CHAPTER 5
Modeling and Analysis
Modeling and Analysis
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Major DSS component
Model base and model management
CAUTION - Difficult Topic Ahead
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Familiarity with major ideas
Basic concepts and definitions
Tool--influence diagram
Model directly in spreadsheets
Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition
Copyright 2001, Prentice Hall, Upper Saddle River, NJ
Modeling and Analysis
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Structure of some successful models and methodologies
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Decision analysis
Decision trees
Optimization
Heuristic programming
Simulation
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New developments in modeling tools / techniques
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Important issues in model base management
Modeling and Analysis Topics
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Modeling for MSS
Static and dynamic models
Treating certainty, uncertainty, and risk
Influence diagrams
MSS modeling in spreadsheets
Decision analysis of a few alternatives (decision tables and trees)
Optimization via mathematical programming
Heuristic programming
Simulation
Multidimensional modeling -OLAP
Visual interactive modeling and visual interactive simulation
Quantitative software packages - OLAP
Model base management
Modeling for MSS
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Key element in most DSS
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Necessity in a model-based DSS
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Can lead to massive cost reduction / revenue
increases
Good Examples of MSS Models
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DuPont rail system simulation model (opening
vignette)
Procter & Gamble optimization supply chain
restructuring models (case application 5.1)
Scott Homes AHP select a supplier model (case
application 5.2)
IMERYS optimization clay production model
(case application 5.3)
Major Modeling Issues
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Problem identification
Environmental analysis
Variable identification
Forecasting
Multiple model use
Model categories or selection (Table 5.1)
Model management
Knowledge-based modeling
Static and Dynamic Models
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Static Analysis
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Single snapshot
Dynamic Analysis
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Dynamic models
Evaluate scenarios that change over time
Time dependent
Trends and patterns over time
Extend static models
Treating Certainty, Uncertainty,
and Risk
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Certainty Models
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Uncertainty
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Risk
Influence Diagrams
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Graphical representations of a model
Model of a model
Visual communication
Some packages create and solve the mathematical model
Framework for expressing MSS model relationships
Rectangle = a decision variable
Circle = uncontrollable or intermediate variable
Oval = result (outcome) variable: intermediate or final
Variables connected with arrows
Example (Figure 5.1)
Unit Price
~
Amount used in advertisement
Income
Units Sold
Profit
Expense
Unit Cost
Fixed Cost
FIGURE 5.1 An Influence Diagram for the Profit Model.
Analytica Influence Diagram of a Marketing
Problem: The Marketing Model (Figure 5.2a)
(Courtesy of Lumina Decision Systems, Los Altos, CA)
Analytica: Price Submodel (Figure 5.2b)
(Courtesy of Lumina Decision Systems, Los Altos, CA)
Analytica: Sales Submodel (Figure 5.2c)
(Courtesy of Lumina Decision Systems, Los Altos, CA)
MSS Modeling in Spreadsheets
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Spreadsheet: most popular end-user modeling tool
Powerful functions
Add-in functions and solvers
Important for analysis, planning, modeling
Programmability (macros)
(More)
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What-if analysis
Goal seeking
Simple database management
Seamless integration
Microsoft Excel
Lotus 1-2-3
Excel spreadsheet static model example of a simple loan
calculation of monthly payments (Figure 5.3)
Excel spreadsheet dynamic model example of a simple loan
calculation of monthly payments and effects of prepayment
(Figure 5.4)
Decision Analysis
of Few Alternatives
(Decision Tables and Trees)
Single Goal Situations
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Decision tables
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Decision trees
Decision Tables
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Investment example
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One goal: maximize the yield after one year
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Yield depends on the status of the economy
(the state of nature)
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Solid growth
Stagnation
Inflation
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%
View Problem as a Two-Person Game
Payoff Table 5.2
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Decision variables (alternatives)
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Uncontrollable variables (states of economy)
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Result variables (projected yield)
Table 5.2: Investment Problem
Decision Table Model
States of Nature
Solid
Stagnation Inflation
Alternatives Growth
Bonds
12%
6%
3%
Stocks
15%
3%
-2%
CDs
6.5%
6.5%
6.5%
Treating Uncertainty
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Optimistic approach
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Pessimistic approach
Treating Risk
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Use known probabilities (Table 5.3)
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Risk analysis: compute expected values
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Can be dangerous
Table 5.3: Decision Under Risk and Its Solution
Solid
Stagnation
Growth
Inflation
Expected
Value
Alternatives
.5
.3
.2
Bonds
12%
6%
3%
Stocks
15%
3%
-2%
8.0%
CDs
6.5%
6.5%
6.5%
6.5%
8.4% *
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Decision Trees
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Other methods of treating risk
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Simulation
Certainty factors
Fuzzy logic
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Multiple goals
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Yield, safety, and liquidity (Table 5.4)
Table 5.4: Multiple Goals
