Decision Support System Course
Dr. Aref Rashad
Part: 2
Modeling and Analysis-1
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Decision Support Systems Course .. Dr. Aref Rashad
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Learning Objectives
Understand basic concepts of DSS modeling.
Describe DSS models interaction.
Understand different model classes.
Structure decision making of alternatives.
Understand the concepts of optimization,
simulation, and heuristics.
• Learn to develop model component in DSS
•
•
•
•
•
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Model Component
Key element in DSS
Many classes of models
Specialized techniques for each model
Allows for rapid examination of alternative
solutions
• Multiple models often included in a DSS
•
•
•
•
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Modeling Concept
The purpose of the model is to represent critical
relationships in such a way to guide decision makers toward
a desired goal
Modeling is the simplification of some phenomenon for the
purpose of understanding its behavior.
Keep the structures which are essential for the Problem and
neglect unnecessary details.
This is the essence of modeling !!!
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Types of models
–Mental (arranging furniture)
–Visual (blueprints, road maps)
–Physical/Scale (aerodynamics, buildings)
–Mathematical (what we’ll be studying)
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Dimensionality of Models
•Representation
•Time Dimension
• Linearity of the Relationship
• Deterministic vs. Stochastic
• Descriptive vs. Normative
• Methodology Dimension
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Representation
Models rely upon either:
• Experiential data
• Objective data
Experiential models rely upon the preparation and
information processing of people, include judgments,
expert opinions, and subjective estimates.
Objective models rely upon specified, detached data and
its analysis
by known techniques. They are considered "objective"
because the data are specified, constant, and independent
of the specific decision maker's experiences.
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Time Dimension
Model Types:
• Static models
• Dynamic models
Static Models
• A snapshot in time of all factors affecting the decision
environment.
• Assume no dependence of later decisions or actions on the
choice under consideration.
• Single interval
• Time can be rolled forward, a photo at a time
• Usually repeatable
• Unvarying Steady state
• Primary tool for process design
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Time Dimension
Dynamic Model
• Consider the decision environment over some specified
time period.
• May consider the same phenomenon during different
periods of time or interrelated decisions that will be
considered during different time periods
• Represent changing situations
• Time dependent
• Varying conditions
• Generate and use trends
• Occurrence may not repeat
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Looking at Intervals of Time for Patterns
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Linearity of the Relationship
Model Types:
• Linear models
• Nonlinear models
Linear models The relation between variables are linear.
They are easier and faster to solve, and generally have a
straightforward approach to solution. They can be used to
approximate the nonlinear data.
Nonlinear models The relation between variables are
nonlinear. They are harder and slower to solve
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Nonlinear Relationships
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Deterministic Versus Stochastic
Deterministic models use specified values for variables in
the model. No randomness are considered
Stochastic models use probabilistic distributions for
one or more variables in the model to view how situations
might evolve over time
The most common form of stochastic modeling is based on
Monte Carlo analysis.
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Nonlinearity with Randomness
Results of a Monte Carlo Analysis
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Descriptive Versus Normative
Descriptive models:
•Report what is happening in the data
• Provide decision makers with a quantitative view of what is
happening in the organization
• Serve as predictive analytics, which attempt to forecast how
factors
Normative models:
• Represent an ideal value
•Illustrate how the current organization is competing relative
to a set of standards or values.
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Methodology Dimension
Complete enumeration, information about all feasible
options is collected and evaluated. Ex: Census
Algorithmic , development of a set of procedures that can be
repeated and will define the desired characteristics of the
decision environment. Ex: Operations Research
Heuristic, applied to large or ill-structured problems that
cannot be solved algorithmically.
Simulation ,to imitate reality either quantitatively or
behaviorally. It involves the repetition of an experiment and
the description of the characteristics of certain variables over
time.
Analytic, the process of breaking up a whole into its parts to
determine their nature, proportion, function, and
interrelationships
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Model Categories
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Structure of Mathematical Model
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Structure of Mathematical Model
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Structure of Mathematical Model
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Example: Iron Works, Inc.
Iron Works, Inc. manufactures two
products made from steel and just received
this month's allocation of b pounds of steel.
It takes a1 pounds of steel to make a unit of product 1
and a2 pounds of steel to make a unit of product 2.
Let x1 and x2 denote this month's production level of
product 1 and product 2, respectively. Denote by p1 and
p2 the unit profits for products 1 and 2, respectively.
