Transcript Model

Modeling
Dr. Saeed Shiry
Amirkabir University of Technology
Computer Engineering & Information Technology Department
Outline
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What is a model?
Using models to support decision making
Modeling
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Transforming the real-world problem into an
appropriate prototype structure.
We attempt to model reality to see how changes
can affect it – hopefully for the better.
Any approach to decision making is a balancing
act between an appropriate accounting of relevant
reality and not getting bogged down in details that
only obscure or mislead.
Introduction
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There is a clear truism in George Box’s 1979 statement
that “all models are wrong, some models are useful.”
Models of reality are, by their very nature, incomplete
depictions and tend to be misleading.
Still worse can be models and associated solutions
that faithfully attempt to do justice to reality by
incorporating many facets of reality into their
structures. Unfortunately, a common result is an
overemphasis of certain issues in decision making.
Models and DSS
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A model is a representation of a system which can be used
to answer questions about the system.
A DSS uses computer models in conjunction with human
judgment:
 Performs computations that assist user with decision
problem
 Design is based on a model of how human user does / ought
to solve decision problem
Model subsystem can be:
 completely automated
 partially automated
 manual with automated support for information entry,
retrieval and display
Models
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Models are constructed from:
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Past data on the system
Past data related to the system
Judgment of subject matter experts
Judgment of experienced model builders
Example: A Simple Model
This example shows how a model can help
shed light on a problem whose solution is
counterintuitive
 Assume that the earth is perfectly round and
smooth, and a string has been placed
completely around equator. Suppose that
some one cuts the string, adds 10 feet, and
distribute such that the string is equally
distant from the earth. Can a mouse crawl
under the string?
Example: Intuition versus
Model
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Many people may believe that as only 10 feet
is added to such a long string the distance
that the lengthened string will be above the
earth would be negligible. Therefore it might
be difficult for a mouse to crawl under the
string!
However using a simple model will help o find
the solution. For a circle he relation for
circumference is: C= 2pr
Example: Using the Model
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After adding10 feet to the circumference we
have:
C+10= 2p(r+d)=2pr + 2pd
 10=2pd  d=19.1 inches
r
Earth
d
Steps in Developing
the Model Subsystem
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Map functions in decision process onto models
Determine input / output requirements for
models
Develop interface specifications for models
with each other and with dialog and data
subsystems. This step may result in additional
modeling activity.
Obtain / develop software realizations of the
models and interfaces
Models for Supporting
Decisions
Models can support decisions in a number of ways:
 Assist with problem formulation
 Find optimal or approximately optimal (according to model)
solution
 Assist in composing solutions to subproblems
 Portray decision-relevant information in a way that makes
decision implications clear
 Draw conclusions from data (data  information
knowledge)
 Predict results of proposed solution(s)
 Evaluate proposed solution(s)
 Can you think of others?
 Different modeling technologies are useful for different
kinds of support
Some Typical Problems to
Model
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Evaluate benefits of proposed policy against costs
Forecast value of variable at some time in the future
Evaluate whether likely return justifies investment
Decide where to locate a facility
Decide how many people to hire & where to assign
them
Plan activities and resources for a project
Develop repair, replacement & maintenance policy
Develop inventory control policy
A Brief Tour of Modeling Options
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A wide variety of modeling approaches is
available
DSS developer must be familiar with broad array
of methods
It is important to know the class of problems for
which each method is appropriate
It is important to know the limitations of each
method
It is important to know the limitations of your
knowledge and when to call in an expert
Decision Analysis Methods
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Value Models: Multiattribute Utility
Uncertainty Models: Decision Trees
 A structured representation for options and outcomes
 A computational architecture for solving for expected utility
 Best with “asymmetric” problems (different actions lead to
qualitatively different worlds)
Uncertainty Models: Influence Diagrams
 A structured representation for options, outcomes and
values
 A computational architecture for solving for expected utility
 Best with “symmetric” problems (different actions lead to
worlds with qualitatively similar structure)
Other Model System
Technologies
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Heuristic methods for solving
optimization problems
Artificial Intelligence and Expert Systems
Statistical Methods
Example Heuristics
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Greedy hill climber
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Decomposition
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Break problem into simpler subproblems
Solve subproblems separately
Recompose solutions
Heuristic search
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Begin with a candidate solution
Change in direction that most improves solution
Never go downhill
Search space can be constructed as tree
