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: 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.

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

Basic Model Types A survey of Models

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.)

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.

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

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

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

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

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

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

Components of Influence Diagrams and Decision Trees DecisionsUncertainties Final Outcomes Decision Alternative A Alternative B Alternative C Alternative D Outcome A Outcome B Outcome C Outcome D

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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!

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

Monte Carlo Simulation The Bakery Problem: how many chocolate donuts to bake each day? Gather sales data for 100 days Sales Frequency Probability 3020 days20 % 3135 days35 % 3225 days25 % 3315 days15 % 34 5 days 5 %

Monte Carlo Simulation Put the probabilities on the roulette wheel… Sales = 30 Sales = 31 Sales = 32 Sales = 33 Sales = 34

Monte Carlo Simulation …and start simulating Generate a random number: Find this number on the roulette-wheel. Find the matching sales-levels Random Number Sales Level donuts donuts donuts

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

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

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

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

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

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

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

Analytic Hierarchy Process Goal Criterio n Alt. 1 Alt. 2 Alt. 3

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

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

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

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

Hierarchical tree - Civic - Saturn - Escort - Miata - Civic - Saturn - Escort - Miata - Civic - Saturn - Escort - Miata

Ranking of criteria Weights? AHP pair-wise relative importance [1:Equal, 3:Moderate, 5:Strong, 7:Very strong, 9:Extreme] StyleReliabilityFuel Economy Style Reliability Fuel Economy 1/11/23/1 2/11/14/1 1/31/41/1

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

squared Row sums Normalized Row sums New iteration gives normalized row sum Difference is: =

Preference Style.3196 Reliability.5584 Fuel Economy.1220

Ranking alternatives Style Civic Saturn Escort 1/1 1/44/1 1/6 4/1 1/14/1 1/4 1/4 1/4 1/11/5 Miata6/1 4/1 5/1 1/1 CivicSaturnEscortMiata Reliability Civic Saturn Escort 1/1 2/15/1 1/1 1/2 1/1 3/1 2/1 1/5 1/3 1/11/4 Miata1/1 1/2 4/1 1/1 CivicSaturnEscortMiata Eigenvector

Fuel Economy (quantitative information) Civic Saturn Escort Miata Miles/gallon Normalized

- Civic Saturn Escort Miata Civic Saturn Escort Miata Civic Saturn Escort Miata.2480

Ranking of alternatives Style Reliability Fuel Economy Civic Escort Miata Saturn * =

Handling Costs Dangers of including Cost as another criterion political, emotional responses? Separate Benefits and Costs hierarchical trees Costs vs. Benefits evaluation Alternative with best benefits/costs ratio

Cost vs. Benefits MIATA$18K CIVIC$12K SATURN$15K ESCORT $9K Cost Normalized Cost Cost/Benefits Ratio

Complex decisions Many levels of criteria and sub-criteria

Application areas strategic planning resource allocation source selection, program selection business policy etc., etc., etc.. AHP software (ExpertChoice) computations sensitivity analysis graphs, tables Group AHP

Model Management Model Base Management System Basic Features: Tracking a large variety of models, model- types, model-versions, purposes, etc. Provide access to model & model descriptions. Provide for new models and model updates to be placed in Model Base.

Model Management Model Base Management System Advanced Features Suggest appropriate models to decision maker. Relate models to required data from DSS database Allow decision maker to customize models or build new models