- 67 Views
- Updated On :

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.

Related searches for Modeling

Download Presentation
## PowerPoint Slideshow about 'Modeling' - fordon

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

### Modeling

Amirkabir University of TechnologyComputer Engineering & Information Technology Department

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.
- 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

- 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

- 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 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

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

- 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

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 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 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

- 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 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

- 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

- Heuristic methods for solving optimization problems
- Artificial Intelligence and Expert Systems
- Statistical Methods

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

- 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)

- 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 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 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

- 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

- 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

- Project planning and scheduling methods
- Milestone charts
- Gantt charts
- Critical Path Method (CPM) charts

- Project monitoring methods
- Earned value 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

- 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

Download Presentation

Connecting to Server..