add-in for Monte Carlo simulation.
7.1. Example Model for Simulation
We illustrate (Figure 13) our approach using Problem 15.9 from Powell and Baker (2007). A small private company is considering an initial public offering.
The initial price of the stock ranges from $10 to $15
with the discrete distribution shown in Table 1.
Figure 12
There is 30% probability that the company will fail
in the first year and this probability remains the same
in each of the first five years. If the company does
not fail, then its stock value increases each year by a
percentage given by a lognormal distribution with a
mean of 1.5% and standard deviation of 0.5%.
We place probability distributions into “Initial
Price” (Cell D19), “Fail or Not” (Cells E22:I22), and “%
Price Increase” (Cells E23:I23) by designating them as
Crystal Ball “Assumptions.”
The company would like to determine the probability distribution for the price of the stock in five years
(Cell D26); hence we designate this cell as a Crystal
Ball “Forecast.”
7.2. Scenarios
We will use the following six scenarios, although in
practice one might use many more. For each scenario,
inputs that are not mentioned are at their base case
values.
• The “Current” scenario is the base case.
• In the “Optimistic” scenario, failure probability
in Year 1 is 15% in the first year and decreases by 2%
Solver Scenario Analysis Summary
A
B
C
1
SCENARIO SELECTED
2
1
$71,446.79
3
2
$125,392.21
4
3
$1,650.45
5
4
$140,130.00
6
5
($1,910.00)
$ (142,040.00)
7
6
$76,097.27
$
8
Objective: Profit
Change
D
E
Q1 Exp
Q2 Exp
F
Q3 Exp
G
Q4 Exp
$7,273
$12,346
$5,117
$15,263
53,945.42
$8,261
$13,822
$5,898
$17,020
$ (123,741.76)
$1,672
$3,980
$692
$5,307
$
$7,273
$12,346
$5,117
$15,263
$
138,479.55
78,007.27
$969
$2,929
$136
$4,056
$10,237
$16,773
$7,459
$20,532
Grossman and Özlük: A Spreadsheet Scenario Analysis Technique with Optimization and Simulation
29
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Figure 13
Core Model for Simulation Example
A
B
C
1 CORE MODEL FOR IPO VALUE
2
3
4
5
INPUTS
6
7
8
Distrn of Increase
9
10
11
IPO Price
12
Probability
13
Year
14
15
Probability of Failure
16
17
MODEL
18
19
Initial Price
20
21
Year
Fail or Not (Fail=0)
22
% Price Increase
23
Value
24
25
Price in 5 years
26
27
28
D
E
F
G
LogNormal Distribution
Mean
Std. dev.
1.50%
0.50%
$
10.00
0.10
0
$
11.00 $
0.20
H
I
Failure Probability
Annual Change
0%
12.00
0.30
1
30%
2
30%
1
1
1.00%
12.12
2
1
1.00%
12.24
$
13.00
0.20
3
30%
$
14.00
0.10
4
30%
$
15.00
0.10
5
30%
12.00
0
12.00
3
1
1.00%
12.36
4
1
1.00%
12.49
5
1
1.00%
12.61
12.61
Notes. The core model is in the INPUTS and MODEL modules. The key output is in Cell D26.
every year. The mean of the lognormal distribution is
2%, and the standard deviation is 0.50%.
• In the “Pessimistic” scenario, failure probability
in Year 1 is 36% for the first year and increases by 3%
every year. The mean of the lognormal distribution is
1%, and the standard deviation is 0.90%.
• In the “High Mean” scenario, the mean of the
lognormal distribution is 4.00%.
• In the “High Year 1 Probability” scenario, failure
probability in Year 1 is 50%, for the first year.
• In the “High S.D.” scenario, the standard deviation of the lognormal distribution is 2%.
7.3. Scenario Engine
We program a Scenario Engine as described in
§§5.1–5.3. In Figure 14, the cells related to the Scenario
Engine are colored a shade of green. The scenarios
themselves are in Rows 33–38. The IN USE scenario
values (which are echoed into the INPUTS module)
are in Row 31. The selected scenario is in Cell B4.
7.4.
Combining Crystal Ball with
the Scenario Engine
To manually connect simulation to the Scenario
Engine, we simply set the scenario selected (Cell B4)
Table 1
Price ($)
Probability
Probability Distribution for Simulation Model
10
11
12
13
14
15
0.10
0.20
0.30
0.20
0.10
0.10
to the desired scenario number and run Crystal Ball.
To simulate multiple scenarios, we repeat this process
using different values in Cell B4. The manual process
of running Crystal Ball and summarizing simulation
results for all the scenarios in a well-organized table
is tedious and error prone (especially with a sizable
number of scenarios). It should be automated.
