Decision Support Systems Modeling and Analysis. Modified from Decision Support Systems and Business Intelligence Systems 9E. 1-2 Learning Objectives Understand

Decision Support Decision Support SystemsSystems

Modeling and AnalysisModeling and Analysis

Modified from Decision Support Systems and Business Intelligence Systems 9E.

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Learning ObjectivesLearning Objectives Understand the basic concepts of

management support system (MSS) modeling

Describe how MSS models interact with data and the users

Understand the well-known model classes and decision making with a few alternatives

Describe how spreadsheets can be used for MSS modeling and solution

Explain the basic concepts of optimization, simulation and heuristics; when to use which


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Learning ObjectivesLearning Objectives Describe how to structure a linear

programming model Understand how search methods are used

to solve MSS models Explain the differences among algorithms,

blind search, and heuristics Describe how to handle multiple goals Explain what is meant by sensitivity

analysis, what-if analysis, and goal seeking Describe the key issues of model

management


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Modeling and Analysis Modeling and Analysis TopicsTopics

Modeling for MSS (a critical component) Static and dynamic models Treating certainty, uncertainty, and risk Influence diagrams (in the posted PDF file) MSS modeling in spreadsheets Decision analysis of a few alternatives Optimization via mathematical

programming Heuristic programming Simulation Model base management


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Major Modeling IssuesMajor Modeling Issues Problem identification and environmental

analysis (information collection) Variable identification

Influence diagrams, cognitive maps Forecasting/predicting

More information leads to better prediction Multiple models: A MSS can include

several models, each of which represents a different part of the decision-making problem Categories of models >>>

Model management


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Categories of ModelsCategories of ModelsCategory Objective Techniques

Optimization of problems with few alternatives

Find the best solution from a small number of alternatives

Decision tables, decision trees

Optimization via algorithm

Find the best solution from a large number of alternatives using a step-by-step process

Linear and other mathematical programming models

Optimization via an analytic formula

Find the best solution in one step using a formula

Some inventory models

Simulation Find a good enough solution by experimenting with a dynamic model of the system

Several types of simulation

Heuristics Find a good enough solution using “common-sense” rules

Heuristic programming and expert systems

Predictive and other models

Predict future occurrences, what-if analysis, …

Forecasting, Markov chains, financial, …


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Static and Dynamic Static and Dynamic ModelsModels

Static Analysis Single snapshot of the situation Single interval Steady state

Dynamic Analysis Dynamic models Evaluate scenarios that change over time Time dependent Represents trends and patterns over time More realistic: Extends static models


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Decision Making:Decision Making:Treating Certainty, Uncertainty Treating Certainty, Uncertainty and Riskand Risk

Certainty Models Assume complete knowledge All potential outcomes are known May yield optimal solution

Uncertainty Several outcomes for each decision Probability of each outcome is unknown Knowledge would lead to less uncertainty

Risk analysis (probabilistic decision making) Probability of each of several outcomes

occurring Level of uncertainty => Risk (expected value)


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Certainty, Uncertainty and RiskCertainty, Uncertainty and Risk


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Influence Diagrams Influence Diagrams (Posted on the Course (Posted on the Course Website)Website)

Graphical representations of a model“Model of a model”

A tool for visual communication Some influence diagram packages create and

solve the mathematical model Framework for expressing MSS model

relationshipsRectangle = a decision variableCircle = uncontrollable or intermediate variableOval = result (outcome) variable: intermediate or final

Variables are connected with arrows indicates the direction of influence (relationship)


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Influence Diagrams: Influence Diagrams: RelationshipsRelationships

Amount inCDs

InterestCollected

Price

Sales

Sales

~Demand

CERTAINTY

UNCERTAINTY

RANDOM (risk) variable: Place a tilde (~) above the variable’s name

The shape of The shape of the arrow the arrow

indicates the indicates the type of type of

relationshiprelationship


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Influence Diagrams: Influence Diagrams: ExampleExample

~Amount used inAdvertisement

Unit Price

Units Sold

Unit Cost

Fixed Cost

Income

Expenses

Profit

An influence diagram for the profit modelAn influence diagram for the profit model

