Download DSS Chapter 1

Decision Support and
Business Intelligence
Systems
(8th Ed., Prentice Hall)
Chapter 4:
Modeling and Analysis
Major Modeling Issues
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problem identification and environmental analysis:
scanning the environment to figure out what problems exist and
can be solved via a model
variable identification: identifying the critical factors in a
model and their relationships
ex: Influence diagram : Graphical representations of a model
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)
4-2
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Major Modeling Issues
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forecasting: predicting the future
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use of multiple models: combining them to solve many parts
of a complex problem
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It is essential for construction models because when a decision
implemented, the results occur in the future.
E-Commerce ( Information about purchases should be analyzed to
predict demand)
5 Rights (How to get the right product(s) to the right customer at
the right price at the right time in the right format
CRM and RMS rely heavily on forecasting techniques
 Predict the most profitable customers
Each of which represents a different part of the decision – making problem
E.g., the Procter and Gamble supply chain DSS include:
 Location model to locate distribution centre , a product strategy model,
a demand- forecasting model, cost generation model ,….
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Major Modeling Issues
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use of multiple models
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Types of models:
1.
2.
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model categories: selecting the right type of model for the
problem or sub-problem (table 4.1)
model management: coordinating a firm’s models and their
use
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Models like data, must be managed to maintain their integrity and
their applicability
Management is done by MBMS
knowledge-based modeling: how to take advantage of
human knowledge in modeling
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Standard : built in to DSS or freestanding soft ware that can
interface with a DSS
Nonstandard : constructed from scratch.
DSS use mostly quantitive models, wheres Expert systems use qualitiative
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Categories of Models
Category
4-5
Table 4.1
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, …
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Static and Dynamic Models
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Static Analysis
 Single snapshot of the situation, every thing occurs in a
single interval
 describes relationships among parts of a system at a point in
time.
 Ex: A decision about buy a product , Annual income
statement.
Dynamic Analysis
 Evaluate scenarios that change over time
 Time dependent
 Ex: In determining how many checkout points should be
open in a supermarket.
 A 5 year Profit and Loss projection in which input data
(costs, prices, and quantities ) change from year to year
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MSS 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 (small programs designed to
extend the capabilities of a spreadsheet package)
Programmability (via macros)
What-if analysis
Goal seeking
Simple database management
Incorporates both static and dynamic models
Examples: Microsoft Excel, Lotus 1-2-3
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Types of Decision Making Environments
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Decision Making under Certainty
Decision Making under Risk (Decision
making with probability)
Decision Making Under Uncertainty
(Decision making without probability)
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The Six Steps in Decision Theory
1.
2.
3.
4.
5.
6.
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Clearly define the problem at hand
List all the possible alternatives (decisions to be
made)
Identify the possible outcomes (state of nature) of
each alternative
List the payoff or the profit of each combination of
alternatives and outcomes
Select one of the mathematical decision theory
models (e.g. Decision Making under Risk)
Apply the model and make your decision
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Certainty, Uncertainty and Risk
The Zones of Decision Making
4-10
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Decision Making:Treating Certainty
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Certainty Models
 Assume complete knowledge
 All potential outcomes are known
 May yield optimal solution
 The decision maker knows exactly what the outcome of each
course of action will be.
 decision maker is to compute the optimal alternative or
outcome with some optimization criterion in mind.
 Ex: if the optimization criterion is least cost and you are
considering two different brands of a product, which appear
to be equal in value to you, one costing 20% less than the
other, then, all other things being equal, you will choose the
less expensive brand.
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decision making under certainty is rare because all other things are rarely equal.
Linear programming is one of the techniques for finding an optimal solution under
certainty
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Decision Making: Uncertainty and Risk
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Uncertainty
 Several outcomes for each decision
 Probability of each outcome is unknown
 Knowledge would lead to less uncertainty
 Decision under uncertainty is very difficult
 Managers attempt to avoid uncertainty.
 Instead they attempt to obtain more
information so it can be treated under certainty
Or
 Some estimated probabilities are assigned to
the outcomes and the decision making is done
as if it is decision making under risk.
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Decision Making Under Uncertainty
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Four Criteria
MAXIMAX - find the alternative that maximizes the maximum
outcome for every alternative (Optimistic approach ) Ex: stocks
MAXIMIN - find the alternative that maximizes the minimum
outcomes for every alternative (Pessimistic approach ) Ex : CDs
EQUALLY LIKELY- find the alternative with the highest
average outcome
MINIMAX REGRET- minimizes the maximum regret (regret is
the difference between the payoff from the best decision and all
the other decision payoffs)
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Decision Analysis: A Few Alternatives
Single Goal Situations
1.
