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

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

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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.

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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.

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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

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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

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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?

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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= 2 r

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Example: Using the Model After adding10 feet to the circumference we have: C+10= 2 (r+d)=2 r + 2 d 10=2 d d=19.1 inches rd Earth

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Steps in Developing the Model Subsystem 1. Map functions in decision process onto models 2. Determine input / output requirements for models 3. Develop interface specifications for models with each other and with dialog and data subsystems. This step may result in additional modeling activity. 4. Obtain / develop software realizations of the models and interfaces

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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

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Some Typical Problems to Model 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

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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

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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)

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

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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

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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)

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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

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Connectionist Models or 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

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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

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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

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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

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

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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

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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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Sensitivity Analysis Dr. Saeed Shiry Amirkabir University of Technology Computer Engineering & Information Technology Department.

Sensitivity Analysis Dr. Saeed Shiry Amirkabir University of Technology Computer Engineering & Information Technology Department.

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