Transcript Modeling and Analysis

Modeling and Analysis
Week 8
Modeling and Analysis Topics
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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
DSS Modeling
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A key element in most DSS
Leads to reduced cost and increased revenue
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DuPont Simulates Rail Transportation System and
Avoids Costly Capital Expenses
Procter & Gamble uses several DSS models
collectively to support strategic decisions
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Locating distribution centers, assignment of DCs to
warehouses/customers, forecasting demand, scheduling
production per product type, etc.
Fiat, Pillowtex (…operational efficiency)…
P&G
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Used optimization models to redesign its distribution
system
Several models used:
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Generating model (algorithm) to estimate transportation
costs
Demand forecasting model (statistics based)
Distribution center location model
Linear programming transportation model to determine best
shipping
Financial and risk simulation model that also considers some
qualitative factors
GIS for a user interface
Some built in the DSS some external and some
accessed as needed
500 employees involved over the course of a year
AMR
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Used models to optimize the altitude
ascent and descent profile for planes
Saved millions in fuel cost per week
Part of SABRE system that used models
extensively incremental revenues
eventually exceeded $1 billion annually
Major Modeling Issues
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Problem identification and environmental
analysis (information collection)
Variable identification
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Forecasting/predicting
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More information leads to better prediction
Multiple models: A DSS can include several
models, each of which represents a different
part of the decision-making problem
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Influence diagrams, cognitive maps
Categories of models >>>
Model management
Knowledge based modeling
Influence Diagrams
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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 DSS model relationships
Rectangle = a decision variable
Circle = uncontrollable or intermediate variable
Oval = result (outcome) variable: intermediate or final
Variables are connected with arrows  indicates the direction
of influence (relationship)
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Influence Diagrams: Relationships
CERTAINTY
Amount in
CDs
Interest
Collected
UNCERTAINTY
Price
Sales
The shape of
the arrow
indicates the
type of
relationship
RANDOM (risk) variable: Place a tilde (~) above the variable’s name
~
Demand
Sales
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Influence Diagrams: Example
An influence diagram for the profit model
Unit Price
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Amount used in
Advertisement
Income
Units Sold
Profit
Profit = Income – Expense
Unit Cost
Income = UnitsSold * UnitPrice
UnitsSold = 0.5 * Advertisement Expense
Expenses = UnitsCost * UnitSold + FixedCost
Fixed Cost
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Expenses
Influence Diagrams: Software
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Analytica, Lumina Decision Systems
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DecisionPro, Vanguard Software Co.
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Integrates influence diagrams and Excel, also supports
Monte Carlo simulations
PrecisionTree, Palisade Co.
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Includes influence diagrams, decision trees and simulation
Definitive Scenario, Definitive Software
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Supports hierarchical (tree structured) diagrams
DATA Decision Analysis, TreeAge Software
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Supports hierarchical (multi-level) diagrams
Creates influence diagrams and decision trees directly in an
Excel spreadsheet
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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Categories of Models
Category
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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, …
Static and Dynamic Models
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Static Analysis
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Dynamic Analysis
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Single snapshot of the situation
Single interval
Steady state
Dynamic models
Evaluate scenarios that change over time
Time dependent
Represents trends and patterns over time
More realistic: Extends static models
Mathematical Models
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4 basic components
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Result variables
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Decision variables
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constraints
Intermediate result variables
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Alternative courses of action
Uncontrollable variables
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Reflect the level of effectiveness of a system
Intermediate outcomes
Mathematical relationships link the
components together
Examples of the Components of Models
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Area
Decision variables
Result variables
Uncontrollable
variables
Financial investment
Investment
alternatives and
amounts
Total profit, risk,
ROI, EPS, liquidity
Inflation rate, prime
rate, competition
Marketing
Ad budget, where to
advertise
Market share,
Customer’s income,
customer satisfaction competitor’s actions
Manufacturing
What and how much
to produce,
inventory levels
Total cost, quality
level
Machine capacity,
material prices
Accounting
Audit schedule
Error rate
Tax rates, legal
requirements
Transportation
Shipments schedule,
use of smart cards
Total transportation
cost
Delivery distance,
regulations
Services
Staffing levels
Customer
satisfaction
Demand for services
Certainty, Uncertainty and Risk
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Decision Making:
Treating Certainty, Uncertainty and Risk
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Certainty Models
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Uncertainty
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Several outcomes for each decision
Probability of each outcome is unknown
Knowledge would lead to less uncertainty
Risk analysis (probabilistic decision making)
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Assume complete knowledge
All potential outcomes are known
May yield optimal solution
Probability of each of several outcomes occurring
Level of uncertainty => Risk (expected value)
DSS Modeling with Spreadsheets
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Spreadsheet: most popular end-user modeling tool
Flexible and easy to use
Powerful functions
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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
Excel spreadsheet - static model example:
Simple loan calculation of monthly payments
F  P(1  i ) n
 i (1  i ) n 
A  P
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n
(
1
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i
)
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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
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Decision trees
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Multiple criteria decision analysis
Features include decision
