decision support and business intelligence...
TRANSCRIPT
Decision Support and Business Intelligence
Systems (9th Ed., Prentice Hall)
Chapter 4: Modeling and Analysis
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Learning Objectives
n Understand the basic concepts of management support system (MSS) modeling
n Describe how MSS models interact with data and the users
n Understand the well-known model classes and decision making with a few alternatives
n Describe how spreadsheets can be used for MSS modeling and solution
n Explain the basic concepts of optimization, simulation and heuristics; when to use which
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Learning Objectives
n Describe how to structure a linear programming model
n Understand how search methods are used to solve MSS models
n Explain the differences among algorithms, blind search, and heuristics
n Describe how to handle multiple goals n Explain what is meant by sensitivity analysis,
what-if analysis, and goal seeking n Describe the key issues of model management
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Opening Vignette:
“Model-Based Auctions Serve More Lunches in Chile”
n Background: problem situation n Proposed solution n Results n Answer and discuss the case questions
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Modeling and Analysis Topics
n Modeling for MSS (a critical component) n Static and dynamic models n Treating certainty, uncertainty, and risk n Influence diagrams (in the posted PDF file) n MSS modeling in spreadsheets n Decision analysis of a few alternatives (with decision
tables and decision trees) n Optimization via mathematical programming n Heuristic programming n Simulation n Model base management
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MSS Modeling
n A key element in most MSS n Leads to reduced cost and increased revenue
n DuPont Simulates Rail Transportation System and Avoids Costly Capital Expenses
n Procter & Gamble uses several DSS models collectively to support strategic decisions
n Locating distribution centers, assignment of DCs to warehouses/customers, forecasting demand, scheduling production per product type, etc.
n Fiat, Pillowtex (…operational efficiency)…
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Major Modeling Issues
n Problem identification and environmental analysis (information collection)
n Variable identification n Influence diagrams, cognitive maps
n Forecasting/predicting n More information leads to better prediction
n Multiple models: A MSS can include several models, each of which represents a different part of the decision-making problem n Categories of models >>>
n Model management
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Categories of Models Category 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
n Static Analysis n Single snapshot of the situation n Single interval n Steady state
n Dynamic Analysis
n Dynamic models n Evaluate scenarios that change over time n Time dependent n Represents trends and patterns over time n More realistic: Extends static models
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Decision Making: Treating Certainty, Uncertainty and Risk
n Certainty Models n Assume complete knowledge n All potential outcomes are known n May yield optimal solution
n Uncertainty n Several outcomes for each decision n Probability of each outcome is unknown n Knowledge would lead to less uncertainty
n Risk analysis (probabilistic decision making) n Probability of each of several outcomes occurring n 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)
n Graphical representations of a model “Model of a model”
n A tool for visual communication n Some influence diagram packages create and solve
the mathematical model n Framework for expressing MSS model relationships
Rectangle = a decision variable Circle = uncontrollable or intermediate variable Oval = result (outcome) variable: intermediate or final
Variables are connected with arrows à 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 – Expense Income = UnitsSold * UnitPrice UnitsSold = 0.5 * Advertisement Expense Expenses = UnitsCost * UnitSold + FixedCost
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Influence Diagrams: Software
n Analytica, Lumina Decision Systems n Supports hierarchical (multi-level) diagrams
n DecisionPro, Vanguard Software Co. n Supports hierarchical (tree structured) diagrams
n DATA Decision Analysis, TreeAge Software n Includes influence diagrams, decision trees and simulation
n Definitive Scenario, Definitive Software n Integrates influence diagrams and Excel, also supports
Monte Carlo simulations
n PrecisionTree, Palisade Co. n 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 n Spreadsheet: most popular end-user modeling tool n Flexible and easy to use n Powerful functions
n Add-in functions and solvers n Programmability (via macros) n What-if analysis n Goal seeking n Simple database management n Seamless integration of model and data n Incorporates both static and dynamic models n 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 Alternatives Single Goal Situations Decision tables
n Multiple criteria decision analysis n Features include decision
variables (alternatives), uncontrollable variables, result variables
n Decision trees n Graphical representation of
relationships n Multiple criteria approach n Demonstrates complex
relationships n Cumbersome, if many
alternatives exists
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Decision Tables
n Investment example
n One goal: maximize the yield after one year
n Yield depends on the status of the economy (the state of nature)
n Solid growth n Stagnation n 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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n Payoff Decision variables (alternatives) n Uncontrollable variables (states of economy) n Result variables (projected yield)
n Tabular representation:
Investment Example: Decision Table
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Investment Example: Treating Uncertainty n Optimistic approach n Pessimistic approach n Treating Risk:
n Use known probabilities n Risk analysis: compute expected values
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Decision Analysis: A Few Alternatives
n Other methods of treating risk n Simulation, Certainty factors, Fuzzy logic
n Multiple goals n Yield, safety, and liquidity
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MSS Mathematical Models
Decision Variables
Mathematical Relationships
Uncontrollable Variables
Result Variables
