CHAPTER 5 Modeling and Analysis.

CHAPTER 5 Modeling and Analysis

Copyright 2001, Prentice Hall, Upper Saddle River, NJ
Modeling and Analysis Major DSS component Model base and model management CAUTION - Difficult Topic Ahead Familiarity with major ideas Basic concepts and definitions Tool--influence diagram Model directly in spreadsheets Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Modeling and Analysis Structure of some successful models and methodologies Decision analysis Decision trees Optimization Heuristic programming Simulation New developments in modeling tools / techniques Important issues in model base management Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Modeling and Analysis Topics
Modeling for MSS Static and dynamic models Treating certainty, uncertainty, and risk Influence diagrams MSS modeling in spreadsheets Decision analysis of a few alternatives (decision tables and trees) Optimization via mathematical programming Heuristic programming Simulation Multidimensional modeling -OLAP Visual interactive modeling and visual interactive simulation Quantitative software packages - OLAP Model base management Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Modeling for MSS Key element in most DSS Necessity in a model-based DSS Can lead to massive cost reduction / revenue increases Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Good Examples of MSS Models
DuPont rail system simulation model (opening vignette) Procter & Gamble optimization supply chain restructuring models (case application 5.1) Scott Homes AHP select a supplier model (case application 5.2) IMERYS optimization clay production model (case application 5.3) Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Major Modeling Issues Problem identification Environmental analysis Variable identification Forecasting Multiple model use Model categories or selection (Table 5.1) Model management Knowledge-based modeling Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Static and Dynamic Models
Static Analysis Single snapshot Dynamic Analysis Dynamic models Evaluate scenarios that change over time Time dependent Trends and patterns over time Extend static models Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Treating Certainty, Uncertainty, and Risk
Certainty Models Uncertainty Risk Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Influence Diagrams Graphical representations of a model Model of a model Visual communication Some packages create and solve the mathematical model Framework for expressing MSS model relationships Rectangle = a decision variable Circle = uncontrollable or intermediate variable Oval = result (outcome) variable: intermediate or final Variables connected with arrows Example (Figure 5.1) Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Analytica Influence Diagram of a Marketing Problem: The Marketing Model (Figure 5.2a) (Courtesy of Lumina Decision Systems, Los Altos, CA) Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Analytica: Price Submodel (Figure 5.2b) (Courtesy of Lumina Decision Systems, Los Altos, CA) Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Analytica: Sales Submodel (Figure 5.2c) (Courtesy of Lumina Decision Systems, Los Altos, CA) Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

MSS Modeling in Spreadsheets
Spreadsheet: most popular end-user modeling tool Powerful functions Add-in functions and solvers Important for analysis, planning, modeling Programmability (macros) (More) Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

What-if analysis Goal seeking Simple database management Seamless integration Microsoft Excel Lotus 1-2-3 Excel spreadsheet static model example of a simple loan calculation of monthly payments (Figure 5.3) Excel spreadsheet dynamic model example of a simple loan calculation of monthly payments and effects of prepayment (Figure 5.4) Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Decision Analysis of Few Alternatives (Decision Tables and Trees)
Single Goal Situations Decision tables Decision trees Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Decision Tables Investment example One goal: maximize the yield after one year Yield depends on the status of the economy (the state of nature) Solid growth Stagnation Inflation Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Possible Situations 1. If solid growth in the economy, bonds yield 12%; stocks 15%; time deposits 6.5% 2. If stagnation, bonds yield 6%; stocks 3%; time deposits 6.5% 3. If inflation, bonds yield 3%; stocks lose 2%; time deposits yield 6.5% Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

View Problem as a Two-Person Game
Payoff Table 5.2 Decision variables (alternatives) Uncontrollable variables (states of economy) Result variables (projected yield) Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Table 5.2: Investment Problem Decision Table Model
States of Nature Solid Stagnation Inflation Alternatives Growth Bonds 12% 6% 3% Stocks 15% 3% -2% CDs 6.5% 6.5% % Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Treating Uncertainty Optimistic approach Pessimistic approach Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Treating Risk Use known probabilities (Table 5.3) Risk analysis: compute expected values Can be dangerous Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Table 5.3: Decision Under Risk and Its Solution
Solid Stagnation Inflation Expected Growth Value Alternatives Bonds 12% 6% 3% 8.4% * Stocks 15% 3% -2% 8.0% CDs 6.5% 6.5% % 6.5% Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Decision Trees Other methods of treating risk Simulation Certainty factors Fuzzy logic Multiple goals Yield, safety, and liquidity (Table 5.4) Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Table 5.4: Multiple Goals Alternatives Yield Safety Liquidity Bonds 8.4% High High Stocks 8.0% Low High CDs 6.5% Very High High Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Table 5.5: Discrete vs. Continuous Probability Distribution
Daily Discrete Continuous Demand Probability Normally distributed with a mean of 7 and a standard deviation of 1.2 9 .2 Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Optimization via Mathematical Programming
Linear programming (LP) Used extensively in DSS Mathematical Programming Family of tools to solve managerial problems in allocating scarce resources among various activities to optimize a measurable goal Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

