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Samenvatting slides Decision analytics (behaald resultaat 16/20)
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Summary of 44 pages for the course Decision analytics at VUB
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Samenvatting decision analyticsChapter 1: Modeling
1.Modeling
Introduction
Data driven decision making
– Fact- or evidence-based versus intuitive decision making
– “In today’s complex economical society companies have to rely on quantitative
information to make daily decisions in a rational and optimal manner”
• Six Sigma
• Competing on analytics: The science of winning
• Profit-driven business analytics
Available information vs. required information:
– Available information may be transformed or used to obtain or estimate the
required information
– How to transform or turn input data into output data?
various approaches discussed in this course
• Data? = Input data
• Information? = Output data
• Knowledge?
• Insight?
• Wisdom
Management science
“Management science, also referred to as decision science or operations research, is an
interdisciplinary branch of applied mathematics devoted to optimal decision planning on
quantitative grounds.”
“It uses various scientific research-based principles, strategies, and analytical methods
including mathematical modeling, statistics, and numerical algorithms to improve an
organization’s ability to enact rational and meaningful management decisions by arriving at
optimal or near optimal solutions to complex decision problems.”
• “In short, management science helps businesses and organizations to achieve their
goals using scientific methods.”
Beer, S., 1968. Management science: the business use of operations research. Science and
technology series. Aldus, London, U.K.
• Scientific methods: modeling, sensitivity analysis, optimization, simulation
– Underneath these methods: mathematics, statistics, numerical algorithms, …
,Model
General definition of a model: a model is a simplified and/or idealized representation of
(part of) reality
– Physical model: prototype
– Graphical model:
– Numerical (mathematical, statistical, computer) model:
model type of interest in this course, generally referred to as model
Set of equations or formulas
Linear regression model: 𝑦 = 𝛽$ + 𝛽&𝑥& + 𝛽 ( 𝑥 (
– Credit risk modeling, fraud detection, churn prediction,…
Modeled (part of) reality: system
System
General definition of a system: in it’s simplest form, a system is a clearly delineated set of
interrelated components which cooperate to realize a set of common objectives
– Broadly applicable concept: cell, human, eco-system, planet, planetary system, …
– Boundaries depend on the adopted perspective
– Subsystems
– Interface – interaction
Model
A model is some description of a system. It might be a drawing, such as the plans for a
house. It might be a description, like the estate’ agent’s details of a house. It might be a
prototype of some kind, …”
“A model is not the thing it is describing. It is some representation of the thing. But in some
very real sense, it looks like the thing.”
Models are written using a notation, e.g. mathematical formulas, pseudo- code, UML, etc.
A model is used anytime calculations are made to obtain certain results
Why do we build models?
– Analysis and decision making
– Communication
– Planning
– Simulation (see next slide), which on its turn allows
– Optimization
–…
Not an end in itself! Models are a tool
Simulation
,A model may allow to simulate the workings of a system and to analyse the system’s
behaviour under varying conditions
The results of simulations performed with a model may help to answer complex business
questions, and to optimize decision making:
– Traffic simulation model: tunnel or bridge to close the beltway around Antwerp
(Oosterweelverbinding), impact on mobility, health, etc.
– Investment analysis: solar energy
– Portfolio optimization in the financial industry: insurance companies
– Cfr. Chapter 3: Searching for good solutions
Model versus algorithm
An algorithm is an ordered sequence of unambiguous, executable steps that describe a
finite process
An algorithm transforms an input into a required output, incorporates a solution strategy or
method, and precisely defines the exact steps to be executed to arrive at a result
A model may be implemented as an algorithm, and an algorithm may represent a model,
but an algorithm is not necessarily a model
– See definition of a model: representation of part of reality
– A mathematical or computer model may be induced by an algorithm, i.e., may be
the output of an algorithm)
Modeling
Modeling is the activity of building a model
– Challenging!
– Technical skills
– Domain knowledge
– Level of complexity?
– User requirements, objectives?
– Iterative approach
– Unexpected results?
– Quality of a model – evaluation?
A model starts from available, raw or basic data: the inputs
By using the inputs in calculations or operations, a number of end-results are obtained: the
output
In other words: the model transforms the input into output
Intermediate- versus end- results or output: depends on perspective
(Numerical) model formally defined
– We have a number of inputs
– Sequentially a series of outputs is obtained using equations of following type:
new output = f(inputs,previous outputs)
Previous outputs explicitly mentioned, but result as well from inputs!
previous output = f(input)
, – Coherence assumption: at each moment all necessary information is available for
the calculation at hand
• Excel: circular reference error
– Values (inputs,outputs) used in the calculations (model) are considered to be
variable
– (Independent) variables, inputs, features, attributes, characteristics, …
– If they would all be constant, why use a model?
Classification of inputs:
– Constant inputs
• Nature constants: g - gravity constant
• Project constants: workforce at our disposal, production capacity, investment
amount, roof surface to install solar panels, …
– Remark: may be variable across projects!
– Models may be re-used for different projects with updated values for
project constants (not for nature constants)
• Technical parameters: efficiency of solar cells, U-level of insulation material,
…
– Control variables
• Value of a control variable can be set, chosen (decision variables)
– Without restrictions
– Within an interval
– Within a half-open interval
– Typically: value to be optimized
Why?
With what aim?
– Uncertain inputs
• Approximate inputs
– Cost per production unit (cost of natural resources)
– Inflation
– – …?
• Inherently uncertain inputs
– – Amount of sun-hours
– – …?
• Difference is subtle, yet existent
• Nonetheless have to be treated in the same manner, taken into account in a
similar fashion
STOCHASTIC VARIABLE
In probability and statistics, a random variable, random quantity, aleatory variable, or
stochastic variable is a variable whose possible values are outcomes of a random
phenomenon.
• Model building is a creative process, with a lot of freedom
for the modeler
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