n Non-Quantitative Models (Qualitative) n Captures symbolic relationships between decision variables, uncontrollable
variables and result variables
n Quantitative Models: Mathematically links decision variables, uncontrollable variables, and result variables n Decision variables describe alternative choices. n Uncontrollable variables are outside decision-maker’s control n Result variables are dependent on chosen combination of decision variables
and uncontrollable variables
Dependent Variables
Intermediate Variables
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Optimization via Mathematical Programming
n 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
n Optimal solution: The best possible solution to a modeled problem n 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 Characteristics
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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Line
Linear Programming Steps
n 1. Identify the … n Decision variables n Objective function n Objective function coefficients n Constraints
n Capacities / Demands
n 2. Represent the model n LINDO: Write mathematical formulation n EXCEL: Input data into specific cells in Excel
n 3. Run the model and observe the results
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LP Example
The Product-Mix Linear Programming Model n MBI Corporation n Decision: How many computers to build next month? n Two types of mainframe computers: CC7 and CC8 n Constraints: Labor limits, Materials limit, Marketing lower limits
CC7 CC8 Rel Limit
Labor (days) 300 500 <= 200,000 /mo Materials ($) 10,000 15,000 <= 8,000,000 /mo Units 1 >= 100 Units 1 >= 200 Profit ($) 8,000 12,000 Max Objective: Maximize Total Profit / Month
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LP Solution
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LP Solution
n Decision Variables: X1: unit of CC-7 X2: unit of CC-8
n Objective Function: Maximize Z (profit) Z=8000X1+12000X2
n Subject To 300X1 + 500X2 ≤ 200K 10000X1 + 15000X2 ≤ 8000K X1 ≥ 100 X2 ≥ 200
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Sensitivity, What-if, and Goal Seeking Analysis
n Sensitivity n Assesses impact of change in inputs on outputs n Eliminates or reduces variables n Can be automatic or trial and error
n What-if n Assesses solutions based on changes in variables or
assumptions (scenario analysis) n Goal seeking
n Backwards approach, starts with goal n Determines values of inputs needed to achieve goal n Example is break-even point determination
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Heuristic Programming
n Cuts the search space n Gets satisfactory solutions more
quickly and less expensively n Finds good enough feasible
solutions to very complex problems
n Heuristics can be n Quantitative n Qualitative (in ES)
n Traveling Salesman Problem >>>
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Heuristic Programming - SEARCH
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Traveling Salesman Problem
n What is it? n A traveling salesman must visit customers in
several cities, visiting each city only once, across the country. Goal: Find the shortest possible route
n 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 Heuristics
When to Use Heuristics n Inexact or limited input data n Complex reality n Reliable, exact algorithm not available n Computation time excessive n For making quick decisions
Limitations of Heuristics n Cannot guarantee an optimal solution
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n Tabu search n Intelligent search algorithm
n Genetic algorithms n Survival of the fittest
n Simulated annealing n Analogy to Thermodynamics
Modern Heuristic Methods
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Simulation
n Technique for conducting experiments with a computer on a comprehensive model of the behavior of a system
n Frequently used in DSS tools
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n Imitates reality and capture its richness n Technique for conducting experiments n Descriptive, not normative tool n 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
n The theory is fairly straightforward n Great deal of time compression n Experiment with different alternatives n The model reflects manager’s perspective n Can handle wide variety of problem types n Can include the real complexities of problems n Produces important performance measures n Often it is the only DSS modeling tool for
non-structured problems
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Limitations of Simulation
n Cannot guarantee an optimal solution n Slow and costly construction process n Cannot transfer solutions and inferences to
solve other problems (problem specific) n So easy to explain/sell to managers, may lead
overlooking analytical solutions n Software may require special skills
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Simulation Methodology n Model real system and conduct repetitive experiments. n Steps:
1. Define problem 5. Conduct experiments 2. Construct simulation model 6. Evaluate results 3. Test and validate model 7. Implement solution 4. Design experiments
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Simulation Types
n Stochastic vs. Deterministic Simulation n In stochastic simulations: We use distributions (Discrete or
Continuous probability distributions)
n Time-dependent vs. Time-independent Simulation n Time independent stochastic simulation via Monte Carlo
technique (X = A + B)
n Discrete event vs. Continuous simulation n Steady State vs. Transient Simulation n Simulation Implementation
n Visual simulation n Object-oriented simulation
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n Visual interactive modeling (VIM) Also called
n Visual interactive problem solving n Visual interactive modeling n Visual interactive simulation
n Uses computer graphics to present the impact of different management decisions
n Often integrated with GIS n Users perform sensitivity analysis n Static or a dynamic (animation) systems
Visual Interactive Modeling (VIM) / Visual Interactive Simulation (VIS)
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Model Base Management
n MBMS: capabilities similar to that of DBMS n But, there are no comprehensive model base
management packages n Each organization uses models somewhat
differently n There are many model classes
n Within each class there are different solution approaches
n Relations MBMS n Object-oriented MBMS
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End of the Chapter
n Questions / Comments…
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