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Decision tables :organize information and knowledge in a
systmatic ,tabular manner to prepare it for analysis
 Multiple criteria decision analysis
 Features include :
 Decision variables: describe alternatives course of
variable),
 Uncontrollable variables, Parameters : factors that
effect the result variables nut not under control of decision
maker
 Result variables: reflect intermediate outcomes in
mathematical models.
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Decision Making: Risk
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Risk analysis (probabilistic decision making)
 Several outcomes for each decision
 Probability of each outcome is known
 Instead of optimizing the outcomes, the general rule is to
optimize the expected outcome.
 As an example: if you are faced with a choice between two
actions one offering a 1% probability of a gain of $10000
and the other a 50% probability of a gain of $400, you as a
rational decision maker will choose the second alternative.
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Investment Example
Decision Making Under Risk
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Let us suppose that based on several economic forecasts, the
investor is able to estimate
 0.50% Solid Growth
 0.30% Stagnation
 0.20% Inflation
State of nature
Alternative
4-16
Solid Growth
.50%
Stagnation
.30%
Inflation
.20%
Bonds
12
6
3
Stocks
15
3
-2
CDs
6.5
6.5
6.5
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Investment Example
Decision Making Under Risk
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Risk analysis
1.
Compute expected values or Expected payoff (EP)
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(outcome of first state of nature)*(its prob.) + (outcome of
second state of nature)*(its prob.)+…+ (outcome of last state
of nature) * (its prob.)
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E.g. , In bonds yield = 12(.5)+6(.3)+3(.2) = 8.4 percent
The Best decision is the one with the greatest EP
If the payoffs were in terms of costs, the best decision would
be the one with the lowest EP
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Investment Example
Decision Making Under Risk
2.
Alternative approach in decision making under risk is to
minimize expected opportunity loss (EOL).
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Opportunity loss, also called regret
EOL for an alternative is sum of all possible regrets of
alternative, each weighted by probability of state of nature for
that regret occurring.
EOL (alternative i ) = (regret of first state of nature) x
(probability of first state of nature) + (regret of second state of
nature) x (probability of second state of nature) + . . . + (regret
of last state of nature) x (probability of last state of nature)
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Investment Example
Decision Making Under Risk
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EOL: Opportunity loss table (=regret table)
State of nature
Alternative
Solid Growth
.50%
Stagnation
.30%
Inflation
.20%
EOL
$
Bonds
3
.5
3.5
2.35
Stocks
0
3.5
8.5
2.75
8.5
0
0
4.25
CDs
4-19
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Min
Investment Example
Decision Making Under Risk
3.
The Maximum Likelihood Criterion
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Identify the state of nature with the largest Probability.
2. Choose the decisions alternative that has the largest
Payoff
State of nature
Alternative
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Solid Growth
.50%
Stagnation
.30%
Inflation
.20%
Bonds
12
6
3
Stocks
15
3
-2
CDs
6.5
6.5
6.5
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Investment Example
Decision Making Under Risk
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Expected Value of Perfect Information (EVPI)
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Is used to place an upper limit on what you should pay for
information that will aid in making a better decision.
Is the increase in the EP that could be obtained if it were
possible to learn the true state of nature before making the
decision
Is the difference between the expected value under certainty
and the expected value under risk
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Investment Example
Decision Making Under Risk
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Expected Value of Perfect Information (EVPI)
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EVPI = A – B
A = expected value with perfect information
B = expected value without perfect information
For A: The optimal values for each value are:
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Max Value (A)= 15*.5 +6.5*.3 +6.5*.2 =10.75
State of nature
Alternative
4-22
Solid Growth
.50%
Stagnation
.30%
Inflation
.20%
Bonds
12
6
3
Stocks
15
3
-2
CDs
6.5
6.5
6.5
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Investment Example
Decision Making Under Risk
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Expected Value of Perfect Information (EVPI)
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B = expected value without perfect information
For B: we compute the expected values for each column first,
and then select the max as below:
EVPI = 10.75-8.4 = 2.55 $
4-23
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Decision Analysis: A Few Alternatives
Single Goal Situations
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Decision trees
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Graphical representation of relationships
Multiple criteria approach
Demonstrates complex relationships
Cumbersome, if many alternatives exists
How can a decision tree be used
in decision making?
By showing the decision maker
the possible outcomes that
could result from a given
choice, the tree gives the
decision maker information by
which to compare choices
4-24
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Decision trees
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The Five Steps
1.