To automate the simulation of each scenario, we
can use the Crystal Ball Sensitivity tool provided in
the Sensitivity ToolKit (2007), the Crystal Ball Decision Table tool (which, despite its name, is actually a
sensitivity analysis tool), or by writing VBA code. The
Crystal Ball Sensitivity tool is easy to use. The Crystal Ball Decision Table tool is slightly more difficult to
use, but it generates the histogram plots of the simulation output values. We used the Crystal Ball Sensitivity tool (Figure 15) to generate the results shown in
Figure 16. Note that in Figure 16 we do not report the
scenario name because Crystal Ball Sensitivity cannot
do this. (If necessary, the scenario name could be programmed using a lookup function.)
This approach is consistent with the use of common
random numbers, because the random numbers are
controlled by the simulation add-in.
This section showed how to perform Monte Carlo
simulation using Crystal Ball on any number of
scenarios. This approach is quick and easy. The prerequisites are a fully specified Crystal Ball model and a
set of scenarios. The analyst must program a Scenario
Engine and then run the Crystal Ball Sensitivity tool.
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Additional information, including supplemental material and rights and permission policies, is available at http://ite.pubs.informs.org.
30
INFORMS Transactions on Education 10(1), pp. 18–33, © 2009 INFORMS
Figure 14
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
Core Model with Scenario Engine Displaying Scenario 3
A
B
C
SCENARIO ANALYSIS FOR IPO VALUE
D
E
F
G
H
I
SCENARIO SELECTED
3
FIXED INPUTS
Year
IPO Price
Probability
$
0
10.00
0.10
$
1
11.00
0.20
$
2
12.00
0.30
INPUTS FROM SELECTED SCENARIO
LogNormal Distribution
Mean
Std. dev.
Distrn of Increase
1.00%
0.90%
Year
Probability of Failure
0
Initial price
12.00
Year
Fail or Not (Fail=0)
% Price Increase
Value
0
12.00
Price in 5 years
12.61
$
3
13.00 $
0.20
4
14.00
0.10
$
5
15.00
0.10
Failure Probability
Annual Change
3%
1
36%
2
39%
3
42%
4
45%
5
48%
1
1
1.00%
12.12
2
1
1.00%
12.24
3
1
1.00%
12.36
4
1
1.00%
12.49
5
1
1.00%
12.61
MODEL
Failure
Probability
Year One
Scenario
Failure
Probability
Annual
Change
LogNormal
Mean
LogNormal
SD
IN USE
3
Name
Pessimistic
Cell E17
0.36
Cell G14
3%
Cell D14
1%
Cell E14
0.90%
SCENARIO
LIST
1
2
3
4
5
6
Current
Optimistic
Pessimistic
High Mean
High Year 1 Prob.
High S.D.
30%
15%
36%
30%
50%
30%
0%
–2%
3%
0%
0%
0%
1.50%
2.00%
1.00%
4.00%
1.50%
1.50%
0.50%
0.10%
0.90%
0.50%
0.50%
2.00%
Notes. The INPUTS module is divided into the FIXED INPUTS and INPUTS FROM SELECTED SCENARIO modules. The Scenario Engine is programmed in Cells
D14, E14, G14, E17:I17, and B33:G33. The scenarios are in Rows 35–40, with documentation in Rows 31–32. The Scenario Engine is controlled using Cell B4.
For an analyst who is comfortable implementing the
Scenario Engine technique and using the Crystal Ball
Sensitivity tool, this requires only a few minutes of
effort.
Because the simulation results generated by Crystal
Ball are static, the simulation scenario analysis is not
dynamic.
8.
Classroom Experience with
the Scenario Engine
We have taught the Scenario Engine to hundreds of
students. With an explanation of the INDEX function
and a bit of practice, both undergraduate and MBA
students are able to learn it in 30–60 minutes of class
time, in a setting where all students have computers. Many of our MBA students are well aware, from
prior experience, of the cumbersome nature of Excel’s
Scenario Manager tool and greatly prefer the Scenario
Engine technique.
With a bit of practice, our students are able to build
a Scenario Engine for any existing spreadsheet model.
Those students who apply themselves tell us they can
do this in less than two minutes—even on a spreadsheet they have not seen before. The only requirement
is that the inputs be organized in a well-documented
inputs module, and that the scenarios be predefined
in a well-documented scenario list such as in Figure 1.
Students’ Excel skills upon entering our course typically range from beginner to expert. We take action
Grossman and Özlük: A Spreadsheet Scenario Analysis Technique with Optimization and Simulation
31
Additional information, including supplemental material and rights and permission policies, is available at http://ite.pubs.informs.org.
