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Decision Support and Business Intelligence
Systems(9th Ed., Prentice Hall)
Chapter 4:Modeling and Analysis
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Learning 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 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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Opening Vignette:“Model-Based Auctions Serve More
Lunches in Chile” Background: problem situation Proposed solution Results Answer and discuss the case
questions
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Modeling and Analysis Topics 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 (with
decision tables and decision trees) Optimization via mathematical programming Heuristic programming Simulation Model base management
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MSS Modeling A key element in most MSS Leads to reduced cost and increased
revenue DuPont Simulates Rail Transportation System
and Avoids Costly Capital Expenses
Procter & Gamble uses several DSS models collectively to support strategic decisions
Locating distribution centers, assignment of DCs to warehouses/customers, forecasting demand, scheduling production per product type, etc.
Fiat, Pillowtex (…operational efficiency)…
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Major 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 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 Models 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:Treating Certainty, Uncertainty and 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 Risk
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Influence Diagrams (Posted on the Course 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: Relationships
Amount inCDs
InterestCollected
Price
Sales
Sales
~Demand
CERTAINTY
UNCERTAINTY
RANDOM (risk) variable: Place a tilde (~) above the variable’s name
The shape of the arrow
indicates the type of
relationship
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Influence Diagrams: Example
~Amount used inAdvertisement
Unit Price
Units Sold
Unit Cost
Fixed Cost
Income
Expenses
Profit
An influence diagram for the profit model
Profit = Income – ExpenseIncome = UnitsSold * UnitPriceUnitsSold = 0.5 * Advertisement ExpenseExpenses = UnitsCost * UnitSold + FixedCost
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Influence Diagrams: Software 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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Analytica Influence Diagram of a Marketing
Problem: The Marketing Model
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Analytica: The Price Submodel
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Analytica: The Sales Submodel
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MSS Modeling with Spreadsheets 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 example: Simple loan calculation of monthly payments
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Excel spreadsheet - Dynamic model example: Simple loan calculation of monthly payments and effects of prepayment
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Decision Analysis: A Few AlternativesSingle 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 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: 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%
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Payoff Decision variables (alternatives) Uncontrollable variables (states of
economy) Result variables (projected yield) Tabular representation:
Investment Example: Decision Table
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Investment Example: Treating Uncertainty Optimistic approach Pessimistic approach Treating Risk:
Use known probabilities Risk analysis: compute expected values
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Decision Analysis: A Few Alternatives Other methods of treating risk
Simulation, Certainty factors, Fuzzy logic
Multiple goals Yield, safety, and liquidity
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MSS Mathematical Models
Decision Variables
MathematicalRelationships
UncontrollableVariables
Result Variables
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
Dependent Variables
IntermediateVariables
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Optimization via Mathematical Programming 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 Characteristics1.Limited quantity of economic resources2.Resources are used in the production of
products or services3.Two or more ways (solutions, programs)
to use the resources4.Each activity (product or service) yields
a return in terms of the goal5.Allocation is usually restricted by
constraints
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Line
Linear Programming Steps 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 ExampleThe 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 ($) 10,000 15,000 <= 8,000,000 /moUnits 1 >= 100Units 1 >= 200Profit ($) 8,000 12,000 Max
Objective: Maximize Total Profit / Month
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LP Solution
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LP Solution Decision Variables:
X1: unit of CC-7X2: unit of CC-8
Objective Function:Maximize Z (profit)Z=8000X1+12000X2
Subject To300X1 + 500X2 200K10000X1 + 15000X2 8000KX1 100X2 200
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Sensitivity, What-if, and Goal Seeking Analysis 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 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 - SEARCH
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Traveling Salesman Problem 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 12 6 60 9 20,160
20 1.22 1018
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When to Use HeuristicsWhen 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 Methods
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Simulation 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 Simulation
!
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Advantages 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 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 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 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 Modeling (VIM) / Visual Interactive Simulation (VIS)
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Model Base Management 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
Relations MBMS Object-oriented MBMS
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End of the Chapter
Questions / Comments…
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