Profit = Income – ExpenseProfit = Income – ExpenseIncome = UnitsSold * UnitPriceIncome = UnitsSold * UnitPriceUnitsSold = 0.5 * Advertisement ExpenseUnitsSold = 0.5 * Advertisement ExpenseExpenses = UnitsCost * UnitSold + FixedCostExpenses = UnitsCost * UnitSold + FixedCost


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Influence Diagrams: Influence Diagrams: SoftwareSoftware

Analytica, Lumina Decision Systems Supports hierarchical (multi-level) diagrams

DecisionPro, Vanguard Software Co. Supports hierarchical (tree structured) diagrams

DATA Decision Analysis, TreeAge Software Includes influence diagrams, decision trees and

simulation Definitive Scenario, Definitive Software

Integrates influence diagrams and Excel, also supports Monte Carlo simulations

PrecisionTree, Palisade Co. Creates influence diagrams and decision trees

directly in an Excel spreadsheet


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MSS Modeling with MSS Modeling with SpreadsheetsSpreadsheets

Spreadsheet: most popular end-user modeling tool

Flexible and easy to use Powerful functions

Add-in functions and solvers Programmability (via macros) What-if analysis Goal seeking Simple database management Seamless integration of model and data Incorporates both static and dynamic

models Examples: Microsoft Excel, Lotus 1-2-3


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Excel spreadsheet - static model Excel spreadsheet - static model example: Simple loan calculation of example: Simple loan calculation of monthly paymentsmonthly payments

1)1(

)1(

)1(

n

n

n

i

iiPA

iPF


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Excel spreadsheet - Excel spreadsheet - Dynamic model Dynamic model example: example: Simple loan Simple loan calculation of calculation of monthly payments monthly payments and effects of and effects of prepaymentprepayment


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Decision Analysis: A Few Decision Analysis: A Few AlternativesAlternatives

Single Goal Situations Decision tables

Multiple criteria decision analysis

Features include decision variables (alternatives), uncontrollable variables, result variables

Decision trees Graphical representation of

relationships Multiple criteria approach Demonstrates complex

relationships Cumbersome, if many

alternatives exists


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Decision TablesDecision 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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Investment Example: Investment Example: Possible SituationsPossible 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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Payoff Decision variables (alternatives) Uncontrollable variables (states of

economy) Result variables (projected yield)

Tabular representation:

Investment Example: Investment Example: Decision TableDecision Table


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Investment Example: Investment Example: Treating UncertaintyTreating Uncertainty Optimistic approach Pessimistic approach Treating Risk:

Use known probabilities Risk analysis: compute expected

values


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Decision Analysis: A Few Decision Analysis: A Few AlternativesAlternatives

Other methods of treating risk Simulation, Certainty factors,

Fuzzy logic Multiple goals

Yield, safety, and liquidity


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MSS Mathematical ModelsMSS Mathematical Models

Decision Decision VariablesVariables

MathematicalMathematicalRelationshipsRelationships

UncontrollableUncontrollableVariablesVariables

Result Result VariablesVariables

Non-Quantitative Models (Qualitative) Captures symbolic relationships between decision variables,

uncontrollable variables and result variables Quantitative Models: Mathematically links decision

variables, uncontrollable variables, and result variables Decision variables describe alternative choices. Uncontrollable variables are outside decision-maker’s control Result variables are dependent on chosen combination of decision

variables and uncontrollable variables

Independent Variables

Independent Variables

Dependent VariablesDependent Variables

IntermediateIntermediateVariablesVariables


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Optimization Optimization via Mathematical via Mathematical ProgrammingProgramming

Mathematical Programming A family of tools designed to help solve managerial problems in which the decision maker must allocate scarce resources among competing activities to optimize a measurable goal

Optimal solution: The best possible solution to a modeled problem Linear programming (LP): A mathematical

model for the optimal solution of resource allocation problems. All the relationships are linear


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LP Problem LP Problem CharacteristicsCharacteristics

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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LineLine

Linear Programming Linear Programming StepsSteps

1. Identify the … Decision variables Objective function Objective function coefficients Constraints

Capacities / Demands

2. Represent the model LINDO: Write mathematical formulation EXCEL: Input data into specific cells in

Excel

3. Run the model and observe the results


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LP ExampleLP Example

The Product-Mix Linear Programming Model MBI Corporation Decision: How many computers to build next month? Two types of mainframe computers: CC7 and CC8 Constraints: Labor limits, Materials limit, Marketing

lower limits

CC7 CC8 Rel LimitLabor (days) 300 500 <= 200,000 /moMaterials ($) 10,00015,000<= 8,000,000 /moUnits 1 >= 100Units 1 >= 200Profit ($) 8,000 12,000Max