Alternatives
Yield
Safety
Liquidity
Bonds
8.4%
High
High
Stocks
8.0%
Low
High
CDs
6.5%
Very High
High
Table 5.5: Discrete vs. Continuous Probability Distribution
Daily
Demand
Discrete
Probability
Continuous
5
6
7
8
9
.1
.15
.3
.25
.2
Normally distributed with
a mean of 7 and a
standard deviation of 1.2
Optimization via Mathematical
Programming
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Linear programming (LP)
Used extensively in DSS
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Mathematical Programming
Family of tools to solve managerial problems in allocating
scarce resources among various activities to optimize a
measurable goal
LP Allocation
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
LP Allocation Model
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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
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Optimal solution: the best, found algorithmically
Linear Programming
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Decision variables
Objective function
Objective function coefficients
Constraints
Capacities
Input-output (technology) coefficients
Line
Lindo LP Product-Mix Model
DSS in Focus 5.4
<< The Lindo Model: >>
MAX
8000 X1 + 12000 X2
SUBJECT TO
LABOR)
300 X1 + 500 X2 <=
200000
BUDGET)
10000 X1 + 15000 X2 <=
8000000
MARKET1)
X1 >=
100
MARKET2)
X2 >=
200
END
<< Generated Solution Report >>
LP OPTIMUM FOUND AT STEP
3
OBJECTIVE FUNCTION VALUE
1)
VARIABLE
X1
X2
5066667.00
VALUE
333.333300
200.000000
REDUCED COST
.000000
.000000
ROW
LABOR)
BUDGET)
MARKET1)
MARKET2)
SLACK OR SURPLUS
.000000
1666667.000000
233.333300
.000000
NO. ITERATIONS=
3
DUAL PRICES
26.666670
.000000
.000000
-1333.333000
RANGES IN WHICH THE BASIS IS UNCHANGED:
VARIABLE
X1
X2
OBJ COEFFICIENT RANGES
CURRENT
ALLOWABLE
ALLOWABLE
COEF
INCREASE
DECREASE
8000.000
INFINITY
799.9998
12000.000
1333.333
INFINITY
RIGHTHAND SIDE RANGES
ROW
CURRENT
RHS
LABOR
200000.000
BUDGET 8000000.000
MARKET1
100.000
MARKET2
200.000
ALLOWABLE
INCREASE
50000.000
INFINITY
233.333
140.000
ALLOWABLE
DECREASE
70000.000
1666667.000
INFINITY
200.000
Heuristic Programming
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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
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Quantitative
Qualitative (in ES)
When to Use Heuristics
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
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
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
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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
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Frequently used DSS tool
Major Characteristics of Simulation
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Imitates reality and capture its richness
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Technique for conducting experiments
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Descriptive, not normative tool
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Often to solve very complex, risky problems
Advantages of Simulation
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
(More)
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
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
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
Simulation Types
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Probabilistic Simulation
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Discrete distributions
Continuous distributions
Probabilistic simulation via Monte Carlo technique
Time dependent versus time independent simulation
Simulation software
Visual simulation
Object-oriented simulation
Multidimensional Modeling
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Performed in online analytical processing (OLAP)
From a spreadsheet and analysis perspective
2-D to 3-D to multiple-D
Multidimensional modeling tools: 16-D +
Multidimensional modeling - 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.)
Graphical Display of the Screen
in Figure 5.6a (Figure 5.6b)
(Courtesy Cognos Inc.)
Environmental Line of Products by Drilling Down (Figure
5.6c)
(Courtesy Cognos Inc.)
Drilled Deep into the Data: Current Month, Water Purifiers, Only in North
America (Figure 5.6d)
(Courtesy Cognos Inc.)
Visual Spreadsheets
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User can visualize models and formulas with
influence diagrams
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Not cells--symbolic elements
Visual Interactive Modeling (VIS) and Visual Interactive Simulation
(VIS)
Visual interactive modeling (VIM) (DSS In Action 5.8)
Also called
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Visual interactive problem solving
Visual interactive modeling
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)
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
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Visual interactive models and DSS
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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 models
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Statistical packages
Management science packages
Revenue (yield) management
Other specific DSS applications
including spreadsheet add-ins
Model Base Management
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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
Desirable Capabilities of MBMS
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Control
Flexibility
Feedback
Interface
Redundancy reduction
Increased consistency
MBMS Design Must Allow the DSS
User to:
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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Modeling languages
Relational MBMS
Object-oriented model base and its management
Models for database and MIS design and their
management
SUMMARY
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Models play a major role in DSS
Models can be static or dynamic
Analysis is under assumed certainty, risk, or
uncertainty
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Influence diagrams
Spreadsheets
Decision tables and decision trees
Spreadsheet models and results in influence diagrams
Optimization: mathematical programming
(More)
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Linear programming: economic-based
Heuristic programming
Simulation - more complex situations
Expert Choice
Multidimensional models - OLAP
(More)
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Quantitative software packages-OLAP (statistical, etc.)
Visual interactive modeling (VIM)
Visual interactive simulation (VIS)
MBMS are like DBMS
AI techniques in MBMS