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Amirkabir University of Technology Computer Engineering & Information Technology Department. Modeling. Dr. Saeed Shiry. Outline. What is a model? Using models to support decision making. Modeling. Transforming the real-world problem into an appropriate prototype structure.

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Modeling

Amirkabir University of TechnologyComputer Engineering & Information Technology Department

Modeling

Dr. Saeed Shiry


Outline
Outline

  • What is a model?

  • Using models to support decision making


Modeling1
Modeling

  • 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
Introduction

  • 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
Models and DSS

  • 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
Models

  • Models are constructed from:

    • 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
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
Example: Intuition versus Model

  • 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

r

d

Earth

Example: Using the Model

  • After adding10 feet to the circumference we have:

    C+10= 2p(r+d)=2pr + 2pd

     10=2pd  d=19.1 inches


Steps in developing the model subsystem
Steps in Developingthe Model Subsystem

  • 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 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
Some Typical Problems to Model

  • Evaluate benefits of proposed policy against costs

  • Forecastvalue 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
A Brief Tour of Modeling Options

  • 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
Decision Analysis Methods

  • 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
Other Model System Technologies

  • Heuristic methods for solving optimization problems

  • Artificial Intelligence and Expert Systems

  • Statistical Methods


Example heuristics
Example Heuristics

  • Greedy hill climber

    • Begin with a candidate solution

    • Change in direction that most improves solution

    • Never go downhill

  • Decomposition

    • Break problem into simpler subproblems

    • Solve subproblems separately

    • Recompose solutions

  • Heuristic search

    • Search space can be constructed as tree

    • Depth first, breadth first, best first: policies for deciding how to expand the tree

  • Approximate and adjust

    • 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
Natural Analogy Heuristics

  • Nature is an efficient optimizer

    • Apply methods based on analogy to natural systems

  • Simulated annealing

    • Modify current solution randomly and evaluate objective function

    • Accept new solution if better than old. Otherwise, accept with probability depending on system "temperature"

    • 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)

    • Apply evolutionary operators to change solutions from generation to generation (e.g., crossover, mutation)


Types of statistical models some examples
Types of Statistical Models (some examples)

  • Regression

    • Estimate an equation relating a dependent variable to one or more independent variables

    • Example: examine relationship between students’ college GPA and high school grades

  • Analysis of variance

    • 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

    • Examine trends and/or cycles in data over time

    • Example: predict price of a stock


Connectionist models or neural networks
Connectionist Modelsor Neural Networks

  • Connectionist philosophy

    • Complex behavior comes from interactions among simple computational units

    • Natural analogy: simulate intelligent behavior using process modeled after human brains

  • A neural network consists of

    • a large set of computationally simple units or nodes

    • links or connections between nodes

  • Learning occurs by adjusting strengths of connections

    • supervised learning: regression

    • unsupervised learning: clustering


Machine learning
Machine Learning

  • 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

    • Extract regularities from samples of data

    • Construct knowledge structures (typically rules) that characterize the regularities

  • Evaluate performance against samples not seen before


Data mining
Data Mining

  • 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
Economic Methods

  • Microeconomic models

    • Analyze economic systems in which firms / agents are modeled as utility maximizers

    • Static: analyze equilibrium

    • Dynamic: analyze behavior over time

  • Game theory

    • Multiple players each have possible actions and objective functions

    • An economy is a many-person game

  • Macroeconomic models (econometrics)

    • Statistical estimation of relationships between economic variables

  • Cost / benefit analysis

    • Benefits of proposed policy option are quantified in dollar terms and evaluated against cost


Management science methods
Management Science Methods

  • Project planning and scheduling methods

    • Milestone charts

    • Gantt charts

    • Critical Path Method (CPM) charts

  • Project monitoring methods

    • Earned value analysis


Sensitivity analysis
Sensitivity Analysis

  • 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

    • 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

    • Sensitivity analysis examines dependence of results on these assumptions


Exercise
Exercise

  • 2 Papers from Book: Handbook of Marketing Decision Models

    • 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


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