Modeling and Analysis

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CHAPTER 5

• Modeling and Analysis

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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)

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Modeling and Analysis Topics

• 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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Good Examples of MSS Models

• 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)

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Major Modeling Issues

• Problem identification and Environmental
  analysis
• The monitoring, scanning, and interpretation of
  collected information.
• Analyze the scope of the domain and the forces
  and dynamics of the environment
• The problem must be understood
• Variable identification
• Decision, result, uncontrollable variables
• Their relationships

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Major Modeling Issues

• Forecasting
• To construct and manipulate models
• To determine what will be, rather than as
  traditional MIS
• Multiple models
• Model categories or selection (Table 5.1)
• Model management
• To maintain their integrity
• Knowledge-based modeling

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Categories of Models
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Categories of Models
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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
• Example (Figure 5.1)

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Figure 5.1
An Influence Diagram for the Profit Model
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Analytica Influence Diagram of a Marketing
Problem The Marketing Model (Figure 5.2a)
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Analytica Price Submodel (Figure 5.2b)(Courtesy
of Lumina Decision Systems, Los Altos, CA)
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Analytica Price Submodel (Figure 5.2c)(Courtesy
of Lumina Decision Systems, Los Altos, CA)
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MSS Modeling in Spreadsheets

• Spreadsheet most popular end-user modeling tool
• Powerful functions
• Add-in functions and solvers
• Programmability (macros)
• What-if analysis
• Goal seeking
• Simple database management
• Seamless integration
• Tools
• Microsoft Excel
• Lotus 1-2-3

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Decision Analysis of Few Alternatives
(Decision Tables and Trees)

• Decision Analysis
• alternatives are listed with their forecasted
  contributions to the goal(s), and the probability
  of obtaining the contribution, in a table or
  graph.
• Single Goal Situations can be modeled with
• 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

• If solid growth in the economy, bonds yield 12
  stocks 15 time deposits 6.5
• If stagnation, bonds yield 6 stocks 3 time
  deposits 6.5
• If inflation, bonds yield 3 stocks lose 2
  time deposits yield 6.5

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View Problem as a Two-Person Game
Payoff Table 5.2

• Decision variables (alternatives)
• Uncontrollable variables (states of economy)
• Result variables (projected yield)

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Table 5.2
Investment Problem Decision Table Model
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Treating Uncertainty

• Optimistic approach
• assumes that the best possible outcome of each
  alternative will occur and then selects the best
  of the bests (stocks)
• Pessimistic approach
• assumes that the worst possible outcome for each
  alternative will occur and selects the best one
  of those (CDs)

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Treating Risk

• Risk analysis compute expected values
• Use known probabilities (Table 5.3)

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Decision Trees

• Shows the relationships of the problem
  graphically
• Can handle complex situations in a compact form.
• Can be cumbersome if there are many alternatives
  or states of nature

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Multiple Goals

• 3 Goals
• Yield, safety, and liquidity (Table 5.4)
• Only one possible consequence is projected for
  each alternative
• Some of results are qualitative
• Method
• Analytic Hierarchy Process (AHP)

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Table 5.4
Multiple Goals
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Optimization via Mathematical Programming

• Mathematical Programming
• Family of tools to solve managerial problems in
  allocating scarce resources among various
  activities to optimize a measurable goal
• Linear programming (LP) is a family of
  mathematical programming
• Used extensively in DSS

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LP Allocation Problem Characteristics

• Limited quantity of economic resources
• Resources are used in the production of products
  or services
• Two or more ways (solutions, programs) to use the
  resources
• Each activity (product or service) yields a
  return in terms of the goal
• Allocation is usually restricted by constraints

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LP Allocation Model

• Rational economic assumptions
• Returns from allocations can be compared in a
  common unit
• Independent returns
• Total return is the sum of different activities
  returns
• All data are known with certainty
• 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
• whose values are unknown and are searched for
• Objective function
• a linear mathematical function that relates the
  decision variables to the goal and measures goal
  attainment and is to be optimized
• Objective function coefficients
• unit profit or cost coefficients indicating the
  contribution to the objective of one unit of a
  decision variable

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Linear Programming

• Constraints
• expressed in the form of linear inequalities or
  equalities that limit resources and/or
  requirements
• Capacities
• describe the upper and lower limits on the
  constraints and variables.
• Input-output (technology) coefficients
• indicate resource utilization for a decision
  variable

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Lindo LP Product-Mix Model
DSS in Focus 5.4
ltlt The Lindo Model gtgt MAX 8000 X1
12000 X2 SUBJECT TO LABOR) 300 X1 500 X2
lt 200000 BUDGET) 10000 X1 15000 X2 lt
8000000 MARKET1) X1 gt 100 MARKET2) X2 gt
200 END
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• ltlt Generated Solution Report gtgt
• LP OPTIMUM FOUND AT STEP 3
• OBJECTIVE FUNCTION VALUE
• 1) 5066667.00
• VARIABLE VALUE REDUCED COST
• X1 333.333300 .000000
• X2 200.000000 .000000