Iron Works has a contract calling for at least m units of product 1 this month.
The firm's facilities are such that at most u units of product 2 may be
produced monthly.
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Example: Iron Works, Inc.
Mathematical Model
– The total monthly profit =
(profit per unit of product 1)
x (monthly production of product 1)
+ (profit per unit of product 2)
x (monthly production of product 2)
= p1x1 + p2x2
We want to maximize total monthly profit:
Max p1x1 + p2x2
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Example: Iron Works, Inc.
Uncontrollable Inputs
$100 profit per unit Prod. 1
$200 profit per unit Prod. 2
2 lbs. steel per unit Prod. 1
3 lbs. Steel per unit Prod. 2
2000 lbs. steel allocated
60 units minimum Prod. 1
720 units maximum Prod. 2
0 units minimum Prod. 2
60 units Prod. 1
626.67 units Prod. 2
Controllable Inputs
Max 100(60) + 200(626.67)
s.t. 2(60) + 3(626.67) < 2000
60
> 60
626.67 < 720
626.67 > 0
Profit = $131,333.33
Steel Used = 2000
Output
Mathematical Model
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Decision Support System Course
Dr. Aref Rashad
Part: 2
Modeling and Analysis-2
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Decision Making Overview
Decision Making
Decision Environment
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Decision Criteria
Certainty
Nonprobabilistic
Uncertainty
Probabilistic
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The Decision Environment
Decision Environment
Certainty
Uncertainty
*
Certainty: The results of decision
alternatives are known
Example:
Must print 10,000 color brochures
Offset press A: $2,000 fixed cost
+ $.24 per page
Offset press B: $3,000 fixed cost
+ $.12 per page
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The Decision Environment
(continued)
Decision Environment
Example:
Certainty
Uncertainty
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Uncertainty: The outcome that will
occur after a choice is unknown
*
You must decide to buy an item now or
wait. If you buy now the price is
$2,000. If you wait the price may drop
to $1,500 or rise to $2,200. There also
may be a new model available later
with better features.
Decision Support Systems Course .. Dr. Aref Rashad
Chap 17-42
Decision Criteria
Nonprobabilistic Decision Criteria:
Decision rules that can be applied
if the probabilities of uncertain
events are not known.
Decision Criteria
*
 maximax criterion
 maximin criterion
Nonprobabilistic
Probabilistic
 minimax regret criterion
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Chap 17-43
Decision Criteria
Probabilistic Decision Criteria:
Consider the probabilities of
uncertain events and select an
alternative to maximize the
expected payoff of minimize the
expected loss
(continued)
Decision Criteria
Nonprobabilistic
*
Probabilistic
 maximize expected value
 minimize expected opportunity loss
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Chap 17-44
Decision Tables
• Multiple criteria decision analysis
• Features include:
– Decision variables (alternatives)
– Uncontrollable variables
– Result variables
• Applies principles of certainty, uncertainty,
and risk
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Decision Tree
•
•
•
•
Graphical representation of relationships
Multiple criteria approach
Demonstrates complex relationships
Cumbersome, if many alternatives
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Add Probabilities and Payoffs
Strong Economy
(.3)
200
Stable Economy
(.5)
50
Weak Economy
(.2)
-120
Strong Economy
(.3)
Stable Economy
(.5)
Weak Economy
(.2)
Strong Economy
(.3)
Small factory
Stable Economy
(.5)
Uncertain Events
(States of Nature)
Weak Economy
(.2)
Large factory
Average factory
Decision
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90
120
-30
Payoffs
40
30
20
Probabilities
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Chap 17-47
Influence Diagrams
•
•
•
•
•
•
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Graphical representation of model
Provides relationship framework
Examines dependencies of variables
Any level of detail
Shows impact of change
Shows what-if analysis
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Influence Diagrams
• An influence diagram is a graphical device showing the
relationships among the decisions, the chance events, and
the consequences.
• Squares or rectangles depict decision nodes.
• Circles or ovals depict chance nodes.
• Diamonds depict consequence nodes.
• Lines or arcs connecting the nodes show the direction of
influence.