INFORMS Transactions on Education 10(1), pp. 18–33, © 2009 INFORMS
Figure 15
Crystal Ball Sensitivity Dialog Boxes
Source. Adapted from Powell and Baker (2007).
Notes. Note that the worksheet name is “with Scenario.”
to fix student spreadsheet deficiencies with minimal
use of class time using “student-led remediation”
described in Grossman (2006). Students need to be
able to use the INDEX function to program the Scenario Engine and Excel’s Data Table tool to build the
scenario summary report. We teach both during class
before we spend the 30–60 minutes on the Scenario
Engine. We present a simple tutorial on INDEX (see
the appendix) that takes 5 to 10 minutes. We provide a
simple handout with screenshots that walks students
through the use of Data Table, described in Grossman (2008). Teaching Data Table takes about 10 minutes with MBAs and 20 minutes with undergraduates.
They have no difficulty learning it, provided that we
motivate them with an interesting context.
When we teach parametric optimization or simulation sensitivity, students have no difficulty combining
these techniques with the Scenario Engine.
9.
Conclusion
Scenario analysis is an important and useful technique for obtaining business insight from a model.
Figure 16
As discussed in Markham and Palocsay (2006), students should be proficient in scenario analysis. We
present a set of 10 desirable scenario analysis properties. Unfortunately, the Excel Scenario Manager satisfies only one of these properties, sorely limiting its
usefulness for serious analytical work.
We present the Scenario Engine technique for scenario analysis in a spreadsheet. It satisfies all 10
desirable scenario analysis properties. The Scenario
Engine can be quickly programmed into any welldesigned spreadsheet model. This approach greatly
reduces manual data entry and copying of outputs
into summary reports, increasing analyst productivity
and accuracy.
We demonstrate the ease with which an analyst
can integrate the Scenario Engine with Solver for
optimization and with Crystal Ball for Monte Carlo
simulation.
Markham and Palocsay (2006) demonstrate the
straightforward integration of the Scenario Manager
tool with the decision analysis add-in TreePlan (SensIt
2008). We believe that integration of the Scenario
Engine with TreePlan for decision analysis would be
Simulation Scenario Analysis Summary for Problem 15.9
A
B
C
D
E
1
SCENARIO SELECTED
Price in 5 years: Mean
Price in 5 years: StDev
Price in 5 years: Min
Price in 5 years: Max
2
1
$
2.26
$
5.04
$
-
$
16.66
3
2
3
4
5
6
$
$
$
$
$
7.62
0.82
2.60
0.40
2.27
$
$
$
$
$
6.83
3.18
5.72
2.27
5.03
$
$
$
$
$
-
$
$
$
$
$
16.67
16.67
18.93
16.48
22.80
4
5
6
7
8
Source. Adapted from Powell and Baker (2007).
Grossman and Özlük: A Spreadsheet Scenario Analysis Technique with Optimization and Simulation
Additional information, including supplemental material and rights and permission policies, is available at http://ite.pubs.informs.org.
32
INFORMS Transactions on Education 10(1), pp. 18–33, © 2009 INFORMS
straightforward, and we see this as an avenue for further research.
We have used the Scenario Engine with undergraduate and MBA students and have found they can
learn it with modest effort. We anticipate that it will
be of value in many business school management science courses.
Acknowledgments
We thank the editors and the anonymous referees for their
thoughtful reviews and valuable comments. We also thank
Patrick O’Beirne for his comments on the OFFSET function.
Appendix
This appendix describes the INDEX function, which might
not be familiar to some readers or their students. We provide to students a spreadsheet containing this information
prior to teaching the Scenario Engine.
Essential Functionality of INDEX
The INDEX function is a convenient way to obtain the contents of a cell located within a particular range of cells. For
the Scenario Engine, we need to make use of only a subset
of the functionality of INDEX, described here.
The syntax for our purposes is =INDEX(range, row_num),
where range is a single column of cells, and row_num is the
row number within the range. The INDEX function returns
the value in the cell at row_num within the range.
Examples (see Figure A.1):
=INDEX(G7:G9,2) returns 20, the value in Cell G8: Row 2
of G7:G9.
=INDEX(G7:G9,5) returns #REF!; Row 5 was specified for
a range with only three rows.
Enrichment: Additional Functionality of INDEX
Note that there is an “advanced” syntax for INDEX that is
not required for the Scenario Engine. It can be desirable to
expand students’ knowledge of Excel by showing them this
functionality.
The “advanced” syntax is =INDEX(range, row_num,
col_num). Range is a rectangular selection of cells, row_num
is the row number within the range, and col_num is the column number within the range. INDEX returns the value in
the cell at row_num and col_num within the range.
