CHAPTER 5 Modelling and Analysis 2 1. Optimization via Mathematical Programming 2 Linear programming...

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 editionCopyright 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


LP Allocation Model

4

Rational economic assumptions1. Returns from allocations can be compared in a common unit2. Independent returns3. Total return is the sum of different activities’ returns4. All data are known with certainty5. The resources are to be used in the most economical manner

Optimal solution: the best, found algorithmically


Linear Programming

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Decision variables Objective function Objective function coefficients Constraints CapacitiesInput-output (technology) coefficients

Line


Lindo LP Product-Mix ModelDSS in Focus 5.4

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<< The Lindo Model: >> MAX 8000 X1 + 12000 X2SUBJECT TO LABOR) 300 X1 + 500 X2 <= 200000 BUDGET) 10000 X1 + 15000 X2 <= 8000000MARKET1) X1 >= 100MARKET2) X2 >= 200END


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<< 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

8

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

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RANGES IN WHICH THE BASIS IS UNCHANGED: OBJ COEFFICIENT RANGESVARIABLE 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 1666667.000MARKET1 100.000 233.333 INFINITYMARKET2 200.000 140.000 200.000

Heuristic Programming

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Cuts the searchGets satisfactory solutions more quickly and less

expensivelyFinds rules to solve complex problemsFinds good enough feasible solutions to complex problemsHeuristics can be

QuantitativeQualitative (in ES)


When to Use Heuristics

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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

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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

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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


Simulation

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Technique for conducting experiments with a computer on a model of a management system

Frequently used DSS tool


Major Characteristics of Simulation

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Imitates reality and capture its richnessTechnique for conducting experimentsDescriptive, not normative toolOften to solve very complex, risky problems


Advantages of Simulation

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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

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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 (@Risk)


Limitations of Simulation

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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

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Model real system and conduct repetitive experiments1. Define problem2. Construct simulation model3. Test and validate model4. Design experiments5. Conduct experiments6. Evaluate results7. Implement solution


Simulation Types

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Probabilistic SimulationDiscrete distributionsContinuous distributionsProbabilistic simulation via Monte Carlo technique Time dependent versus time independent simulationSimulation softwareVisual simulationObject-oriented simulation


Multidimensional Modelling

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Performed in online analytical processing (OLAP)From a spreadsheet and analysis perspective2-D to 3-D to multiple-DMultidimensional modelling tools: 16-D +Multidimensional modelling - 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 (Figure 5.6a)

(Courtesy Cognos Inc.)

22 Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th editionCopyright 2001, Prentice Hall, Upper Saddle River, NJ

Graphical Display of the Screen in Figure 5.6a (Figure 5.6b)



Environmental Line of Products by Drilling Down (Figure 5.6c)



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

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User can visualize models and formulas with influence diagrams

Not cells--symbolic elements


Visual Interactive Modelling (VIS) and Visual Interactive Simulation (VIS)

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Visual interactive modelling (VIM) (DSS In Action 5.8)Also called

Visual interactive problem solvingVisual interactive modellingVisual interactive simulation

Use computer graphics to present the impact of different management decisions.

Can integrate with GIS Users perform sensitivity analysisStatic or a dynamic (animation) systems (Figure 5.7)


Generated Image of Traffic at an Intersection from the Orca Visual

Simulation Environment (Figure 5.7)(Courtesy Orca Computer, Inc.)


Visual Interactive Simulation (VIS)

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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


Quantitative Software Packages-OLAP

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Preprogrammed models can expedite DSS programming time

Some models are building blocks of other modelsStatistical packagesManagement science packagesRevenue (yield) managementOther specific DSS applications

including spreadsheet add-ins


Model Base Management

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MBMS: capabilities similar to that of DBMSBut, there are no comprehensive model base management

packagesEach organization uses models somewhat differentlyThere are many model classesWithin each class there are different solution approachesSome MBMS capabilities require expertise and reasoning


Desirable Capabilities of MBMS

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ControlFlexibilityFeedbackInterfaceRedundancy reductionIncreased consistency


MBMS Design Must Allow the DSS User to:

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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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Modelling languagesRelational MBMSObject-oriented model base and its

managementModels for database and MIS design and their

management


SUMMARY

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Models play a major role in DSSModels can be static or dynamicAnalysis is under assumed certainty, risk, or

uncertaintyInfluence diagramsSpreadsheetsDecision tables and decision trees

Spreadsheet models and results in influence diagramsOptimization: mathematical programming

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Linear programming: economic-basedHeuristic programmingSimulation - more complex situationsExpert ChoiceMultidimensional models - OLAP

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Quantitative software packages-OLAP (statistical, etc.)Visual interactive modelling (VIM) Visual interactive simulation (VIS)MBMS are like DBMSAI techniques in MBMS


CHAPTER 5 Modelling and Analysis 2 1. Optimization via Mathematical Programming 2 Linear programming...

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