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Modeling Decision Process

Modeling Decision Process. Chapter 5. The What's & Whys of Modeling. What is a model? A replica of a real system or object. An abstraction of reality Model formats: Physical Graphical Verbal Mathematical. The What's & Whys of Modeling. Why do we use models:

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Modeling Decision Process

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  1. Modeling Decision Process Chapter 5

  2. The What's & Whys of Modeling • What is a model? • A replica of a real system or object. • An abstraction of reality • Model formats: • Physical • Graphical • Verbal • Mathematical

  3. The What's & Whys of Modeling • Why do we use models: • Understanding through simplification. • Demonstrating and evaluating cause and effect relationships. • Experimenting with decision alternatives on the real system is infeasible, too expensive, too dangerous, or just plain impossible. • Need for time compression for analysis of a system or prediction of future values.

  4. The Whats & Whys of Modeling • 3 conditions under which models operate: • Certainty: outcome of each alternative is known • Uncertainty: possible outcomes of each alternative can be identified. Cannot estimate the probability of occurrence of the possible outcomes • Risk: possible outcomes of each alternative can be identified with probabilities attached

  5. Basic Model Types A survey of Models

  6. Basic Model Types • Descriptive/Predictive/Prescriptive • Static/Dynamic • Static – no explicit acknowledgement of time • Dynamic – explicit inclusion of time as an element (time dependent) • Deterministic/Stochastic (based on the use of random numbers and probability statistics to investigate problems.)

  7. Decision Model Classification • Deterministic – optimization, linear programming, financial planning, production planning, convex programming. • Probabilistic – queuing theory, linear regression, logic analysis, path analysis, time series. • Simulation – production modeling, transportation and logistics analysis, econometrics.

  8. Modeling Steps • Define & analyze the problem • Select and/or construct the model • Variables: controllable • Parameters: not controllable • Objectives: singular or multiple • Constraints: limits on possible solution • The model establishes relationships among variables, parameters, objectives, and constraints

  9. Modeling Steps • Validate the model: does the model accurately represent the real system? • Compare model output with historical or real world data • Have model evaluated by experts • Have model evaluated by decision-makers • Compare model output with expectations based on experience & expertise

  10. Modeling Steps • Acquire input data • Input data must be accurate & timely. • Use data to design modeling experiments • Solve the model / develop the solution • Test the model solution • Is it realistic ? Is it valid? • Sensitivity analysis of modeling results • Implementation of modeling results

  11. Modeling & Decision-Making Strategies • Optimization • Economic Optimization • Utility Optimization • Satisficing • “Good enough” solution • Application of Heuristics • Elimination-by-Aspects • Stepwise application of decision criteria

  12. Modeling & Decision-Making Strategies • Incrementalism • Decision are based on past decision outcomes • Mixed Scanning • Elimination of alternatives through increasing amounts of information gathering

  13. Influence Diagrams and Decision Trees • Influence Diagram • A simple graphical representation of a model • Decision Tree • Complement influence diagram • Modeling of choices and uncertainties

  14. Decisions Uncertainties Final Outcomes Alternative A Outcome A Alternative B Outcome B Decision Outcome C Alternative C Outcome D Alternative D Components of Influence Diagrams and Decision Trees

  15. Low 0.30 Medium 0.50 Sales Volume High 0.20 Uncertainty Model with Outcomes

  16. Win Contest Win large return on wager Enter Contest Lose wager Lose Contest Lose/Gain nothing Do Not Enter Contest Simple Decision Tree

  17. Uncertainty Price goes up Gain Buy Stock Loss Price goes down Lose/Gain nothing Decision Objective Do Not Buy Stock Basic Risky Decision

  18. $X Vikes Win Bet on Vikes Vikes Lose -$Y -$X Vikes Win Bet Against Vikes Vikes Lose $Y Decision Tree for Odds Forecasting Method

  19. European Vacation Win Uncertainty Game Lose -$100 European Vacation (P) Reference Game (1 – P) -$100 Decision Tree for Comparison Forecasting Method

  20. A Variety of Models • Decision Tables • Game Theory • Mathematical & Linear Programming • Simulation • Forecasting • Analytic Hierarchy Process

  21. Decision Tables • Decision Alternatives • Controllable • State of Nature • Not controllable • Uncertainty or Risk • Payoffs • Product of Decision Alternative and states of Nature

  22. Decision Tables • Decision Goal: what new store to open State of Nature Alternative recision recovery economic boom Stereo Eqpmt 10,000 30,000 60,000 Book Store 30,000 45,000 20,000 Food Store 55,000 30,000 10,000

  23. Decision Tables / Uncertainty • State of Nature • Alternative recision recovery economic boom • Stereo Eqpmt 10,000 30,000 60,000 • Book Store 30,000 45,000 20,000 • Food Store 55,000 30,000 10,000 • Optimistic Criterion: Stereo Equipment • Highest payoff in table • Pessimistic criterion: Book Store • Take best of the worst payoffs of each alternatives • Equal likelihood Criterion: Stereo Eqpmt. • Highest average payoff per alternative

  24. Decision Tables / Risk • State of Nature • Alternative recision recovery economic boom • Stereo Eqpmt 10,000 30,000 60,000 • Book Store 30,000 45,000 20,000 • Food Store 55,000 30,000 10,000 • Expected Value = Sum(Payoff * respective Prob.) • Expected Value Criterion: Book Store • E.V. Stereo Equipment = $30,000 • E.V. Book Store = $35,500 • E.V. Discount Foods = $33,500

  25. Game Theory • Two (or more) players. • Players act in self-interest only. • Players have full information on each other’s strategies or payoffs. • Zero-Sum Game: one player’s profit is the other player’s loss • Non-Zero-Sum Game: both players may win or lose simultaneously.