variables (alternatives),
uncontrollable variables, result
variables
Graphical representation of
relationships
Multiple criteria approach
Demonstrates complex
relationships
Cumbersome, if many
alternatives exists
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
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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Investment Example:
Decision Table
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Payoff Decision variables (alternatives)
Uncontrollable variables (states of economy)
Result variables (projected yield)
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Tabular representation:
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Investment Example:
Treating Uncertainty
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Optimistic approach
Pessimistic approach
Treating Risk:
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Use known probabilities
Risk analysis: compute expected values
Decision Analysis: A Few Alternatives
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Other methods of treating risk
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Multiple goals
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Simulation, Certainty factors, Fuzzy logic
Yield, safety, and liquidity
DSS Mathematical Models
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Non-Quantitative Models (Qualitative)
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Captures symbolic relationships between decision variables, uncontrollable
variables and result variables
Quantitative Models: Mathematically links decision variables,
uncontrollable variables, and result variables
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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
Uncontrollable
Variables
Decision
Variables
Mathematical
Relationships
Intermediate
Variables
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Result
Variables
Optimization
via Mathematical Programming
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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
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Optimal solution: The best possible solution
to a modeled problem
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Linear programming (LP): A mathematical model
for the optimal solution of resource allocation
problems. All the relationships are linear
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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Linear Programming Steps
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1. Identify the …
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Decision variables
Objective function
Objective function coefficients
Constraints
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2. Represent the model
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Capacities / Demands
LINDO: Write mathematical formulation
EXCEL: Input data into specific cells in Excel
3. Run the model and observe the results
Line
LP Example
The Product-Mix Linear Programming Model
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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
Labor (days) 300
500
Materials ($) 10,000 15,000
Units
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Units
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Profit ($)
8,000
12,000
Rel
<=
<=
>=
>=
Max
Limit
200,000 /mo
8,000,000 /mo
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200
Objective: Maximize Total Profit / Month
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LP Solution
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LP Solution
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Decision Variables:
X1: unit of CC-7
X2: unit of CC-8
Objective Function:
Maximize Z (profit)
Z=8000X1+12000X2
Subject To
300X1 + 500X2  200K
10000X1 + 15000X2  8000K
X1  100
X2  200
Sensitivity, What-if, and
Goal Seeking Analysis
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Sensitivity
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What-if
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Assesses solutions based on changes in variables or
assumptions (scenario analysis)
Goal seeking
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Assesses impact of change in inputs on outputs
Eliminates or reduces variables
Can be automatic or trial and error
Backwards approach, starts with goal
Determines values of inputs needed to achieve goal
Example is break-even point determination
Heuristic Programming
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Cuts the search space
Gets satisfactory solutions more
quickly and less expensively
Finds good enough feasible
solutions to very complex
problems
Heuristics can be
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Quantitative
Qualitative (in ES)
Traveling Salesman Problem
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Heuristic Programming - SEARCH
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Traveling Salesman Problem
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What is it?
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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
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12
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60
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20,160
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1.22 1018
When to Use Heuristics
When to Use Heuristics
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Inexact or limited input data
Complex reality
Reliable, exact algorithm not available
Computation time excessive
For making quick decisions
Limitations of Heuristics
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Cannot guarantee an optimal solution
Simulation
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Technique for conducting experiments with a
computer on a comprehensive model of the
behavior of a system
Frequently used in DSS tools
Major Characteristics of Simulation
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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
Advantages of Simulation
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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
Limitations of Simulation
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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
Simulation Methodology
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Model real system and conduct repetitive experiments.
Steps:
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Define problem
Construct simulation model
Test and validate model
Design experiments
5. Conduct experiments
6. Evaluate results
7. Implement solution
Simulation Types
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Stochastic vs. Deterministic Simulation
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Time-dependent vs. Time-independent Simulation
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Time independent stochastic simulation via Monte Carlo
technique (X = A + B)
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Discrete event vs. Continuous simulation
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Simulation Implementation
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In stochastic simulations: We use distributions (Discrete or
Continuous probability distributions)
Visual simulation
Visual Interactive Modeling (VIM) /
Visual Interactive Simulation (VIS)
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Visual interactive modeling (VIM)
Also called
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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
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
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Within each class there are different solution
approaches
Relations MBMS
Object-oriented MBMS