Model-Based Decision Making: Optimization and Multi-Criteria Systems

Question 2
Chapter 9:

Model-Based Decision Making: Optimization and Multi-Criteria Systems

Business Intelligence and Analytics: Systems for Decision Support

(10th Edition)

Business Intelligence and Analytics: Systems for Decision Support

(10th Edition)

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Learning Objectives

Understand the basic concepts of analytical decision modeling

Describe how prescriptive models interact with data and the user

Understand some different, well-known model classes

Understand how to structure decision making with a few alternatives

Describe how spreadsheets can be used for analytical modeling and solution

(Continued)

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Learning Objectives

Explain the basic concepts of optimization and when to use them

Describe how to structure a linear programming model

Describe how to handle multiple goals

Explain what is meant by sensitivity analysis, what-if analysis, and goal seeking

Describe the key issues of multi-criteria decision making

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Opening Vignette

Midwest ISO Saves Billions by Better Planning of Power Plant Operations and Capacity Planning

Company background

Problem description

Proposed solution

Results

Answer & discuss the case questions…

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Questions for the Opening Vignette

In what ways were the individual companies in Midwest ISO better off being part of MISO as opposed to operating independently?

The dispatch problem was solved with a linear programming method. Explain the need of such method in light of the problem discussed in the case.

What were the two main optimization algorithms used? Briefly explain the use of each algorithm.

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Decision Support Systems Modeling

DSS modeling (optimization & simulation) contribute to organizational success. Examples include:

Pillowtex (see ProModel, 2013),

Fiat (see ProModel, 2006),

Procter & Gamble (see Camm et al., 1997),

and others.

INFORMS publications such as Interfaces, ORMS Today, and Analytics magazine have plenty of such example cases

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Application Case 9.1

Optimal Transport for ExxonMobil Downstream Through a DSS

Questions for Discussion

List three ways in which manual scheduling of ships could result in more operational cost as compared to the tool developed.

In what other ways can ExxonMobil leverage the decision support tool developed to expand and optimize their other business operations?

What are some strategic decisions that could be made by decision makers using the tool developed?

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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: An MSS can include several models, each of which represents a different part of the decision-making problem

Categories of models >>>

Model management DBMS vs. MBDM

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Categories of Models

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Model Categories 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

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Application Case 9.2

Optimal Transport for ExxonMobil Downstream Through a DSS

Company

Problem description

Proposed solution

Results

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Model Categories Current Trends in Modeling

Development of Model/Solution Libraries

NEOS Server for Optimization

neos.mcs.anl.gov/neos/index.html

Resources link at informs.org

lionhrtpub.com/ORMS.shtml

Web-based modeling (optimization/simulation/)

Multidimensional analysis (modeling)

Influence Diagrams

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Structure of Mathematical Models for Decision Support

Decision

Variables

Mathematical

Relationships

Uncontrollable

Variables

Result

Variables

Non-Quantitative Models (Qualitative)

Quantitative Models: Mathematically links decision variables, uncontrollable variables, and result variables

Independent Variables

Dependent Variable

Intermediate

Variables

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Examples – Components of Models

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The Structure of a Mathematical Model

The components of a quantitative model are linked together by mathematical (algebraic) expressionsequations or inequalities.

Example Profit –

whereP= profit, R= revenue, and C= cost

Example – Simple Present-Value –

whereP= present value, F= future cash-flow, i= interest-rate, and n = number of period (years)

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Modeling and Decision Making – Under Certainty, Uncertainty, and Risk

Certainty

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)

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Modeling and Decision Making – Under Certainty, Uncertainty, and Risk

The Zones of Decision Making

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Application Case 9.3

American Airlines Uses Should-Cost Modeling to Assess the Uncertainty of Bids for Shipment Routes

Questions for Discussion

Besides reducing the risk of overpaying or underpaying suppliers, what are some other benefits AA would derive from its should be model?

Can you think of other domains besides air transportation where such a model could be used?

Discuss other possible methods with which AA could have solved its bid overpayment and underpayment problem.