  26. Mathematical Programming • Modeling using mathematical equations • Usually requires solving for variables and for simultaneous equations • Linear Programming • Standard, programmable solution techniques • Non-Linear Programming • Usually requires mathematical expertise

  27. Linear Programming • Furniture Makers Production Mix Problem: • Which production combination yields the highest profit? Tables Chairs Hours Avail. Carpentry 4 hrs 3 hrs 240 hours Painting 2 hrs 1 hr 100 hours Profit/Unit $7 $5

  28. Linear Programming • Objective Function Max 7 T + 5 C • Constraints: Carpentry: 4 T + 3 C <= 240 Painting: 2 T + 1 C <=100 Non-negativity T,C >=0 • Optimal Solution: Tables = 30 Chairs = 40 Revenue = 410

  29. Simulation • “The use of a model to represent the critical characteristics of a system and to observe the system’s operations over time.” • Most common dynamic process modeling type. • Given heavy use of computers, simulation now very much resembles programming!

  30. Monte Carlo Simulation • Simulation of randomness into a system, using • Random Number Generator • Cumulative Probability Distribution

  31. Monte Carlo Simulation • The Bakery Problem: how many chocolate donuts to bake each day? • Gather sales data for 100 days Sales Frequency Probability 30 20 days 20 % 31 35 days 35 % 32 25 days 25 % 33 15 days 15 % 34 5 days 5 %

  32. Monte Carlo Simulation • Put the probabilities on the roulette wheel… 94 Sales = 30 Sales = 31 Sales = 32 Sales = 33 Sales = 34 80 95 79 99 0 79 19 79 20

  33. Monte Carlo Simulation • …and start simulating • Generate a random number: 00-99 • Find this number on the roulette-wheel. • Find the matching sales-levels Random Number Sales Level 35 31 donuts 82 33 donuts 01 30 donuts

  34. Forecasting • The prediction of future values, based on past experience. • Prediction based on personal expertise. • Prediction based on a mathematical model.

  35. Mathematical Forecasting • A variety of techniques • Linear & Nonlinear regression • Time Series / Box –Jenkins Technique • Etc • These techniques differ in predictive quality, applicability, and ease of use

  36. Forecasting - Regression • The fitting of a line to a cloud of observation-points, based on minimizing the distance between the line and the set of points Dependent variable Independent variable

  37. Forecasting - Regression • Standard linear regression function: Y = a + bX Y = dependent(forecast) variable X = independent variable a = intercept b = slope

  38. Forecasting - Regression • Multiple regression function: Y = a + b1 X1 + b2 X2 + b3 X3 Y = dependent(forecast) variable X = independent variable a = intercept b = slope

  39. Analytic Hierarchy Process • Method to solve Multiple-criteria decision-making • Specifies: • Decision goal • Decision Criteria • Decision Alternatives • Real world decision problems • multiple, diverse criteria • qualitative as well as quantitative information

  40. Analytic Hierarchy Process Comparing apples and oranges? Spend on defense or agriculture? Open the refrigerator - apple or orange?

  41. Analytic Hierarchy Process Goal Criterion Criterion Criterion Alt. 1 Alt. 2 Alt. 1 Alt. 2 Alt. 1 Alt. 2 Alt. 3 Alt. 3 Alt. 3

  42. Analytic Hierarchy Process • Each criterion is rated against each other criterion for its importance in achieving the goal • For each criterion separately, each alternative is rated against each other alternative for its capacity for satisfying the criterion • For large decisions, this will involve a large number of pair-wise comparisons

  43. Analytic Hierarchy Process • AHP computer programs determine the consistency of the pair-wise comparisons. • Sometimes, the comparison-phase will need to be repeated • If consistent, the AHP program will provide a rank-order of the alternatives

  44. AHP • Information is decomposed into a hierarchy of alternatives and criteria • Information is then synthesized to determine relative ranking of alternatives • Both qualitative and quantitative information can be compared using informed judgements to derive weights and priorities

  45. Example: Car Selection • Objective • Selecting a car • Criteria • Style, Reliability, Fuel-economy Cost? • Alternatives • Civic Coupe, Saturn Coupe, Ford Escort, Mazda Miata

  46. Hierarchical tree - Civic - Saturn - Escort - Miata - Civic - Saturn - Escort - Miata - Civic - Saturn - Escort - Miata

  47. Style Reliability Fuel Economy Style 1/1 1/2 3/1 2/1 1/1 4/1 Reliability 1/3 1/4 1/1 Fuel Economy Ranking of criteria • Weights? • AHP • pair-wise relative importance • [1:Equal, 3:Moderate, 5:Strong, 7:Very strong, 9:Extreme]

  48. Ranking of priorities • Eigenvector [Ax = x] Iterate 1. Take successive squared powers of matrix 2. Normalize the row sums Until difference between successive row sums is less than a pre-specified value

  49. 1 0.5 3 2 1 4 0.333 0.25 1.0 0.3196 0.5584 0.1220 0.3194 0.5595 0.1211 0.3196 0.5584 0.1220 3.0 1.75 8.0 5.3332 3.0 14.0 1.1666 0.6667 3.0 squared Normalized Row sums 0.3194 0.5595 0.1211 1.0 Row sums 12.75 22.3332 4.8333 39.9165 • New iteration gives normalized row sum - 0.0002 0.0011 - 0.0009 • Difference is: - =

  50. Preference • Style .3196 • Reliability .5584 • Fuel Economy .1220

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