Objective: Maximize Total Profit / Month


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LP SolutionLP Solution


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LP SolutionLP Solution

Decision Variables:X1: unit of CC-7

X2: unit of CC-8 Objective Function:

Maximize Z (profit)Z=8000X1+12000X2

Subject To300X1 + 500X2 200K

10000X1 + 15000X2 8000KX1 100

X2 200


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Sensitivity, What-if, and Sensitivity, What-if, and Goal Seeking Goal Seeking AnalysisAnalysis

Sensitivity Assesses impact of change in inputs on

outputs Eliminates or reduces variables Can be automatic or trial and error

What-if Assesses solutions based on changes in

variables or assumptions (scenario analysis) Goal seeking

Backwards approach, starts with goal Determines values of inputs needed to

achieve goal Example is break-even point determination


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Heuristic ProgrammingHeuristic Programming

Cuts the search space Gets satisfactory

solutions more quickly and less expensively

Finds good enough feasible solutions to very complex problems

Heuristics can be Quantitative Qualitative (in ES)

Traveling Salesman Problem >>>


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Heuristic Programming - Heuristic Programming - SEARCHSEARCH


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Traveling Salesman Traveling Salesman ProblemProblem

What is it? A traveling salesman must visit

customers in several cities, visiting each city only once, across the country. Goal: Find the shortest possible route

Total number of unique routes (TNUR):TNUR = (1/2) (Number of Cities – 1)!Number of Cities TNUR

5 126 609 20,160

20 1.22 1018


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When to Use HeuristicsWhen to Use Heuristics

When to Use Heuristics Inexact or limited input data Complex reality Reliable, exact algorithm not

available Computation time excessive For making quick decisions

Limitations of Heuristics Cannot guarantee an optimal solution


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Tabu search Intelligent search algorithm

Genetic algorithms Survival of the fittest

Simulated annealing Analogy to Thermodynamics

Modern Heuristic MethodsModern Heuristic Methods


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SimulationSimulation

Technique for conducting experiments with a computer on a comprehensive model of the behavior of a system

Frequently used in DSS tools


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Imitates reality and capture its richness

Technique for conducting experiments Descriptive, not normative tool Often to “solve” very complex

problems

!Simulation is normally used only when a problem is too complex to be treated using numerical optimization techniques

Major Characteristics of Major Characteristics of SimulationSimulation


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Advantages of SimulationAdvantages of Simulation

The theory is fairly straightforward Great deal of time compression Experiment with different alternatives The model reflects manager’s perspective Can handle wide variety of problem types Can include the real complexities of

problems Produces important performance measures Often it is the only DSS modeling tool for

non-structured problems


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Limitations of SimulationLimitations of Simulation

Cannot guarantee an optimal solution Slow and costly construction process Cannot transfer solutions and

inferences to solve other problems (problem specific)

So easy to explain/sell to managers, may lead overlooking analytical solutions

Software may require special skills


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Simulation MethodologySimulation Methodology Model real system and conduct repetitive

experiments. Steps:

1. Define problem 5. Conduct experiments2. Construct simulation model 6. Evaluate results3. Test and validate model 7. Implement solution4. Design experiments


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Simulation TypesSimulation Types Stochastic vs. Deterministic Simulation

In stochastic simulations: We use distributions (Discrete or Continuous probability distributions)

Time-dependent vs. Time-independent Simulation Time independent stochastic simulation via

Monte Carlo technique (X = A + B) Discrete event vs. Continuous simulation Steady State vs. Transient Simulation Simulation Implementation

Visual simulation Object-oriented simulation


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Visual interactive modeling (VIM) Also called Visual interactive problem solving Visual interactive modeling Visual interactive simulation

Uses computer graphics to present the impact of different management decisions

Often integrated with GIS Users perform sensitivity analysis Static or a dynamic (animation)

systems

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


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End of the Chapter End of the Chapter

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Decision Support Systems Modeling and Analysis. Modified from Decision Support Systems and Business Intelligence Systems 9E. 1-2 Learning Objectives Understand