Examples (see Figure A.1):
=INDEX(G7:K9,1,1) returns 10, the value in Cell G7:
Row 1, Column 1 of G7:K9.
=INDEX(H8:J9,1,1) returns 70, the value in Cell H8:
Row 1, Column 1 of H8:J9.
=INDEX(G7:K9,2,5) returns 220, the value in Cell K8:
Row 2, Column 5 of G7:K9.
=INDEX(G7:K9,4,5) returns the error message #REF!; the
range has only three rows.
Figure A.1
INDEX Example for Additional Functionality
G
7
8
9
10
H
10
20
30
I
60
70
80
J
110
120
130
K
160
170
180
210
220
230
Choice of Lookup Functions
Excel provides a class of “lookup” functions that are useful
for extracting data from a list. We recommend the INDEX
function. However, Tennent and Friend (2001) use OFFSET,
and Powell and Baker (2007) use CHOOSE. Each of these
three functions is capable of providing the necessary functionality. However, from a spreadsheet engineering perspective, OFFSET should be avoided whenever possible, and
CHOOSE requires excessive programming and can be difficult to verify. INDEX has none of these difficulties and
therefore is preferred. (Note that VLOOKUP does not work
well for this application because it requires a column number that has to be changed for each column. LOOKUP can
be used for this application, but it requires one more range
argument than INDEX and is therefore more challenging to
program.)
OFFSET. The OFFSET function (along with the INDIRECT function) works not by the usual spreadsheet cell
referencing but instead by addressing a cell that is a specified number of rows and columns away from a specified
location in the spreadsheet. This poses serious problems for
accurate, reliable programming. In general in Excel, when
a user drags-and-drops (or cuts-and-pastes) a cell containing a formula, the spreadsheet automatically adjusts and
cells return the same values they contained prior to the edit.
However, OFFSET does not reliably exhibit this behavior.
A simple drag-and-drop can cause the value returned by the
OFFSET function to change. Likewise, in general in Excel,
when a user inserts or deletes a new row, the spreadsheet automatically adjusts, and cells return the same values they contained prior to the row insertion. However,
OFFSET does not reliably exhibit this behavior. If a row
is inserted or deleted between the “range” of OFFSET and
the offset location, the value returned by the OFFSET function changes. Due to this unusual behavior in response to
normally benign programming actions, a spreadsheet containing OFFSET must be considered inherently risky.
Furthermore, OFFSET does not work properly with
Excel’s formula auditing tools. A cell whose value is
returned by OFFSET does not provide an arrow to the OFFSET cell when Trace Dependents is used. This can cause
such a cell to be perceived as “orphan data” (and therefore
a candidate for deletion during routine quality assurance),
when in fact it is used by the OFFSET function. Finally,
OFFSET is one of a handful of “volatile” functions (meaning that it always recalculates), which increases calculation
time in larger spreadsheets.
CHOOSE. The CHOOSE function is unwieldy and
requires excessive programming. With CHOOSE, the programmer cannot provide a single range for all scenarios but
must program an individual argument for each scenario.
For example, with six scenarios the programmer might
write CHOOSE(Scenario_Number, L14, L15, L16, L17, L18,
L19) but cannot write this as CHOOSE(Scenario_Number,
L14:L19). If there were 20 scenarios, the CHOOSE function
would require 21 separate arguments, which is impractical
as well as hard to verify.
In addition, in Excel 2003 and earlier, CHOOSE was limited to 29 scenarios. This has increased in Excel 2007 to 254
scenarios (requiring 255 arguments). Conceptually, there is
Grossman and Özlük: A Spreadsheet Scenario Analysis Technique with Optimization and Simulation
Additional information, including supplemental material and rights and permission policies, is available at http://ite.pubs.informs.org.
INFORMS Transactions on Education 10(1), pp. 18–33, © 2009 INFORMS
33
no limit on the number of scenarios a user might want to
deploy; hence, Excel’s limitation to 254 scenarios compromises scalability.
Grossman, T. A., V. Mehrotra, Ö. Özlük. 2007. Lessons from
mission-critical spreadsheets. Comm. Assoc. Inform. Systems
20(60) 1009–1042.
INDEX. In contrast, the INDEX function has none of the
above shortcomings. Unlike OFFSET, it uses standard cell
referencing and hence is well behaved with regard to cutand-paste and row insertions and deletions. It works well
with Excel’s Trace Dependents feature, and like most Excel
functions, is nonvolatile. In contrast to CHOOSE, it accepts
a single range for all the scenarios; it is therefore faster to
program and easier to verify.
Markham, I. S., S. W. Palocsay. 2006. Scenario analysis in spreadsheets with Excel’s scenario tool. INFORMS Trans. Ed. 6(2)
23–31, http://ite.pubs.informs.org/.
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