CHAPTER 5 Modelling and Analysis 2 1

Optimization via Mathematical Programming 2 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 3 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 4 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 5 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 Lindo LP Product-Mix Model DSS in Focus > MAX 8000 X X2 SUBJECT TO LABOR) 300 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

7 > LP OPTIMUM FOUND AT STEP 3 OBJECTIVE FUNCTION VALUE 1) VARIABLE VALUE REDUCED COST X X

8 ROW SLACK OR SURPLUS DUAL PRICES LABOR) BUDGET) MARKET1) MARKET2) NO. ITERATIONS= 3

9 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

Heuristic Programming 10 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 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 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 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

Simulation 14 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 15 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 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

17 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 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 19 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 20 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 Modelling 21 Performed in online analytical processing (OLAP) From a spreadsheet and analysis perspective 2-D to 3-D to multiple-D Multidimensional modelling tools: 16-D + Multidimensional modelling - 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.)PowerPlay 22 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.) 23 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.) 24 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.) 25

Visual Spreadsheets 26 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 Modelling (VIS) and Visual Interactive Simulation (VIS) 27 Visual interactive modelling (VIM) (DSS In Action 5.8) Also called Visual interactive problem solving Visual interactive modelling 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.) 28 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) 29 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 30 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 31 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 32 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: 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

34 Modelling 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 35 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

36 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

37 Quantitative software packages-OLAP (statistical, etc.) Visual interactive modelling (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