Transcript MSS and alternatives views of the subject

MSS: Active Support for Decision
Making
Modeling and Analysis
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Modeling and Analysis
Structure of some successful models and
methodologies
Decision analysis
Decision trees
Optimization
Heuristic programming
Simulation
New developments in modeling tools / techniques
Important issues in model base management
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Modeling and Analysis Topics
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
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Modeling for MSS
Key element in most DSS
Necessity in a model-based DSS
Can lead to massive cost reduction /
revenue increases
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Major Modeling Issues
Problem identification
Environmental analysis
Variable identification
Forecasting
Multiple model use
Model categories or selection
Model management
Knowledge-based modeling
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Static and Dynamic Models
Static Analysis
Single snapshot
Dynamic Analysis
Dynamic models
Evaluate scenarios that change over time
Time dependent
Trends and patterns over time
Extend static models
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Treating Certainty,
Uncertainty, and Risk
Certainty Models
Uncertainty
Risk
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Influence Diagrams
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
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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.
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MSS Modeling in Spreadsheets
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
Excel spreadsheet dynamic model example of a
simple loan calculation of monthly payments and
effects of prepayment
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Decision Analysis
of Few Alternatives
(Decision Tables and Trees)
Single Goal Situations
Decision tables
Decision trees
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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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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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View Problem as a Two-Person Game
Decision variables (alternatives)
Uncontrollable variables (states of
economy)
Result variables (projected yield)
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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%
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Treating Uncertainty
Optimistic approach
Pessimistic approach
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Treating Risk
Use known probabilities
Risk analysis: compute expected values
Can be dangerous
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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%
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8.4% *
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Decision Trees
Other methods of treating risk
Simulation
Certainty factors
Fuzzy logic
Multiple goals
Yield, safety, and liquidity
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Multiple Goals
Alternatives Yield
Safety
Liquidity
Bonds
8.4%
High
High
Stocks
8.0%
Low
High
CDs
6.5%
Very High
High
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Optimization via Mathematical
Programming
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
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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
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LP Allocation Model
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
Optimal solution: the best, found algorithmically
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Linear Programming
Decision variables
Objective function
Objective function coefficients
Constraints
Capacities
Input-output (technology) coefficients
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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
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<< Generated Solution Report >>
LP OPTIMUM FOUND AT STEP
3
OBJECTIVE FUNCTION VALUE
1)
VARIABLE
X1
X2
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5066667.00
VALUE
333.333300
200.000000
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REDUCED COST
.000000
.000000
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ROW
LABOR)
BUDGET)
MARKET1)
MARKET2)
SLACK OR SURPLUS
.000000
1666667.000000
233.333300
.000000
NO. ITERATIONS=
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DUAL PRICES
26.666670
.000000
.000000
-1333.333000
3
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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
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ALLOWABLE
INCREASE
50000.000
INFINITY
233.333
140.000
Info 2007
ALLOWABLE
DECREASE
70000.000
1666667.000
INFINITY
200.000
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Lingo LP Product-Mix Model
DSS in Focus 5.5
<< The Model >>>
MODEL:
! The Product-Mix Example;
SETS:
COMPUTERS /CC7, CC8/ : PROFIT, QUANTITY, MARKETLIM ;
RESOURCES /LABOR, BUDGET/ : AVAILABLE ;
RESBYCOMP(RESOURCES, COMPUTERS) : UNITCONSUMPTION ;
ENDSETS
DATA:
PROFIT MARKETLIM =
8000, 100,
12000, 200;
AVAILABLE = 200000, 8000000 ;
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UNITCONSUMPTION =
300, 500,
10000, 15000 ;
ENDDATA
MAX = @SUM(COMPUTERS: PROFIT * QUANTITY) ;
@FOR( RESOURCES( I):
@SUM( COMPUTERS( J):
UNITCONSUMPTION( I,J) * QUANTITY(J)) <=
AVAILABLE( I));
@FOR( COMPUTERS( J):
QUANTITY(J) >= MARKETLIM( J));
! Alternative
@FOR( COMPUTERS( J):
@BND(MARKETLIM(J), QUANTITY(J),1000000));
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<< (Partial ) Solution Report >>
Global optimal solution found at step:
Objective value:
5066667.
Variable
PROFIT( CC7)
PROFIT( CC8)
QUANTITY( CC7)
QUANTITY( CC8)
MARKETLIM( CC7)
MARKETLIM( CC8)
AVAILABLE( LABOR)
AVAILABLE( BUDGET)
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Value
8000.000
12000.00
333.3333
200.0000
100.0000
200.0000
200000.0
8000000.
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Reduced Cost
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
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UNITCONSUMPTION(
UNITCONSUMPTION(
UNITCONSUMPTION(
UNITCONSUMPTION(
Row
1
2
3
4
5
LABOR, CC7)
LABOR, CC8)
BUDGET, CC7)
BUDGET, CC8)
Slack or Surplus
5066667.
0.0000000
1666667.
233.3333
0.0000000
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300.00
500.00
10000.
15000.
0.00
0.00
0.00
0.00
Dual Price
1.000000
26.66667
0.0000000
0.0000000
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Heuristic Programming
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
Quantitative
Qualitative (in ES)
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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
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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
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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
Heuristics successfully applied to vehicle routing
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Simulation
Technique for conducting experiments with a
computer on a model of a management system
Frequently used DSS tool
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Major Characteristics of Simulation
Imitates reality and capture its richness
Technique for conducting experiments
Descriptive, not normative tool
Often to solve very complex, risky problems
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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)
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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)
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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
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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
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Simulation Types
Probabilistic Simulation
Discrete distributions
Continuous distributions
Probabilistic simulation via Monte Carlo technique
Time dependent versus time independent simulation
Simulation software
Visual simulation
Object-oriented simulation
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Multidimensional Modeling
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
Tool can compare, rotate, and slice and dice
corporate data across different management
viewpoints
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Visual Spreadsheets
User can visualize models and
formulas with influence diagrams
Not cells--symbolic elements
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Visual Interactive Modeling (VIM) and
Visual Interactive Simulation (VIS)
Visual interactive modeling (VIM)
Also called
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
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Generated Image of Traffic at an Intersection from the
Orca Visual Simulation Environment)
(Courtesy Orca Computer, Inc.)
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Visual Interactive Simulation (VIS)
Decision makers interact with the simulated
model and watch the results over time
Visual interactive models and DSS
Queueing
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Quantitative Software Packages-OLAP
Preprogrammed models can expedite DSS
programming time
Some models are building blocks of other models
Statistical packages
Management science packages
Revenue (yield) management
Other specific DSS applications
including spreadsheet add-ins
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SUMMARY
Models play a major role in DSS
Models can be static or dynamic
Analysis is under assumed certainty, risk, or
uncertainty
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
REFERENCE
Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition
Copyright 2001, Prentice Hall, Upper Saddle River, NJ
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