LP Allocation Problem Characteristics
1. Limited quantity of economic resources 2. Resources are used in the production of products or services 3. Two or more ways (solutions, programs) to use the resources 4. Each activity (product or service) yields a return in terms of the goal 5. Allocation is usually restricted by constraints Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

LP Allocation Model Rational economic assumptions 1. Returns from allocations can be compared in a common unit 2. Independent returns 3. Total return is the sum of different activities’ returns 4. All data are known with certainty 5. The resources are to be used in the most economical manner Optimal solution: the best, found algorithmically Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Linear Programming Decision variables Objective function Objective function coefficients Constraints Capacities Input-output (technology) coefficients Line Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Lindo LP Product-Mix Model DSS in Focus 5.4
<< The Lindo Model: >> MAX X X2 SUBJECT TO LABOR) X X2 <= BUDGET) X X2 <= MARKET1) X1 >= 100 MARKET2) X2 >= 200 END Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

<< Generated Solution Report >> LP OPTIMUM FOUND AT STEP OBJECTIVE FUNCTION VALUE 1) VARIABLE VALUE REDUCED COST X X Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

ROW SLACK OR SURPLUS DUAL PRICES LABOR) BUDGET) MARKET1) MARKET2) NO. ITERATIONS= Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

RANGES IN WHICH THE BASIS IS UNCHANGED: OBJ COEFFICIENT RANGES VARIABLE CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE X INFINITY X INFINITY RIGHTHAND SIDE RANGES ROW CURRENT ALLOWABLE ALLOWABLE RHS INCREASE DECREASE LABOR BUDGET INFINITY MARKET INFINITY MARKET Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Lingo LP Product-Mix Model DSS in Focus 5.5
<< The Model >>> MODEL: ! The Product-Mix Example; SETS: COMPUTERS /CC7, CC8/ : PROFIT, QUANTITY, MARKETLIM ; RESOURCES /LABOR, BUDGET/ : AVAILABLE ; RESBYCOMP(RESOURCES, COMPUTERS) : UNITCONSUMPTION ; ENDSETS DATA: PROFIT MARKETLIM = 8000, 100, 12000, 200; AVAILABLE = , ; Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

UNITCONSUMPTION = 300, 500, 10000, ; ENDDATA MAX PROFIT * QUANTITY) ; @FOR( RESOURCES( I): @SUM( COMPUTERS( J): UNITCONSUMPTION( I,J) * QUANTITY(J)) <= AVAILABLE( I)); @FOR( COMPUTERS( J): QUANTITY(J) >= MARKETLIM( J)); ! Alternative @BND(MARKETLIM(J), QUANTITY(J), )); Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

<< (Partial ) Solution Report >> Global optimal solution found at step: Objective value: Variable Value Reduced Cost PROFIT( CC7) PROFIT( CC8) QUANTITY( CC7) QUANTITY( CC8) MARKETLIM( CC7) MARKETLIM( CC8) AVAILABLE( LABOR) AVAILABLE( BUDGET) Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

UNITCONSUMPTION( LABOR, CC7) UNITCONSUMPTION( LABOR, CC8) UNITCONSUMPTION( BUDGET, CC7) UNITCONSUMPTION( BUDGET, CC8) Row Slack or Surplus Dual Price Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Heuristic Programming
Cuts the search Gets satisfactory solutions more quickly and less expensively Finds rules to solve complex problems Finds good enough feasible solutions to complex problems Heuristics can be Quantitative Qualitative (in ES) Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

When to Use Heuristics 1. Inexact or limited input data 2. Complex reality 3. Reliable, exact algorithm not available 4. Computation time excessive 5. To improve the efficiency of optimization 6. To solve complex problems 7. For symbolic processing 8. For making quick decisions Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Advantages of Heuristics
1. Simple to understand: easier to implement and explain 2. Help train people to be creative 3. Save formulation time 4. Save programming and storage on computers 5. Save computational time 6. Frequently produce multiple acceptable solutions 7. Possible to develop a solution quality measure 8. Can incorporate intelligent search 9. Can solve very complex models Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Limitations of Heuristics
1. Cannot guarantee an optimal solution 2. There may be too many exceptions 3. Sequential decisions might not anticipate future consequences 4. Interdependencies of subsystems can influence the whole system Heuristics successfully applied to vehicle routing Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Heuristic Types Construction Improvement Mathematical programming Decomposition Partitioning Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Modern Heuristic Methods
Tabu search Genetic algorithms Simulated annealing Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Simulation Technique for conducting experiments with a computer on a model of a management system Frequently used DSS tool Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Major Characteristics of Simulation
Imitates reality and capture its richness Technique for conducting experiments Descriptive, not normative tool Often to solve very complex, risky problems Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Advantages of Simulation
1. Theory is straightforward 2. Time compression 3. Descriptive, not normative 4. MSS builder interfaces with manager to gain intimate knowledge of the problem 5. Model is built from the manager's perspective 6. Manager needs no generalized understanding. Each component represents a real problem component (More) Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