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Decision Modeling with Spreadsheets

Spreadsheet

Most popular end-user modeling tool

Flexible and easy to use

Powerful functions (add-in functions)

Programmability (via macros)

What-if analysis and goal seeking

Simple database management

Seamless integration of model and data

Incorporates both static and dynamic models

Examples: Microsoft Excel, Lotus 1-2-3

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Application Case 9.4

Showcase Scheduling at Fred Astaire East Side Dance Studio

Company

Problem description

Proposed solution

Results

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Excel spreadsheet – static model example: (Simple loan calculation of monthly payments)

Static model example:

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

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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.

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Application Case 9.5

Spreadsheet Model Helps Assign Medical Residents

Company

Problem description

Proposed solution

Results

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LP 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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Linear Programming Steps

Identify the

Decision variables

Objective function

Objective function coefficients

Constraints

Capacities / Demands /

Represent the model

LINDO: Write mathematical formulation

EXCEL: Input data into specific cells in Excel

Run the model and observe the results

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Modeling in LP – An Example

The Product-Mix Linear Programming Model

MBI Corporation

Decision variable: How many computers to build next month?

Two types of mainframe computers: CC-7 and CC-8

Constraints: Labor limits, Materials limit, Marketing lower limits CC-7 CC-8 Rel Limit Labor (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

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LP Solution Algebraic Formulations

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LP Solution with Excel

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

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Illustrating the Power of Spreadsheet Modeling

Election Resource Allocation Problem

Analysis of swing states for the 2012 election

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Common Optimization Models

Product-mix problems (how many of each product to produce for max profit)

Transportation (minimize cost of shipments)

Assignment (best matching of objects)

Investment (maximizing rate of return)

Network optimization models for planning and scheduling

Replacement (capital budgeting),

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Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking

Multiple Goals

Simple-goal vs. multiple goals

Vast majority of managerial problems has multiple goals (objectives) to achieve

Attaining simultaneous goals

Methods of handling multiple goals

Utility theory

Goal programming

Expression of goals as constraints, using LP

A points system

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Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking

Certain difficulties may arise when analyzing multiple goals

Difficult to obtain a single organizational goal

The importance of goals change over time

Goals and sub-goals are viewed differently

Goals change in response to other changes

Dynamics of groups of decision makers

Assessing the importance (priorities)

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Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking

Sensitivity analysis

It is the process of assessing the impact of change in inputs on outputs

Helps to

eliminate (or reduce) variables

revise models to eliminate too-large sensitivities

adding details about sensitive variables or scenarios

obtain better estimates of sensitive variables

alter a real-world system to reduce sensitivities

Can be automatic or trial and error

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Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking

What-if analysis

Assesses solutions based on changes in variables or assumptions (scenario analysis)

What if we change our capacity at the milling station by 40% [what would be the impact]

Goal seeking

Backwards approach, starts with the goal and determines values of inputs needed

Example is break-even point determination

In-order to break even (profit = 0), how many products do we have to sell each month

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Decision Analysis with Decision Tables and Decision Trees

Decision Tables a tabular representation of the decision situation (alternatives)

Investment Example

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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Decision Table – 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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Payoff decision variables (alternatives)

Uncontrollable variables (states of economy)

Result variables (projected yield)

Tabular representation:

Decision Table Investment Example: Decision Table

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Decision Table Investment Example: Treating Uncertainty

Optimistic approach

Pessimistic approach

Treating Risk/Uncertainty:

Use known probabilities

Expected values

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Decision Table Investment Example: Multiple Goals

Multiple goals

Yield, safety, and liquidity

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Decision Trees

Graphical representation of relationships

Multiple criteria approach

Demonstrates complex relationships

Cumbersome, if many alternatives exists

Tools include

Mind Tools Ltd., mindtools.com

TreeAge Software Inc., treeage.com

Palisade Corp., palisade.com

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Decision Trees An Example

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Multi-Criteria Decision Making with Pairwise Comparisons

Having more than one criterion makes decision-making process complicated

Usually some type of weighing algorithm is used to analyze such problems

The Analytic Hierarchy Process

Developed by Thomas Saaty (1995, 1996)

A very popular technique for MCDM

Popular Tools – ExpertChoice.com

Web-based Tools – Web-HIPRE (hipre.aalto.fi)