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Influence Diagrams
Variables:
Decision
Intermediate
or
uncontrollable
Result or outcome
(intermediate or
final)
Arrows indicate type of relationship and direction of influence
Amount
in CDs
Certainty
Uncertainty
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Interest
earned
Sales
Price
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Influence Diagrams
Random (risk)
~
Demand
Sales
Place tilde above
variable’s name
Sleep all
day
Graduate
University
Preference
(double line arrow)
Get job
Ski all
day
Arrows can be one-way or bidirectional, based upon the
direction of influence
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Sensitivity, What-if, and Goal Seeking Analysis
• Sensitivity
–
–
–
–
Assesses impact of change in inputs or parameters on solutions
Allows for adaptability and flexibility
Eliminates or reduces variables
Can be automatic or trial and error
• What-if
– Assesses solutions based on changes in variables or assumptions
• Goal seeking
– Backwards approach, starts with goal
– Determines values of inputs needed to achieve goal
– Example is break-even point determination
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Search Methods
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Search Approaches
• Analytical techniques (algorithms) for structured
problems
– General, step-by-step search
– Obtains an optimal solution
• Blind search
– Complete enumeration
• All alternatives explored
– Incomplete
• Partial search
– Achieves particular goal
– May obtain optimal goal
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Search Approaches
• Heurisitic
– Repeated, step-by-step searches
– Rule-based, so used for specific situations
– “Good enough” solution, but, eventually, will obtain
optimal goal
– Examples of heuristics
• Tabu search
– Remembers and directs toward higher quality choices
• Genetic algorithms
– Randomly examines pairs of solutions and mutations
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Network model
• A network model is one which can be represented by
a set of nodes, a set of arcs, and functions (e.g. costs,
supplies, demands, etc.) associated with the arcs
and/or nodes.
• Transportation, assignment, PERT/CPM and
transshipment problems are all examples of network
problems.
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Transportation Problem
Network Representation
s1
s2
1
2
c23
d1
2
d2
3
d3
c12
c13
c21
Sources
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c11
1
c22
Destinations
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Transportation Problem
Network Representation
s1
s2
1
2
c23
d1
2
d2
3
d3
c12
c13
c21
Sources
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c11
1
c22
Destinations
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Example: Shortest Route
Find the Shortest Route From Node 1 to All Other Nodes
in the Network:
5
2
4
3
7
1
4
6
2
3
3
1
5
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5
2
6
8
7
6
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Project Network
Start
B
D
3
3
G
F
6
A
3
3
E
C
7
2
Finish
H
2
PERT/CPM is used to plan the scheduling of individual activities that make up a
project.
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Simulation
•
•
•
•
•
•
•
Imitation of reality
Allows for experimentation and time compression
Descriptive, not normative
Can include complexities, but requires special skills
Handles unstructured problems
Optimal solution not guaranteed
Methodology
–
–
–
–
–
–
–
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Problem definition
Construction of model
Testing and validation
Design of experiment
Experimentation
Evaluation
Implementation
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Simulation
• Probabilistic independent variables
– Discrete or continuous distributions
• Time-dependent or time-independent
• Visual interactive modeling
– Graphical
– Decision-makers interact with simulated
model
– may be used with artificial intelligence
• Can be objected oriented
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Simulation Process
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Multicriteria Decisions
• Goal Programming
• Goal Programming: Formulation
and Graphical Solution
• Scoring Models
• Analytic Hierarchy Process (AHP)
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Goal Programming
• Goal programming may be used to solve
linear programs with multiple objectives,
with each objective viewed as a "goal".
• In goal programming, di+ and di- , deviation
variables, are the amounts a targeted goal i is
overachieved or underachieved, respectively.
• The goals themselves are added to the
constraint set with di+ and di- acting as the
surplus and slack variables.
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Goal Programming
• One approach to goal programming is to satisfy
goals in a priority sequence. Second-priority
goals are pursued without reducing the firstpriority goals, etc.
• For each priority level, the objective function is to
minimize the (weighted) sum of the goal
deviations.
• Previous "optimal" achievements of goals are
added to the constraint set so that they are not
degraded while trying to achieve lesser priority
goals.
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Scoring Model
• Step 1: List the decision-making criteria.
• Step 2: Assign a weight to each criterion.
• Step 3: Rate how well each decision alternative
satisfies each criterion.
• Step 4: Compute the score for each decision
alternative.
• Step 5: Order the decision alternatives from
highest score to lowest score. The alternative
with the highest score is therecom mended
alternative.
