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CHAPTER 5 Modeling and Analysis

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**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

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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

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**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

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**Modeling for MSS Key element in most DSS**

Necessity in a model-based DSS Can lead to massive cost reduction / revenue increases

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**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)

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**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

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**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

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**Treating Certainty, Uncertainty, and Risk**

Certainty Models Uncertainty Risk

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**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)

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Analytica Influence Diagram of a Marketing Problem: The Marketing Model (Figure 5.2a) (Courtesy of Lumina Decision Systems, Los Altos, CA)

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**Analytica: Price Submodel (Figure 5**

Analytica: Price Submodel (Figure 5.2b) (Courtesy of Lumina Decision Systems, Los Altos, CA)

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**Analytica: Sales Submodel (Figure 5**

Analytica: Sales Submodel (Figure 5.2c) (Courtesy of Lumina Decision Systems, Los Altos, CA)

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**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)

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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)

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**Decision Analysis of Few Alternatives (Decision Tables and Trees)**

Single Goal Situations Decision tables Decision trees

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**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

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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%

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**View Problem as a Two-Person Game**

Payoff Table 5.2 Decision variables (alternatives) Uncontrollable variables (states of economy) Result variables (projected yield)

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**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% %

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Treating Uncertainty Optimistic approach Pessimistic approach

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**Treating Risk Use known probabilities (Table 5.3)**

Risk analysis: compute expected values Can be dangerous

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**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%

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**Other methods of treating risk**

Decision Trees Other methods of treating risk Simulation Certainty factors Fuzzy logic Multiple goals Yield, safety, and liquidity (Table 5.4)

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**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

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**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

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**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

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**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

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**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

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**Linear Programming Decision variables Objective function**

Objective function coefficients Constraints Capacities Input-output (technology) coefficients Line

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**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

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**<< Generated Solution Report >>**

LP OPTIMUM FOUND AT STEP OBJECTIVE FUNCTION VALUE 1) VARIABLE VALUE REDUCED COST X X

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**ROW SLACK OR SURPLUS DUAL PRICES**

LABOR) BUDGET) MARKET1) MARKET2) NO. ITERATIONS=

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**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

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**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)

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**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

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**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

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**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

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Simulation Technique for conducting experiments with a computer on a model of a management system Frequently used DSS tool

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**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

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**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)

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**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

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**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

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**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

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**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

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**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

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**Entire Data Cube from a Query in PowerPlay (Figure 5**

Entire Data Cube from a Query in PowerPlay (Figure 5.6a) (Courtesy Cognos Inc.)

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**Graphical Display of the Screen in Figure 5. 6a (Figure 5**

Graphical Display of the Screen in Figure 5.6a (Figure 5.6b) (Courtesy Cognos Inc.)

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**Environmental Line of Products by Drilling Down (Figure 5**

Environmental Line of Products by Drilling Down (Figure 5.6c) (Courtesy Cognos Inc.)

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Drilled Deep into the Data: Current Month, Water Purifiers, Only in North America (Figure 5.6d) (Courtesy Cognos Inc.)

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Visual Spreadsheets User can visualize models and formulas with influence diagrams Not cells--symbolic elements

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**Visual interactive modeling (VIM) (DSS In Action 5.8) Also called**

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)

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Generated Image of Traffic at an Intersection from the Orca Visual Simulation Environment (Figure 5.7) (Courtesy Orca Computer, Inc.)

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**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

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**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

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**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

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**Desirable Capabilities of MBMS**

Control Flexibility Feedback Interface Redundancy reduction Increased consistency

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**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

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Modeling languages Relational MBMS Object-oriented model base and its management Models for database and MIS design and their management

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**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)

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**Linear programming: economic-based**

Heuristic programming Simulation - more complex situations Expert Choice Multidimensional models - OLAP (More)

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**Quantitative software packages-OLAP (statistical, etc.)**

Visual interactive modeling (VIM) Visual interactive simulation (VIS) MBMS are like DBMS AI techniques in MBMS

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