DS235
INTRODUCTION TO
DECISION SCIENCE
LUIZ BRANDAO
Visiting Associate Professor, The University of Texas at Austin
AGENDA
• Instructor and TA introductions
• Course overview
• Key policies and procedures
• Excel modeling and DADM software
• Eldorado Wind Farm example
• Sensitivity analysis
• Class exercise: Data tables in Excel
• Homework Assignment
LUIZ BRANDAO
• BS, Civil Engineer, PUC-Rio, Brazil
• MSc. Civil Engineering, Stanford University
• MBA, Stanford Graduate School of Business
• PhD Industrial Engineering, PUC-Rio
• Visiting Scholar, McCombs, UT Austin (2001-2004)
• Associate Professor, PUC-Rio (2005 -
)
• Visiting Associate Professor, UT Austin (2021-2023)
• IAG Business School of PUC-Rio - (https://iag.puc-rio.br/en/home_en/)
• Graders: Darren Huang, Mark Hatanpaa and Sia Shah
• Support: Gregory Molina, Jeffery Tran, Luke Morgan
3
SOFTWARE
• There are many software packages that help analyze data.
• DADM_Tools Add-In
• This Excel add-in tool implements decision trees and simulation, as well as
forecasting and several basic data analysis tools.
• While less powerful than the Palisade software, which may not be available in
your place of employment, this add-in is freely available
• Palisade DecisionTools Suite:
• @RISK, that can run multiple replications of a spreadsheet simulation and
perform sensitivity analysis
• PrecisionTree, used to built decision tree models used to analyze decisions with
uncertainty.
COURSE TOPICS
Risk Analysis
• Measuring and modeling
uncertainty
• Sensitivity analysis over
model inputs
• Many uncertainties
• Few decisions up-front
Decision Trees
• Supports the decisionmaking process
• Decisions and
uuncertainties
• Sequential events
• Future decisions
Optimization
• Problems where there
is no uncertainty
• Many decisions
• Many potential
solutions
• Which is the best one?
COURSE TOPICS
Risk Analysis
Decision Trees
▪ Sensitivity Analysis
▪ Decision Trees
▪ Monte Carlo Simulation
▪ Value of Information and
Correlated Inputs
▪ Multi-period Models
▪ Optimization with Excel
Solver
▪ Applications in
Control
▪ Monte Carlo with
Optimization
▪ Bayes´s Rule
▪ Valuing Options
Operations & Finance
▪ Integer Programming
▪ Nonlinear programming
EXCEL
DADM
Structuring Decision Problems
Solver
INTRODUCTION
• Living in the age of technology has implications for everyone
entering the business world.
• Technology makes it possible to collect large amounts of data.
• Ex: Google, Facebook, Youtube, Netflix, Online shopping, IOT
• Technology has given people and firms the power to analyze data and
use it to make corporate decisions.
• A large amount of data already exists and will only increase in the
future.
• This has led to the development of business analytics, also
known as data analytics or Big Data.
BETTER DECISIONS WITH DATA
• Business Analytics involves the analysis of data to help solve
business problems and make better decisions.
• By using quantitative methods to uncover the information in these
data sets and then acting on this information—again guided by
quantitative analysis—companies are able to gain a competitive
advantage.
• The goal of this course is to teach you how to use a variety of
quantitative methods to analyze data and make decisions in a very
hands-on way.
KEY POLICIES AND PROCEDURES
• Attendance: you are expected to attend class in person unless excused
for extenuating circumstances
• Bring your laptop to class
• 9 Homeworks, can drop 2. To be submitted to Canvas. Homework will be
released on Thursdays at 4PM and must be submitted by Monday 10AM
• 3 group case studies. Each group member must submit a Powerpoint and
a Spreadsheet to Canvas
• 3 in-class exams, one for each section of the course
• Re-grading requests: you have 7 days from the date an assignment is
returned (grades/answers posted) to request a review and potential
regrade
KEY POLICIES AND PROCEDURES
• No classes or homework assignments on exam week.
