Modeling Analysis By Daniel Damaris NS LOGO LOGO
Modeling & Analysis By Daniel Damaris NS LOGO
LOGO Modeling & Analysis v. Structure of some successful models and methodologies § § § Decision analysis Decision trees Optimization Heuristic programming Simulation
LOGO Modeling & Analysis Topics v Optimization via v Modeling for MSS v Static and dynamic models mathematical programming v Heuristic programming v Treating certainty, v Simulation uncertainty, and risk v Multidimensional modeling v Influence diagrams OLAP v MSS modeling in v Visual interactive modeling spreadsheets and visual interactive v Decision analysis of a few alternatives (decision tables simulation v Quantitative software and trees) packages - OLAP v Model base management
LOGO Categories of Models
LOGO Modeling for MSS v Key element in most DSS v Necessity in a model-based DSS v Can lead to massive cost reduction/revenue increases v Modeling: § Statistic Model (Regression Analysis) § Financial Model § Optimization Model (Linear Programming)
LOGO Static & Dynamic Analysis v. Static Analysis § Single snapshot v. Dynamic Analysis § § § Dynamic models Evaluate scenarios that change over time Time dependent Trends and patterns over time Extend static models
LOGO Influence Diagram v Graphical representations of a model v Model of a model v Visual communication v Some packages create and solve the mathematical model v 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
LOGO Influence Diagram (cont. )
LOGO Influence Diagram (cont. )
LOGO Influence Diagram (cont. )
LOGO Influence Diagram (cont. )
LOGO Decision Support Mathematic Model
LOGO Decision Support Mathematic Model
LOGO The MSS Mathematic Model
LOGO MSS Modeling with Spreadsheet
LOGO MSS Modeling with Spreadsheet
LOGO Treating Certainty, Uncertainty & Risk
Decision Tables and Trees LOGO Single Goal Situations v Decision tables v Decision trees
LOGO Decision Tables v. Investment example v. One goal: maximize the yield after one year v. Yield depends on the status of the economy (the state of nature) § Solid growth § Stagnation § Inflation
LOGO 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%
LOGO View Problem as a Two-Person Game v Decision variables (alternatives) v Uncontrollable variables (states of economy) v Result variables (projected yield)
Investment Problem Decision Table Model LOGO States of Nature Solid Stagnation Inflation Alternatives Growth Bonds 12% 6% 3% Stocks 15% 3% -2% CDs 6. 5%
LOGO Treating Uncertainty v Optimistic approach v Pessimistic approach
LOGO Treating Risk v Use known probabilities v Risk analysis: compute expected values v Can be dangerous
Decision Under Risk and Its Solution LOGO Solid Stagnation Growth Inflation Expected Value Alternatives . 5 . 3 . 2 Bonds 12% 6% 3% Stocks 15% 3% -2% 8. 0% CDs 6. 5% 8. 4% *
LOGO v Other methods of treating risk § Simulation § Certainty factors § Fuzzy logic v Multiple goals v Yield, safety, and liquidity Decision Tree
Multiple Goals LOGO Alternatives Yield Safety Liquidity Bonds 8. 4% High Stocks 8. 0% Low High CDs 6. 5% Very High
LOGO Discrete vs. Continuous Probability Distribution Daily Demand Discrete Probability Continuous 5 6 7 8 9 . 1. 15. 3. 25. 2 Normally distributed with a mean of 7 and a standard deviation of 1. 2
LOGO 1. 2. 3. 4. Linear Programming Allocation Problem Characteristics Limited quantity of economic resources Resources are used in the production of products or services Two or more ways (solutions, programs) to use the resources Each activity (product or service) yields a return in terms of the goal 5. Allocation is usually restricted by constraints
LOGO LP Allocation Model v 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 v Optimal solution: the best, found algorithmically
LOGO Linear Programming v Decision variables v Objective function coefficients v Constraints v Capacities v Input-output (technology) coefficients
LOGO Lindo LP Product-Mix Model << The Lindo Model: >> Max 8000 X 1 + 12000 X 2 Subject to Labor) 300 X 1 + 500 X 2 <= 200000 Budget) 10000 X 1 + 15000 X 2 <= 8000000 Market 1) X 1 >= 100 Market 2) X 2 >= 200 END
Lindo LP Product-Mix Model LOGO << Generated Solution Report >> LP OPTIMUM FOUND AT STEP 3 OBJECTIVE FUNCTION VALUE 1) VARIABLE X 1 X 2 5066667. 00 VALUE 333300 200. 000000 REDUCED COST. 000000
Lindo LP Product-Mix Model LOGO ROW LABOR) BUDGET) MARKET 1) MARKET 2) SLACK OR SURPLUS. 000000 1666667. 000000 233. 333300. 000000 NO. ITERATIONS= 3 DUAL PRICES 26. 666670. 000000 -1333. 333000