2.
3.
4.
Define the problem
Structure or draw the decision tree
Assign probabilities to the states of nature
Estimate the payoffs for each possible combination of
alternative and state of nature Solve the problem by
computing expected payoff (EP) for each state of nature
node
5. Make your decision
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Decision Tree Example (Self Study)
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This is just a beginning of ADM2302 course and Andrew does not know if he
should attend all classes. He consulted some other students and came to the
following conclusions:
• chances of passing a course while attending all classes are 80%
• chances of passing a course while attending randomly are 50%.
It is well known that professor who is teaching that course is giving second
chance to the students who failed. They have to solve a pretty nasty case
study.
Again, Andrew estimates that chances of solving this case if he would go to all
the classes are 60%, while they drop to just 10% if he would attend classes
randomly.
Andrew would be very happy if he passes the course (5 on a happiness scale
of 0 - 5). Clearly, he would be very disappointed if he fails (0 on a
happiness scale).
Going to a classroom requires an effort and diminished happiness associated
with passing the course.
It goes down by 3 points (happiness scale) for attending all classes and 1
point for 39 random attendance.
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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
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
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Limited quantity of economic resources
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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
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Line
Sensitivity, What-if, and
Goal Seeking Analysis
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Sensitivity
 Assesses impact of change in inputs on outputs
 Eliminates or reduces variables
 Can be automatic or trial and error
1.
2.
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Automatic Sensitivity analysis is performed in standard
quantitative model implementation such as LP
Trial and Error
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Change in any variable or in several
 Two approaches: What-if and Goal Seeking
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Sensitivity, What-if, and
Goal Seeking Analysis
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What-if
 Assesses solutions based on changes in variables or
assumptions (scenario analysis)
 Ex: What will happen to the total inventory cost if the cost
of carrying inventories increases by 10 percent?
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Sensitivity, What-if, and
Goal Seeking Analysis
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Goal seeking
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Backwards approach, starts with goal
Determines values of inputs needed to achieve goal
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Ex: what annual R&D budget is needed for an annual
growth rate of 15 percent by 2014?
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Sensitivity, What-if, and
Goal Seeking Analysis
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Computing a Break-Even Point Using Goal Seeking
 Values that generate zero profit
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Break –Even= Fixed cost / (selling cost – variable cost)
Where : fixed cost =cost that not change such as tax,
insurance ,..
Selling price: the price that a unit sold for
Variable cost : related to production unit.
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Problem –Solving Search Methods
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Search methods used in the choice phase of problem
solving includes:
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Analytical techniques , algorithms , blind searching and heuristic
searching
For normative models (Comparing all the outcomes of alternative) :
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For descriptive models(a comparison of a limited number of
alternatives is used) :
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analytical approach is used
blindly or heuristic s are used.
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Problem –Solving Search Methods
Analytical Techniques
 Use mathematical formulas to derive optimal solution
 Solving structured problems (tactical or operational)
 Ex: inventory management, resource allocation.
 Analytical Techniques may use Algorithms
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Algorithms
Step by step search process
Obtaining an optimal solution
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Web search engines use algorithms To
speed searches and produces accurate
results
4-34
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Problem –Solving Search Methods
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Blind Searching
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Problem solving is done by searching through the possible solutions
The first search methods of problem solving
Arbitrary search approaches that are not guided
Two types:
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Heuristic Searching
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A complete enumeration : all alternatives are considered to find an optimal
solution.
Incomplete (Partial) : continues until a good –enough solution is found
Informal judgmental knowledge of an application area that
constitute the rules of the good judgment in the field.
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Simulation
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Simulation is a process of designing a model
of real system a model of real system
purpose of understanding the behavior for
the operation of the behavior for the
operation of the system.
Frequently used in DSS tools
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Simulation
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System:
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Collection of entities, ex: people machines that act and interact towards the
accomplishment.
State:
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1.
Collection of variables necessary to describe a system at a particular time
relative to the objective of study
Bank model: Could include number of busy tellers, time of arrival of each
customer, etc
System can be
Discrete
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State variables change instantaneously at separated points in
time
Bank model: State changes occur only when a customer
arrives or departs
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2.
Continuous
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State variables change that continuously tracks system
response over time
Airplane flight: State variables like position, velocity change
continuously
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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
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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
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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)
Software may require special skills
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Simulation Methodology
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Model real system and conduct repetitive experiments.
Steps:
1.
2.
3.
4.
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Define problem
Construct simulation model
Test and validate model
Design experiments
5. Conduct experiments
6. Evaluate results
7. Implement solution
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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
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