7. Wide variation in problem types 8. Can experiment with different variables 9. Allows for real-life problem complexities 10. Easy to obtain many performance measures directly 11. Frequently the only DSS modeling tool for nonstructured problems 12. Monte Carlo add-in spreadsheet packages Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Limitations of Simulation
1. Cannot guarantee an optimal solution 2. Slow and costly construction process 3. Cannot transfer solutions and inferences to solve other problems 4. So easy to sell to managers, may miss analytical solutions 5. Software is not so user friendly Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Simulation Methodology
Model real system and conduct repetitive experiments 1. Define problem 2. Construct simulation model 3. Test and validate model 4. Design experiments 5. Conduct experiments 6. Evaluate results 7. Implement solution Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Simulation Types Probabilistic Simulation Discrete distributions Continuous distributions Probabilistic simulation via Monte Carlo technique Time dependent versus time independent simulation Simulation software Visual simulation Object-oriented simulation Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Multidimensional Modeling
Performed in online analytical processing (OLAP) From a spreadsheet and analysis perspective 2-D to 3-D to multiple-D Multidimensional modeling tools: 16-D + Multidimensional modeling - OLAP (Figure 5.6) Tool can compare, rotate, and slice and dice corporate data across different management viewpoints Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Entire Data Cube from a Query in PowerPlay (Figure 5.6a) (Courtesy Cognos Inc.) Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Graphical Display of the Screen in Figure 5.6a (Figure 5.6b) (Courtesy Cognos Inc.) Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Environmental Line of Products by Drilling Down (Figure 5.6c) (Courtesy Cognos Inc.) Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Drilled Deep into the Data: Current Month, Water Purifiers, Only in North America (Figure 5.6d) (Courtesy Cognos Inc.) Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Visual Spreadsheets User can visualize models and formulas with influence diagrams Not cells--symbolic elements Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Visual Interactive Modeling (VIS) and Visual Interactive Simulation (VIS) Visual interactive modeling (VIM) (DSS In Action 5.8) Also called Visual interactive problem solving Visual interactive modeling Visual interactive simulation Use computer graphics to present the impact of different management decisions. Can integrate with GIS Users perform sensitivity analysis Static or a dynamic (animation) systems (Figure 5.7) Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Generated Image of Traffic at an Intersection from the Orca Visual Simulation Environment (Figure 5.7) (Courtesy Orca Computer, Inc.) Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Visual Interactive Simulation (VIS)
Decision makers interact with the simulated model and watch the results over time Visual interactive models and DSS VIM (Case Application W5.1 on book’s Web site) Queueing Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Quantitative Software Packages-OLAP
Preprogrammed models can expedite DSS programming time Some models are building blocks of other models Statistical packages Management science packages Revenue (yield) management Other specific DSS applications including spreadsheet add-ins Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Model Base Management MBMS: capabilities similar to that of DBMS But, there are no comprehensive model base management packages Each organization uses models somewhat differently There are many model classes Within each class there are different solution approaches Some MBMS capabilities require expertise and reasoning Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Desirable Capabilities of MBMS
Control Flexibility Feedback Interface Redundancy reduction Increased consistency Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

MBMS Design Must Allow the DSS User to:
1. Access and retrieve existing models. 2. Exercise and manipulate existing models 3. Store existing models 4. Maintain existing models 5. Construct new models with reasonable effort Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Modeling languages Relational MBMS Object-oriented model base and its management Models for database and MIS design and their management Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

SUMMARY Models play a major role in DSS Models can be static or dynamic Analysis is under assumed certainty, risk, or uncertainty Influence diagrams Spreadsheets Decision tables and decision trees Spreadsheet models and results in influence diagrams Optimization: mathematical programming (More) Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Linear programming: economic-based Heuristic programming Simulation - more complex situations Expert Choice Multidimensional models - OLAP (More) Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

Quantitative software packages-OLAP (statistical, etc.) Visual interactive modeling (VIM) Visual interactive simulation (VIS) MBMS are like DBMS AI techniques in MBMS Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

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