Modeling & Analysis By Daniel Damaris NS

Modeling & Analysis Structure of some successful models and methodologies Decision analysis Decision trees Optimization Heuristic programming Simulation

Modeling & Analysis Topics Optimization via mathematical programming Heuristic programming Simulation Multidimensional modeling -OLAP Visual interactive modeling and visual interactive simulation Quantitative software packages - OLAP Model base management 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)

Categories of Models

Modeling for MSS Key element in most DSS Necessity in a model-based DSS Can lead to massive cost reduction/revenue increases Modeling: Statistic Model (Regression Analysis) Financial Model Optimization Model (Linear Programming)

Static & Dynamic Analysis Static Analysis Single snapshot Dynamic Analysis Dynamic models Evaluate scenarios that change over time Time dependent Trends and patterns over time Extend static models

Influence Diagram 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

Influence Diagram (cont.)

Influence Diagram (cont.)

Influence Diagram (cont.)

Influence Diagram (cont.)

Decision Support Mathematic Model

Decision Support Mathematic Model

The MSS Mathematic Model

MSS Modeling with Spreadsheet

MSS Modeling with Spreadsheet

Treating Certainty, Uncertainty & Risk

Decision Tables and Trees Single Goal Situations Decision tables Decision trees

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

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%

View Problem as a Two-Person Game Decision variables (alternatives) Uncontrollable variables (states of economy) Result variables (projected yield)

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% 6.5%

Treating Uncertainty Optimistic approach Pessimistic approach

Treating Risk Use known probabilities Risk analysis: compute expected values Can be dangerous

Decision Under Risk and Its Solution Solid Stagnation Inflation Expected Growth Value Alternatives .5 .3 .2 Bonds 12% 6% 3% 8.4% * Stocks 15% 3% -2% 8.0% CDs 6.5% 6.5% 6.5% 6.5%

Decision Tree Other methods of treating risk Multiple goals Simulation Certainty factors Fuzzy logic Multiple goals Yield, safety, and liquidity

Multiple Goals Alternatives Yield Safety Liquidity Bonds 8.4% High High Stocks 8.0% Low High CDs 6.5% Very High High

Discrete vs. Continuous Probability Distribution Daily Discrete Continuous Demand Probability 5 .1 Normally distributed with 6 .15 a mean of 7 and a 7 .3 standard deviation of 1.2 8 .25 9 .2

Linear Programming 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

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

Linear Programming Decision variables Objective function Objective function coefficients Constraints Capacities Input-output (technology) coefficients

Lindo LP Product-Mix Model << The Lindo Model: >> Max 8000 X1 + 12000 X2 Subject to Labor) 300 X1 + 500 X2 <= 200000 Budget) 10000 X1 + 15000 X2 <= 8000000 Market 1) X1 >= 100 Market 2) X2 >= 200 END

Lindo LP Product-Mix Model << Generated Solution Report >> LP OPTIMUM FOUND AT STEP 3 OBJECTIVE FUNCTION VALUE 1) 5066667.00 VARIABLE VALUE REDUCED COST X1 333.333300 .000000 X2 200.000000 .000000

Lindo LP Product-Mix Model ROW SLACK OR SURPLUS DUAL PRICES LABOR) .000000 26.666670 BUDGET) 1666667.000000 .000000 MARKET1) 233.333300 .000000 MARKET2) .000000 -1333.333000 NO. ITERATIONS= 3

Lindo LP Product-Mix Model RANGES IN WHICH THE BASIS IS UNCHANGED: OBJ COEFFICIENT RANGES VARIABLE CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE X1 8000.000 INFINITY 799.9998 X2 12000.000 1333.333 INFINITY RIGHTHAND SIDE RANGES ROW CURRENT ALLOWABLE ALLOWABLE RHS INCREASE DECREASE LABOR 200000.000 50000.000 70000.000 BUDGET 8000000.000 INFINITY 1666667.000 MARKET1 100.000 233.333 INFINITY MARKET2 200.000 140.000 200.000

Lindo LP Product-Mix Model (with computer program) << 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 = 200000, 8000000 ;

Lindo LP Product-Mix Model (with computer program) UNITCONSUMPTION = 300, 500, 10000, 15000 ; ENDDATA MAX = @SUM(COMPUTERS: 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),1000000));

Lindo LP Product-Mix Model (with computer program) << (Partial ) Solution Report >> Global optimal solution found at step: 2 Objective value: 5066667. Variable Value Reduced Cost PROFIT( CC7) 8000.000 0.0000 PROFIT( CC8) 12000.00 0.0000 QUANTITY( CC7) 333.3333 0.0000 QUANTITY( CC8) 200.0000 0.0000 MARKETLIM( CC7) 100.0000 0.0000 MARKETLIM( CC8) 200.0000 0.0000 AVAILABLE( LABOR) 200000.0 0.0000 AVAILABLE( BUDGET) 8000000. 0.0000

Lindo LP Product-Mix Model (with computer program) UNITCONSUMPTION( LABOR, CC7) 300.00 0.00 UNITCONSUMPTION( LABOR, CC8) 500.00 0.00 UNITCONSUMPTION( BUDGET, CC7) 10000. 0.00 UNITCONSUMPTION( BUDGET, CC8) 15000. 0.00 Row Slack or Surplus Dual Price 1 5066667. 1.000000 2 0.0000000 26.66667 3 1666667. 0.0000000 4 233.3333 0.0000000 5 0.0000000 -1333.333

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)

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

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

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

Heuristic Types Construction Improvement Mathematical programming Decomposition Partitioning

Modern Heuristic Methods Tabu search Genetic algorithms Simulated annealing

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

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

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)

Advantages of Simulation 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 (@Risk)

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

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

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

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

Entire Data Cube from a Query in PowerPlay

Graphical Display of the Screen (Courtesy Cognos Inc.)

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

Drilled Deep into the Data (Courtesy Cognos Inc.)

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

Visual Interactive Modeling (VIM) and Visual Interactive Simulation (VIS) 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

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

Visual Interactive Simulation (VIS) Decision makers interact with the simulated model and watch the results over time Visual interactive models and DSS VIM Queueing

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