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• ROW SLACK OR SURPLUS DUAL PRICES
• LABOR) .000000 26.666670
• BUDGET) 1666667.000000 .000000
• MARKET1) 233.333300 .000000
• MARKET2) .000000 -1333.333000
• NO. ITERATIONS 3

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• RANGES IN WHICH THE BASIS IS UNCHANGED
• OBJ COEFFICIENT RANGES
• VARIABLE CURRENT ALLOWABLE ALLOWABLE
• COEF INCREASE DECREASE
• X1 8000.000 INFINITY 799.9998
• X2 12000.000 1333.333 INFINITY
• RIGHTHAND SIDE RANGES
• ROW CURRENT ALLOWABLE ALLOWABLE
• RHS INCREASE DECREASE
• LABOR 200000.000 50000.000 70000.000
• BUDGET 8000000.000 INFINITY 1666667.000
• MARKET1 100.000 233.333 INFINITY
• MARKET2 200.000 140.000 200.000

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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
• Use only for the specific situation
• Heuristics can be
• Quantitative
• Qualitative (in ES)

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Heuristic Programming

• Methodology
• searching, learning, evaluating, judging then
  researching, relearning, and reappraising
• Knowledge gained from success or failure and
  modifies the search process
• Tabu search based on intelligent search
  strategies to reduce the search for high quality
  solutions.
• Genetic algorithms start with a set of randomly
  generated solutions and recombine pairs of them
  at random to produce offspring

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Flow Diagram
Genetic Algorithm Process
start
Describe problem
Generate initial solution
Test Is solution best (good enough)?
Stop
Yes
Step 1
No
Select best parents (performers) to reproduce
Step 2
Step 3 Step 4 Step 5
Apply crossover process and create offspring
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Heuristics
When to use

• Inexact or limited input data
• Complex reality
• Reliable, exact algorithm not available
• Computation time excessive
• To improve the efficiency of optimization
• To solve complex problems
• For symbolic processing
• For making quick decisions

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Heuristics
Advantages

• Simple to understand
• easier to implement and explain
• Help train people to be creative
• Save formulation time
• Save programming and storage on computers
• Save computational time
• Frequently produce multiple acceptable solutions
• Possible to develop a solution quality measure
• Can incorporate intelligent search
• Can solve very complex models

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Heuristics
Limitations

• Cannot guarantee an optimal solution
• There may be too many exceptions
• Sequential decisions might not anticipate future
  consequences
• Interdependencies of subsystems can influence the
  whole system
• Heuristics successfully applied to vehicle routing

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Heuristics
Types

• Construction
• Improvement
• Mathematical programming
• Decomposition
• Partitioning

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Simulations

• Technique for conducting experiments with a
  computer on a model of a management system
• Frequently used DSS tool

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Simulation
Major Characteristics

• 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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Simulation
Advantages

• Theory is straightforward
• Time compression
• Descriptive, not normative
• MSS builder interfaces with manager to gain
  intimate knowledge of the problem
• Model is built from the manager's perspective
• Manager needs no generalized understanding. Each
  component represents a real problem component

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Simulation
Advantages

• Wide variation in problem types
• Can experiment with different variables
• Allows for real-life problem complexities
• Easy to obtain many performance measures directly
• Frequently the only DSS modeling tool for
  nonstructured problems
• Monte Carlo add-in spreadsheet packages (_at_Risk)

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Simulation
Limitations

• Cannot guarantee an optimal solution
• Slow and costly construction process
• Cannot transfer solutions and inferences to solve
  other problems
• So easy to sell to managers, may miss analytical
  solutions
• Software is not so user friendly

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Simulation
Methodology

• Model real system and conduct repetitive
  experiments
• Define problem
• Construct simulation model
• Test and validate model
• Design experiments
• Conduct experiments
• Evaluate results
• Implement solution

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Simulation
The Process
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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 - OLAP (Figure 5.6)
• Tool can compare, rotate, and slice and dice
  corporate data across different management
  viewpoints

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Entire Data Cube from a Queryin PowerPlay
(Figure 5.6a)
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Graphical Display of the Screen in Figure 5.6a
(Figure 5.6b)
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Environmental Line of Products by Drilling Down
(Figure 5.6c)
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Drilled Deep into the Data Current Month, Water
Purifiers, Only in North America (Figure 5.6d)
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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

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Generated Image of Traffic at an Intersection
from the Orca Visual Simulation Environment
(Figure 5.7)
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Visual Interactive Simulation (VIS)

• Decision makers interact with the simulated model
  and watch the results over time
• The user can try different decision strategies
  online
• Enhance learning about the problem and the impact
  of the alternatives tested

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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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Model Base Management

• MBMS capabilities similar to that of DBMS
• No standardized MBMS
• 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

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Desirable Capabilities of MBMS

• Control
• Flexibility
• Feedback
• Interface
• Redundancy reduction
• Increased consistency

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MBMS Design Must Allow the DSS User to

• Access and retrieve existing models.
• Exercise and manipulate existing models
• Store existing models
• Maintain existing models
• Construct new models with reasonable effort