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Application Case 9.6

U.S. HUD Saves the House by Using AHP for Selecting IT Projects

Company

Problem description

Proposed solution

Results

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Tutorial – Applying AHP Using Web-HIPRE

Goal: select the most appropriate movie

Identify some criteria for making this decision

The main and sub-criteria for movie selection are

a. Genre: Action, Comedy, Sci-Fi, Romance

b. Language: English, Hindi

c. Day of Release: weekday, weekend

d. User/Critics Rating: High, Average, Low

Alternatives are the following current movies:

SkyFall, The Dark Knight Rises, The Dictator, Dabaang, Alien, and DDL

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Tutorial – Applying AHP Using Web-HIPRE

Step 1: define the goal, criteria, and alternatives

Web-HIBRE allows defining all of these and relationships within an easy-to-use Web-based interface.

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Tutorial – Applying AHP Using Web-HIPRE

Step 2: the main criteria are then ranked as they relate to the goal

A comparative ranking scale from 1 to 9 (with ascending order of importance) is used

The ranking is done using a Pairwise comparison procedure (i.e., divide-and-concur) between any two criteria for all combinations of twos

The tool readily normalizes the rankings of each of the main criteria over one another to a scale ranging from 0 to 1 and then calculates the row averages to arrive at an overall importance rating ranging from 0 to 1

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Tutorial – Applying AHP Using Web-HIPRE

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Tutorial – Applying AHP Using Web-HIPRE

Step 3: All of the subcriteria related to each of the main criteria are then ranked with their relative importance over one another

Step 4: Each alternative is ranked with respect to all of the subcriteria that are linked with the alternatives in a similar fashion using the relative scale of 09; then the overall importance of each alternative is calculated

Step 5: The final result are obtained from the composite priority analysis involving all the subcriteria and main criteria

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Tutorial – Applying AHP Using Web-HIPRE

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Tutorial – Applying AHP Using Web-HIPRE

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Tutorial – Applying AHP Using Web-HIPRE

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Chapter 10:

Modeling and Analysis: Heuristic Search Methods and Simulation

Business Intelligence and Analytics: Systems for Decision Support

(10th Edition)

Business Intelligence and Analytics: Systems for Decision Support

(10th Edition)

9-#

Learning Objectives

Explain the basic concepts of simulation and heuristics, and when to use them

Understand how search methods are used to solve some decision support models

Know the concepts behind and applications of genetic algorithms

Explain the differences among algorithms, blind search, and heuristics

(Continued)

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Learning Objectives

Understand the concepts and applications of different types of simulation

Explain what is meant by system dynamics, agent-based modeling, Monte Carlo, and discrete event simulation

Describe the key issues of model management

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Opening Vignette

System Dynamics Allows Fluor

Corporation to Better Plan for Project and Change Management

Background

Problem description

Proposed solution

Results

Answer & discuss the case questions…

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Questions for the Opening Vignette

Explain the use of system dynamics as a simulation tool for solving complex problems.

In what ways was it applied in Fluor Corporation to solve complex problems?

How does a what-if analysis help a decision maker to save on cost?

In your own words, explain the factors that might have triggered the use of system dynamics to solve change management problems in Fluor Corporation

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Problem-Solving Search Methods

Search: choice phase of decision making

Search is the process of identifying the best possible solution / course of action [under limitations such as time, ]

Search techniques include

analytical techniques,

algorithms,

blind searching, and

heuristic searching

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Problem-Solving Search Methods

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Problem-Solving Search Methods – Algorithmic/Heuristic

Cuts the search space

Gets satisfactory solutions more quickly and less expensively

Finds good enough feasible solutions to complex problems

Heuristics can be

Quantitative

Qualitative (in ES)

Traveling Salesman Problem see the example next >>>

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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 Cities TNUR

5 12

6 60

9 20,160

20 1.22 1018

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Traveling Salesman Problem

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Traveling Salesman Problem

Rule 1: Starting from home base, go to the closest city

Rule 2: Always follow an exterior route

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Application Case 10.1

Chilean Government Uses Heuristics to Make Decisions on School Lunch Providers

Questions for Discussion

What were the main challenges faced by JUNAEB?

What operation research methodologies were employed in achieving homogeneity across territorial units?

What other approaches could you use in this case study?