Depth first, breadth first, best first: policies for deciding how to
expand the tree
Approximate and adjust
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Use cheap / fast / available approximation method
Adjust solution e.g., use linear programming on integer problem and
move to nearest integer solution
Natural Analogy Heuristics
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Nature is an efficient optimizer
 Apply methods based on analogy to natural systems
Simulated annealing
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Modify current solution randomly and evaluate objective function
 Accept new solution if better than old. Otherwise, accept with
probability depending on system "temperature"
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Gradually decrease temperature (make it harder to accept worse
solutions)
Evolutionary algorithms
 Maintain "population" of solutions
 Solutions reproduce with # offspring depending on objective
function (survival of fittest)
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Apply evolutionary operators to change solutions from
generation to generation (e.g., crossover, mutation)
Types of Statistical Models
(some examples)
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Regression
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Analysis of variance
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Estimate an equation relating a dependent variable to one or
more independent variables
Example: examine relationship between students’ college GPA
and high school grades
Evaluate whether average value of a response is different for
different groups of individuals
Example: evaluate whether patients taking a drug do better
than patients taking a placebo
Time series models
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Examine trends and/or cycles in data over time
Example: predict price of a stock
Connectionist Models
or Neural Networks
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Connectionist philosophy
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A neural network consists of
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Complex behavior comes from interactions among simple
computational units
Natural analogy: simulate intelligent behavior using process
modeled after human brains
a large set of computationally simple units or nodes
links or connections between nodes
Learning occurs by adjusting strengths of connections
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supervised learning: regression
unsupervised learning: clustering
Machine Learning
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Machine learning is the discipline devoted to
development of methods that allow computers to
“learn” (improve performance based on results of
past performance)
Machine learning draws from artificial intelligence,
traditional computer science, and statistics
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Extract regularities from samples of data
Construct knowledge structures (typically rules) that
characterize the regularities
Evaluate performance against samples not seen
before
Data Mining
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The IT revolution has created vast archives of data
Data mining is a collection of methods from statistics,
computer science, engineering, and artificial intelligence for
sifting through large stores of data to identify interesting
patterns
There is a great deal of overlap with machine learning
 In machine learning the emphasis is on using data to
improve performance on a well-defined task according to
some performance measure (induction)
 In data mining the emphasis is on identifying interesting
patterns in large volumes of data (discovery)
 Both machine learning and data mining make heavy use of
statistical methods
The term data mining is sometimes used pejoratively to
mean fishing for spurious patterns and concocting post-hoc
explanations
Economic Methods
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Microeconomic models
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Game theory
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Multiple players each have possible actions and objective functions
An economy is a many-person game
Macroeconomic models (econometrics)
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Analyze economic systems in which firms / agents are modeled as utility
maximizers
Static: analyze equilibrium
Dynamic: analyze behavior over time
Statistical estimation of relationships between economic variables
Cost / benefit analysis
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Benefits of proposed policy option are quantified in dollar terms and
evaluated against cost
Management Science Methods
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Project planning and scheduling methods
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Milestone charts
Gantt charts
Critical Path Method (CPM) charts
Project monitoring methods
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Earned value analysis
Sensitivity Analysis
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Sensitivity analysis means varying the inputs to a
model to see how the results change
Sensitivity analysis is a very important component of
exploratory use of models
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model is not regarded as “correct”
sensitivity analysis helps user explore implications of
alternate assumptions
human computer interface for sensitivity analysis is difficult
to design well
In many models we need to make assumptions we
cannot test
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Sensitivity analysis examines dependence of results on
these assumptions
Exercise
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2 Papers from Book: Handbook of Marketing
Decision Models
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Advances in Marketing Management Support
Systems
Neural Nets and Genetic Algorithms in Marketing
Models of Customer Value
Models for Sales Management Decisions
Or Any other papers by your Choice