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### Modeling and Analysis

Week 8

Modeling and Analysis Topics

- 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

- A key element in most DSS
- Leads to reduced cost and increased revenue
- DuPont Simulates Rail Transportation System and Avoids Costly Capital Expenses
- Procter & Gamble uses several DSS models collectively to support strategic decisions
- Locating distribution centers, assignment of DCs to warehouses/customers, forecasting demand, scheduling production per product type, etc.
- Fiat, Pillowtex (…operational efficiency)…

P&G

- Used optimization models to redesign its distribution system
- Several models used:
- 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

- 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

- Problem identification and environmental analysis (information collection)
- Variable identification
- Influence diagrams, cognitive maps
- Forecasting/predicting
- 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
- Categories of models >>>
- Model management
- Knowledge based modeling

Influence Diagrams

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)

Influence Diagrams: Relationships

The shape of the arrow indicates the type of relationship

Influence Diagrams: Example

An influence diagram for the profit model

Profit = Income – Expense

Income = UnitsSold * UnitPrice

UnitsSold = 0.5 * Advertisement Expense

Expenses = UnitsCost * UnitSold + FixedCost

Influence Diagrams: Software

Analytica, Lumina Decision Systems

Supports hierarchical (multi-level) diagrams

DecisionPro, Vanguard Software Co.

Supports hierarchical (tree structured) diagrams

DATADecision Analysis, TreeAge Software

Includes influence diagrams, decision trees and simulation

Definitive Scenario, Definitive Software

Integrates influence diagrams and Excel, also supports Monte Carlo simulations

PrecisionTree, Palisade Co.

Creates influence diagrams and decision trees directly in an Excel spreadsheet

Analytica Influence Diagram of a Marketing Problem: The Marketing Model

Static and Dynamic Models

- Static Analysis
- Single snapshot of the situation
- Single interval
- Steady state
- Dynamic Analysis
- Dynamic models
- Evaluate scenarios that change over time
- Time dependent
- Represents trends and patterns over time
- More realistic: Extends static models

Mathematical Models

- 4 basic components
- Result variables
- Reflect the level of effectiveness of a system
- Decision variables
- Alternative courses of action
- Uncontrollable variables
- constraints
- Intermediate result variables
- Intermediate outcomes
- Mathematical relationships link the components together

Decision Making:Treating Certainty, Uncertainty and Risk

- Certainty Models
- Assume complete knowledge
- All potential outcomes are known
- May yield optimal solution
- Uncertainty
- Several outcomes for each decision
- Probability of each outcome is unknown
- Knowledge would lead to less uncertainty
- Risk analysis (probabilistic decision making)
- Probability of each of several outcomes occurring
- Level of uncertainty => Risk (expected value)

DSS Modeling with Spreadsheets

- Spreadsheet: most popular end-user modeling tool
- Flexible and easy to use
- Powerful functions
- 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

Excel spreadsheet - Dynamic model example: Simple loan calculation of monthly payments and effects of prepayment

Decision Analysis: A Few Alternatives

Single Goal Situations

Decision tables

- Multiple criteria decision analysis
- Features include decision variables (alternatives), uncontrollable variables, result variables
- Decision trees
- Graphical representation of relationships
- Multiple criteria approach
- Demonstrates complex relationships
- Cumbersome, if many alternatives exists

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

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%

Investment Example: Decision Table

- Payoff Decision variables (alternatives)
- Uncontrollable variables (states of economy)
- Result variables (projected yield)
- Tabular representation:

Investment Example: Treating Uncertainty

- Optimistic approach
- Pessimistic approach
- Treating Risk:
- Use known probabilities
- Risk analysis: compute expected values

Decision Analysis: A Few Alternatives

- Other methods of treating risk
- Simulation, Certainty factors, Fuzzy logic
- Multiple goals
- Yield, safety, and liquidity

Dependent Variables

DSS Mathematical Models- Non-Quantitative Models (Qualitative)
- Captures symbolic relationships between decision variables, uncontrollable variables and result variables
- Quantitative Models: Mathematically links decision variables, uncontrollable variables, and result variables
- 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

Mathematical

Relationships

Decision

Variables

Result

Variables

Intermediate

Variables

Optimization via Mathematical Programming

- 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

- Optimal solution: The best possible solution to a modeled problem
- 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

Linear Programming Steps

- 1. Identify the …
- Decision variables
- Objective function
- Objective function coefficients
- Constraints
- Capacities / Demands
- 2. Represent the model
- 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

- 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 limitsCC7CC8RelLimitLabor (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

LP Solution

- 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

- Sensitivity
- Assesses impact of change in inputs on outputs
- Eliminates or reduces variables
- Can be automatic or trial and error
- What-if
- Assesses solutions based on changes in variables or assumptions (scenario analysis)
- Goal seeking
- Backwards approach, starts with goal
- Determines values of inputs needed to achieve goal
- Example is break-even point determination

Heuristic Programming

- Cuts the search space
- Gets satisfactory solutions more quickly and less expensively
- Finds good enough feasible solutions to very complex problems
- Heuristics can be
- Quantitative
- Qualitative (in ES)
- Traveling Salesman Problem >>>

Traveling Salesman Problem

- What is it?
- 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 CitiesTNUR

5 12

6 60

9 20,160

20 1.22 1018

When to Use Heuristics

When to Use Heuristics

- Inexact or limited input data
- Complex reality
- Reliable, exact algorithm not available
- Computation time excessive
- For making quick decisions

Limitations of Heuristics

- Cannot guarantee an optimal solution

Simulation

- 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

- 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

- 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

- 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

- Model real system and conduct repetitive experiments.
- 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

Simulation Types

- Stochastic vs. Deterministic Simulation
- In stochastic simulations: We use distributions (Discrete or Continuous probability distributions)
- Time-dependent vs. Time-independent Simulation
- Time independent stochastic simulation via Monte Carlo technique (X = A + B)
- Discrete event vs. Continuous simulation
- Simulation Implementation
- Visual simulation

Visual Interactive Modeling (VIM) / Visual Interactive Simulation (VIS)

- Visual interactive modeling (VIM)

Also called

- 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

- 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
- Relations MBMS
- Object-oriented MBMS

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