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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

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Tabu search

Intelligent search algorithm

Genetic algorithms

Survival of the fittest

Simulated annealing

Analogy to Thermodynamics

Ant colony and other Meta-heuristics

Modern Heuristic Methods

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Genetic Algorithms

It is a popular heuristic search technique

Mimics the biological process of evolution

Genetic algorithms

Software programs that learn/search in evolutionary manner, similar to the way biological systems evolve

An efficient, domain-independent search heuristic for a broad spectrum of problem domains

Main theme: Survival of the fittest

Moving toward better and better solutions by letting only the fittest parents create the future generations

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Evolutionary Algorithm

10010110

01100010

10100100

10011001

01111101

. . .

10010110

01100010

10100100

10011101

01111001

. . .

Selection

Reproduction

. Crossover

. Mutation

Current

generation

Elitism

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Each candidate solution is called a chromosome

A chromosome is a string of genes

Chromosomes can copy themselves, mate, and mutate via evolution

In GA we use specific genetic operators

Reproduction

Crossover

Mutation

GA Structure and GA Operators

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Genetic Algorithms – Example: The Vector Game

Description of the Vector Game

Identifying a string of 5 binary digits

Default Strategy: Random Trial and Error

Improved Strategy: Use of Genetic Algorithms

In an iterative fashion, using genetic algorithm process and genetic operators, find the opponents digit sequence

See your book for functional details

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Item: 1 2 3 4 5 6 7

Benefit: 5 8 3 2 7 9 4

Weight: 7 8 4 10 4 6 4

Knapsack holds a maximum of 22 pounds

Need to fill it for maximum benefit (one per item)

Solutions take the form of a string of 1s

Example Solution: 1 1 0 0 1 0 0

Means choose items 1, 2, 5:

Weight = 21, Benefit = 20

Evolver solution works in Microsoft Excel ?

A Classic GA Example: The Knapsack Problem

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Define the objective function and constraint(s)

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Identify the decision variables and their characteristics

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Observe and analyze the results

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Observe and analyze the results

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The Knapsack Problem at Evolver

Monitoring the solution generation process

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Genetic Algorithms

Limitations of Genetic Algorithms

Does not guarantee an optimal solution (often settles in a sub optimal solution / local minimum)

Not all problems can be put into GA formulation

Development and interpretation of GA solutions requires both programming and statistical skills

Relies heavily on the random number generators

Locating good variables for a particular problem and obtaining the data for the variables is difficult

Selecting methods by which to evolve the system requires experimentation and experience

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Genetic Algorithm Applications

Dynamic process control

Optimization of induction rules

Discovery of new connectivity topologies (NNs)

Simulation of biological models of behavior

Complex design of engineering structures

Pattern recognition

Scheduling, transportation, and routing

Layout and circuit design

Telecommunication, graph-based problems,

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Simulation

Simulation is the appearance of reality

It is often used to conduct what-if analysis on the model of the actual system

It is a popular DSS technique for conducting experiments with a computer on a comprehensive model of the system to assess its dynamic behavior

Often used when the system is too complex for other DSS techniques

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Application Case 10.3

Simulating Effects of Hepatitis B Interventions

Questions for Discussion

Explain the advantage of operations research methods such as simulation over clinical trial methods in determining the best control measure for Hepatitis B.

In what ways do the decision and Markov models provide cost-effective ways of combating the disease?

Discuss how multidisciplinary background is an asset in finding a solution for the problem described in the case.

Besides healthcare, in what other domain could such a modeling approach help reduce cost?

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Imitates reality and captures its richness both in shape and behavior

Represent versus Imitate

Technique for conducting experiments

Descriptive, not normative tool

Often to solve [i.e., analyze] very complex systems/problems

Simulation should be used only when a numerical optimization is not possible

Major Characteristics of Simulation

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Advantages of Simulation

The theory is fairly straightforward

Great deal of time compression

Experiment with different alternatives

The model reflects managers 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

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Disadvantages 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 to overlooking analytical solutions

Software may require special skills

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Simulation Methodology

Steps:

1. Define problem 5. Conduct experiments

2. Construct the model 6.

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Model-Based Decision Making: Optimization and Multi-Criteria Systems

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