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Scoring Model for Job Selection
Mathematical Model
Sj = S wi rij
i
where:
rij = rating for criterion i and decision
alternative j
Sj = score for decision alternative j
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Scoring Model
Decision Alternative
Analyst
Accountant Auditor
Criterion
Chicag
Denver Houston
Career advancement
8
6
4
Location
3
8
7
Management
5
6
9
Salary
6
7
5
Prestige
7
5
4
Job security
4
7
6
Enjoyable work
8
6
5
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Analytic Hierarchy Process
The Analytic Hierarchy Process (AHP), is a
procedure designed to quantify managerial
judgments of the relative importance of
each of several conflicting criteria used in
the decision making process.
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Analytic Hierarchy Process
• Step 1: List the Overall Goal, Criteria, and Decision
Alternatives
------- For each criterion, perform steps 2 through 5 -------
• Step 2: Develop a Pairwise Comparison Matrix
Rate the relative importance between each
pair of decision alternatives. The matrix lists the
alternatives horizontally and vertically and has the
numerical ratings comparing the horizontal (first)
alternative with the vertical (second) alternative.
Ratings are given as follows:
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Analytic Hierarchy Process
Step 2: Pairwise Comparison Matrix
Compared to the second
alternative, the first alternative is: Numerical rating
extremely preferred
9
very strongly preferred
7
strongly preferred
5
moderately preferred
3
equally preferred
1
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Analytic Hierarchy Process
Step 2: Pairwise Comparison Matrix
Intermediate numeric ratings of 8, 6, 4, 2 can
be assigned. A reciprocal rating (i.e. 1/9, 1/8, etc.)
is assigned when the second alternative is
preferred to the first. The value of 1 is always
assigned when comparing an alternative with
itself.
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Analytic Hierarchy Process
• Step 3: Develop a Normalized Matrix
Divide each number in a column of the
pairwise comparison matrix by its column sum.
• Step 4: Develop the Priority Vector
Average each row of the normalized matrix.
These row averages form the priority vector of
alternative preferences with respect to the
particular criterion. The values in this vector
sum to 1.
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Analytic Hierarchy Process
Step 5: Calculate a Consistency Ratio
The consistency of the subjective input in
the pairwise comparison matrix can be
measured by calculating a consistency ratio. A
consistency ratio of less than .1 is good. For
ratios which are greater than .1, the subjective
input should be re-evaluated.
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Analytic Hierarchy Process
Step 6: Develop a Priority Matrix
After steps 2 through 5 has been performed for all
criteria, the results of step 4 are summarized in a
priority matrix by listing the decision alternatives
horizontally and the criteria vertically. The column
entries are the priority vectors for each criterion.
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Analytic Hierarchy Process
Step 7: Develop a Criteria Pairwise Development
Matrix
This is done in the same manner as that used to
construct alternative pairwise comparison matrices
by using subjective ratings (step 2). Similarly,
normalize the matrix (step 3) and develop a criteria
priority vector (step 4).
• Step 8: Develop an Overall Priority Vector
Multiply the criteria priority vector (from step 7)
by the priority matrix (from step 6).
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Analytic Hierarchy Process
Determining the Consistency Ratio
• Step 1:
For each row of the pairwise comparison matrix,
determine a weighted sum by summing the multiples of
the entries by the priority of its corresponding (column)
alternative.
• Step 2:
For each row, divide its weighted sum by the
priority of its corresponding (row) alternative.
• Step 3:
Determine the average, max, of the results of step 2.
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Analytic Hierarchy Process
Determining the Consistency Ratio
• Step 4:
Compute the consistency index, CI, of the n
alternatives by: CI = (max - n)/(n - 1).
• Step 5:
Determine the random index, RI, as follows:
Number of
Random
Number of
Random
Alternative (n) Index (RI) Alternative (n) Index (RI)
3
0.58
6
1.24
4
0.90
7
1.32
5
1.12
8
1.41
• Step 6:
Compute the consistency ratio: CR = CR/RI.
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Group Decision Making Techniques
Brainstorming
The process of brainstorming involves members discussing and suggesting
opinions as well as alternatives for a decision. The brainstorming session is
facilitated by the group or team leader who will solicit ideas from the
members and note them down. e divided into two groups who will debate
on the pros and cons of the alternatives.
Nominal Group Technique
A structured approach in decision making, the nominal group technique
requires each member to develop a list of possible alternatives in writing. After
that, the alternatives are presented to the group and are ranked according to
order of preference.
Delphi Technique
The Delphi technique is applicable only when the members are on separate
physical locations. The decision making process is usually done through email,
fax or other forms of online technology where the members can meet and
discuss.