• Group Chat: there is only one group chat allowed for this course – a
GroupMe has been created and managed by the TA’s
• Contact the TA’s using the course email ds235brandao@utexas.edu
RISK ANALYSIS
WHY DO PROJECTS FAIL?
FAILED PROJECTS
65% of megaprojects with investment over 1 billion USD failed to
deliver the expected returns*. Some examples:
• Ford Edsel (1957)
• Crescent Dune Solar (2010)
• Sony Betamax (1975)
• Google Glass (2013)
• DeLorean DMC-12 (1981)
• Chevron Gorgon Project (2014)
• New Coke (1985)
• Amazon Fire Phone (2015)
• Motorola Iridium (1992)
• Galaxy Note 7 (2016)
• Apple Newton (1993)
• Boeing 737 Max (2020)
• Denver Airport (1995)
• Brandenburg Airport Berlin (2021)
• Segway (2001)
• California High Speed Rail (2022)
* Why projects fail (http://calleam.com/WTPF/)
“The revolutionary idea that defines the
boundary between modern times and
the past is the mastery of risk: the
notion that the future is more than a
whim of the gods and that men and
women are not passive about nature.
Until human beings discovered a way
across that boundary, the future was the
murky domain of oracles and
soothsayers who held a monopoly over
knowledge of anticipated events.
Like Prometheus, they defied the gods
and probed the darkness in search of
the light that converted the future from
an enemy into an opportunity.”*
*Against the Gods: The remarkable story of risk.
Peter Bernstein, John Wiley & Sons, Inc., NY, 1996
King of Troy and his staff planning for
the upcoming battle with the Greeks:
“I
spoke with two farmers today.
They saw an eagle flying with a
serpent clutched in its talons.
This is a sign from Apollo.”
“We will win a great victory
tomorrow. Troy is the eagle.
The Greeks are the serpent”
Archeptolemus, High Priest of Troy.
“Bird signs! You want to plan our
strategy based on bird signs?”
Hector, Prince of Troy.
SPREADSHEETS
• Business analytics tools can are easily modeled in an Excel
spreadsheet.
• The goal of this section is to get you “up to speed” in using Excel
effectively for the rest of the course.
• Most spreadsheet models involve inputs, decision variables, and
outputs.
• The inputs have given fixed values, at least for the purposes of the
model.
• The decision variables are those a decision maker controls.
• The outputs are the ultimate values of interest; they are determined by
the inputs and the decision variables.
SPREADSHEETS
• Spreadsheet modeling is the process of entering the inputs and
decision variables into a spreadsheet and then relating them
appropriately, by means of formulas, to obtain the outputs.
• After this you may
• Perform a sensitivity analysis,
• Run a simulation model
• Maximize or minimize a particular output,
• Create charts to show how certain parameters are related.
• Care should be taken when building spreadsheets, as errors are
easy to make.
UK COVID RESULTS LOST IN EXCEL
In 2020 the UK government lost track of 16,000
coronavirus cases due to an error in Excel.
In order to do contact tracing, test results
submitted by commercial firms to discover who
has the virus were put in Excel before being
uploaded to a central system.
The problem is that they used an old file format to
do this, known as XLS.
As a consequence, each template could handle
only about 65,000 rows of data rather than the
one million-plus rows that Excel is actually
capable of.
Whenever that total was reached, additional
cases were simply left off.
ENRON SPREADSHEET ANALYSIS
Felienne Hermans and Emerson Murphy
Hill analyzed over 15,000 spreadsheets
extracted from the Enron Email Archive.
These spreadsheets were used within
the Enron Corporation.
Their analysis showed that 24% of Enron
spreadsheets had at least one formula
with an Excel error.
