Modeling

1. Amirkabir University of TechnologyComputer Engineering & Information Technology Department Modeling Dr. Saeed Shiry

2. Outline • What is a model? • Using models to support decision making

3. 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.

4. 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.

5. 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

6. 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

7. 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?

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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)

15. Other Model System Technologies • Heuristic methods for solving optimization problems • Artificial Intelligence and Expert Systems • Statistical Methods

16. 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

17. 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)

18. 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

19. 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

20. 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

21. 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

22. 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

23. Management Science Methods • Project planning and scheduling methods • Milestone charts • Gantt charts • Critical Path Method (CPM) charts • Project monitoring methods • Earned value analysis

24. 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

25. 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