Lindo LP Product-Mix Model LOGO RANGES IN WHICH THE BASIS IS UNCHANGED: VARIABLE X 1 X 2 OBJ COEFFICIENT RANGES CURRENT ALLOWABLE COEF INCREASE DECREASE 8000. 000 INFINITY 799. 9998 12000. 000 1333. 333 INFINITY RIGHTHAND SIDE RANGES ROW CURRENT RHS LABOR 200000. 000 BUDGET 8000000. 000 MARKET 1 100. 000 MARKET 2 200. 000 ALLOWABLE INCREASE 50000. 000 INFINITY 233. 333 140. 000 ALLOWABLE DECREASE 70000. 000 1666667. 000 INFINITY 200. 000
LOGO Lindo LP Product-Mix Model (with computer program) << The Model >>> MODEL: ! The Product-Mix Example; SETS: COMPUTERS /CC 7, CC 8/ : PROFIT, QUANTITY, MARKETLIM ; RESOURCES /LABOR, BUDGET/ : AVAILABLE ; RESBYCOMP(RESOURCES, COMPUTERS) : UNITCONSUMPTION ; ENDSETS DATA: PROFIT MARKETLIM = 8000, 12000, 200; AVAILABLE = 200000, 8000000 ;
LOGO 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 @FOR( COMPUTERS( J): @BND(MARKETLIM(J), QUANTITY(J), 1000000));
LOGO Lindo LP Product-Mix Model (with computer program) << (Partial ) Solution Report >> Global optimal solution found at step: Objective value: 5066667. Variable PROFIT( CC 7) PROFIT( CC 8) QUANTITY( CC 7) QUANTITY( CC 8) MARKETLIM( CC 7) MARKETLIM( CC 8) AVAILABLE( LABOR) AVAILABLE( BUDGET) Value 8000. 000 12000. 00 3333 200. 0000 100. 0000 200000. 0 8000000. 2 Reduced Cost 0. 0000 0. 0000
LOGO Lindo LP Product-Mix Model (with computer program) UNITCONSUMPTION( Row 1 2 3 4 5 LABOR, CC 7) LABOR, CC 8) BUDGET, CC 7) BUDGET, CC 8) Slack or Surplus 5066667. 0. 0000000 1666667. 233. 3333 0. 0000000 300. 00 500. 00 10000. 15000. Dual Price 1. 000000 26. 66667 0. 0000000 -1333. 333 0. 00
LOGO Heuristic Programming v Cuts the search v Gets satisfactory solutions more quickly and less expensively v Finds rules to solve complex problems v Finds good enough feasible solutions to complex problems v Heuristics can be § Quantitative § Qualitative (in ES)
LOGO 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
LOGO 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
LOGO 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 v Heuristics successfully applied to vehicle routing
LOGO Heuristic Types v. Construction v. Improvement v. Mathematical programming v. Decomposition v. Partitioning
LOGO Modern Heuristic Methods v. Tabu search v. Genetic algorithms v. Simulated annealing
LOGO Simulation v Technique for conducting experiments with a computer on a model of a management system v Frequently used DSS tool
LOGO Major Characteristics of Simulation v Imitates reality and capture its richness v Technique for conducting experiments v Descriptive, not normative tool v Often to solve very complex, risky problems
LOGO 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)
LOGO 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)
LOGO 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
LOGO 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
LOGO Simulation Types v 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
LOGO Multidimensional Modeling v Performed in online analytical processing (OLAP) v From a spreadsheet and analysis perspective v 2 -D to 3 -D to multiple-D v Multidimensional modeling tools: 16 -D + v Multidimensional modeling - OLAP (Figure 5. 6) v Tool can compare, rotate, and slice and dice corporate data across different management viewpoints
LOGO Entire Data Cube from a Query in Power. Play
LOGO Graphical Display of the Screen (Courtesy Cognos Inc. )
LOGO Environmental Line of Products by Drilling Down (Courtesy Cognos Inc. )
LOGO Drilled Deep into the Data (Courtesy Cognos Inc. )
LOGO Visual Spreadsheets v User can visualize models and formulas with influence diagrams v Not cells--symbolic elements
LOGO Visual Interactive Modeling (VIM) and Visual Interactive Simulation (VIS) v Visual interactive modeling (VIM) Also called § Visual interactive problem solving § Visual interactive modeling § Visual interactive simulation v Use computer graphics to present the impact of different management decisions. v Can integrate with GIS v Users perform sensitivity analysis v Static or a dynamic (animation) systems
LOGO Generated Image of Traffic at an Intersection from the Orca Visual Simulation Environment (Courtesy Orca Computer, Inc. )
LOGO Visual Interactive Simulation (VIS) v Decision makers interact with the simulated model and watch the results over time v Visual interactive models and DSS § VIM § Queueing
LOGO
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