Hermans, Felienne (2015): Enron. figshare. Journal contribution.
https://doi.org/10.6084/m9.figshare.1222882.v2
European Spreadsheet Risk Interest Group
http://www.eusprig.org/horror-stories.htm
TWO PHASES OF ANALYSIS
Phase I
• Analyst tries to envision the
possible outcomes from an
investment
• Analyst prepares estimates
and forecast
• Analysis forms the basis for
estimating an expected value
for the investment along with
NPV, IRR, and other measures
of investment worth
Phase II
• Analyst details underlying
sources of risk
• Identify value drivers and
uncertainty
• Determines probability
distribution of uncertainties
analysis
• Analyst seeks ways to mitigate
risks and monitors throughout
the life of the project
• Sensitivity of value to risks
THE ELDORADO WIND FARM
ELDORADO WIND FARM
• You are analyzing an opportunity to invest in the Eldorado wind
farm in West Texas.
• The unit will have a capacity of 40MW and a life of ten years and
cost $50M to build
• Your estimate that the electricity prices will average $100/MWh,
fixed costs will be $2.5 million per year, variable costs of energy
generation will be $8/MWh, and the load factor, which is the
efficiency of the wind turbine relative to its capacity, to be 45%.
• The expected tax rate is 25% and the discount rate is 10%
• You develop a spreadsheet with this data and determine the NPV
and the IRR.
PHASE I - EXPECTED NPV
Inputs
Discount rate
Hours of operation
Installed capacity
10% per year
8.760 per year
40 MW
Load Factor
Generation costs
Fixed costs
Electricity price
Taxes
Capital investment
45%
$8
$2.500
$100
25%
$50
per MWh
$M/yr
per MWh
($MM)
Model
Year
Annual Capacity (MWh)
0
Load Factor
Annual Generation (MWh)
Eletricity price
1
2
3
4
5
6
7
8
9
10
350.400 350.400 350.400 350.400 350.400 350.400 350.400 350.400 350.400 350.400
45%
45%
45%
45%
45%
45%
45%
45%
45%
157.680 157.680 157.680 157.680 157.680 157.680 157.680 157.680 157.680
100
100
100
100
100
100
100
100
100
45%
157.680
100
Values $1,000
Revenues
Generation costs
Fixed costs
Profit
Taxes
Capital investment
Project Cash Flows
-50.000
-50.000
15.768
-1.261
-2.500
12.007
-3.002
15.768
-1.261
-2.500
12.007
-3.002
15.768
-1.261
-2.500
12.007
-3.002
15.768
-1.261
-2.500
12.007
-3.002
15.768
-1.261
-2.500
12.007
-3.002
15.768
-1.261
-2.500
12.007
-3.002
15.768
-1.261
-2.500
12.007
-3.002
15.768
-1.261
-2.500
12.007
-3.002
15.768
-1.261
-2.500
12.007
-3.002
15.768
-1.261
-2.500
12.007
-3.002
9.005
9.005
9.005
9.005
9.005
9.005
9.005
9.005
9.005
9.005
Result
NPV
$5.331 $MM
IRR
12,4%
RISK ANALYSIS
• Phase I is complete: We have an NPV estimate of the Eldorado
Wind Farm investment
• How confident can we be that the project will unfold as we expect?
• What are the key value drivers of the project that the firm should
monitor over the life of the investment to ensure its success?
• For Phase II we use a variety of tools to address these concerns
• Scenario analysis
• Sensitivity analysis
• Simulation analysis
MODELING UNCERTAINTY
Variable
Min
Most Likely
Max
Unit
Load Factor
40%
45%
50%
%
Electricity Price
$60
$100
$140
$/MWh
Variable
Min
Max
Unit
Taxes
Fixed costs
20%
$2,400
30%
$2,600
%
$M/ano
Variable
Value1
Value2
Value3
Unit
$7
$8
$9
$/MWh
30%
40%
30%
Prob
Mean
Std Deviation
Unit
$50
$5
$MM
Generation costs
Variable
Capital Investment
SCENARIO ANALYSIS
• What would happen to the Eldorado project NPV if we applied a
pessimistic estimate of electricity price of $60?
• NPV value drops to -$23.7 million
• Negative NPV investment
• We could also analyze scenarios involving multiple sets of
changes in assumptions and forecasts.
• Evaluate the project using optimistic and pessimistic estimates for the
value drivers
SENSITIVITY ANALYSIS IN
EXCEL
• Changes in 1 or 2 Value Drivers?
• Use Data Tables
• Changes in multiple Value Drives
• Use Scenario Manager
DATA TABLES
Price
140
130
120
110
100
90
80
70
60
5.331
Link to calculated NPV
RESULTS OF DATA TABLE
Price
140
130
120
110
100
90
80
70
60
NPV
5.331
34.398
27.131
19.864
12.598
5.331
-1.935
-9.202
-16.468
-23.735
NPV
40.000
30.000
20.000
10.000
0
‐10.000
‐20.000
‐30.000
140
130
120
110
100
90
80
70
60
TWO-WAY DATA TABLE
$5.331
140
130
120
110
100
Price
90
80
70
60
Load Factor
40%
43%
45%
48%
50%
TWO-WAY DATA TABLE
$5.331
140
130
120
110
100
Price
90
80
70
60
40%
23.740
17.281
10.822
4.362
-2.097
-8.556
-15.015
-21.474
-27.933
Load Factor
43%
29.069
22.206
15.343
8.480
1.617
-5.246
-12.108
-18.971
-25.834
45%
34.398
27.131
19.864
12.598
5.331
-1.935
-9.202
-16.468
-23.735
48%
39.726
32.056
24.386
16.716
9.045
1.375
-6.295
-13.965
-21.636
50%
45.055
36.981
28.907
20.833
12.759
4.685
-3.389
-11.463
-19.536
TWO-WAY DATA TABLE
$5.331
140
130
120
110
100
Price
90
80
70
60
40%
23.740
17.281
10.822
4.362
-2.097
-8.556
-15.015
-21.474
-27.933
Load Factor
43%
29.069
22.206
15.343
8.480
1.617
-5.246
-12.108
-18.971
-25.834
45%
34.398
27.131
19.864
12.598
5.331
-1.935
-9.202
-16.468
-23.735
48%
39.726
32.056
24.386
16.716
9.045
1.375
-6.295
-13.965
-21.636
50%
45.055
36.981
28.907
20.833
12.759
4.685
-3.389
-11.463
-19.536
SENSITIVITY ANALYSIS
• Sensitivity analysis provides us the possible outcomes for a
particular range of values of a variable
• On the other hand, it assumes the other variables remain static
and provides no information on the probability of each outcome
occurring.
• For this, we need to use another tool, known as Monte Carlo
Simulation
• Unlike sensitivity analysis, Simulation considers the impact of
changes of all variables simultaneously
TIME VALUE OF MONEY
• In the Eldorado project, the net result was measured as the project
NPV
• But what is a NPV?
• NPV is the value of the sum of all project free cash flows taking
into account the time that they occur
• It is used as an indication of the amount of money a project will
contribute to the firm net of taxes after all operational and capital
costs are taken into account
• Basically, if a project earns a positive NPV it should be accepted.
TIME VALUE OF MONEY
• Most business investment decisions are based on the net result of
the forecasted investment costs and expected future revenues
• But money earned in the future is less valuable than money earned today,
since money earned today can be invested to earn interest.
• Similarly, costs incurred in the future are less “costly” than costs incurred
today.
• This is why revenues and costs cannot be simply summed up in a
multiperiod model.
• You instead discount future revenues and costs for a fair comparison with
revenues and costs incurred today.
• The sum of these discounted cash flows is known as the Net
Present Value (NPV) is the cornerstone of much of financial theory
TIME VALUE OF MONEY
• NPV
• The NPV function takes two arguments, the discount rate (entered as a
decimal, such as 0.075 for 7.5%) and a stream of cash flows.
• These cash flows are assumed to occur in consecutive years, starting
at the end of year 1.
• If there is an initial cash flow at the beginning of year 1, such as an
initial investment, it must be entered outside the NPV function.
• Decision Criteria with NPV
• NPV calculations are typically used to decide whether a project should
be undertaken.
• If the NPV is positive, the project is worth pursuing.
• If the NPV is negative, the company should look for other places to
invest its money
DS235
INTRODUCTION TO
DECISION SCIENCE
LUIZ BRANDAO
Visiting Associate Professor, The University of Texas at Austin