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Brainstorming/Filtering
•
•
•
•
•
•
Prepare for the Brainstorming
Determine the Brainstorming Method to use
Generate Ideas
Create Filters
Apply Filters
Wrap up the Brainstorming Session
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Nominal Group Technique
•
•
•
•
•
•
•
Define the problem to be solved/decision
Silently generate ideas
State and record ideas
Clarify each on the list
Rank items silently; list rankings
Tally rankings
Wrap up NGT session
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Paired Choice Matrix
•
•
•
•
•
•
Identify the issue, options, goals
Prepare for the session
Make decisions between pairs
Tally scores of paired choices
Discuss and clarify results
Wrap up
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Criteria Rating Technique
•
•
•
•
•
•
•
Start session and list alternatives
Brainstorm decision criteria
Discuss the relative importance of each criteria
Establish a rating scale, then rate the alternatives
Calculate the final score
Select the best alternative
Wrap up
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The Delphi Technique
•
•
•
•
•
•
•
•
Define the decision or problem
Team provides Round 1 input
Summarize Round 1: ask for Round 2 input
Team provides Round 2 input**
Summarize Round 2: ask for Round 3 input
Team provides Round 3 input
Summarize Round 3
Wrap Up
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Decision Support System Course
Dr. Aref Rashad
Part: 2
Modeling and Analysis-3
Model-Based Management System
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Model-Based Management System
Easy Access to Models
The library of models is provided so as to allow decision
makers easy access to the models.
Easy access to the models means that users need not know
the specifics of how the model runs or the specific format
rules for commanding the model
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Model-Based Management System
• Software that allows model organization
with transparent data processing
• Capabilities
–
–
–
–
–
–
–
DSS user has control
Flexible in design
Gives feedback
GUI based
Reduction of redundancy
Increase in consistency
Communication between combined models
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Model-Based Management System
• Relational model base management system
– Virtual file
– Virtual relationship
• Object-oriented model base management system
– Logical independence
• Database and MIS design model systems
– Data diagram, ERD diagrams managed by CASE tools
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Simple Model Selection
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Understandability of Results
In addition, the DSS should provide the results back to the
user in an understandable form.
Most models provide information to the user employing at
least some cryptic form that is not comprehensible for
people who do not use the package frequently.
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Manipulation of a Model
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Traditional Results Format
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Results with Decision Support
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Model Support
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Passive Warning of Model Problems
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Active Warning of Model Problems
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Integrating Models
Another task of the MBMS is to help integrate one model
with another. For example, suppose the user needs to make
choices about inventory policy and selects an economic
order quantity (EOQ) model
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Integration of Models
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Modeling Results with Interpretative Support
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Model Results with Better Interpretative Support
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Model Management Support Tools
The kinds of issues associated with model-generated
questions like those in the two examples
will, of course, depend upon what model is being used.
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Passive Prompting for Further Analysis
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Active Prompting for Further Analyses
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Sensitivity of a Decision
Sensitivity of a Decision
One of the tasks of the model base management system
in a DSS is to help the decision maker understand the
implications of using a model
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Problems of Models
•The failure to identify an important variable
•Select an inappropriate time horizon
•Overfit the model to some time period
•Not knowing if the assumptions are true
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Basic Spreadsheet Modeling
Concepts and Best Practices
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Modeling with Spreadsheets
•
•
•
•
•
•
Flexible and easy to use
End-user modeling tool
Allows linear programming and regression analysis
Features what-if analysis, data management, macros
Seamless and transparent
Incorporates both static and dynamic models
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Spreadsheet modeling
The process of entering the inputs and decision variables
into a spreadsheet and then relating them
appropriately, by means of formulas, to obtain the
outputs.
Once a model is created there are several directions in
which to proceed.
– Sensitivity analysis to see how one or more outputs
change as selected inputs or decision variables
change.
– Finding the value of a decision variable that
maximizes or minimizes a particular output.
– Create graphs to show graphically how certain
parameters of the model are related.
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• Good spreadsheet modeling practices are essential.
• Spreadsheet models should be designed with
readability in mind.
• Several features that improve readability include:
• A clear logical layout to the overall model
• Separation of different parts of a model
• Clear headings for different sections of the model
• Liberal use of range names
• Liberal use of formatting features
• Liberal use of cell comments
• Liberal use of text boxes for assumptions, lists or
explanations
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Building a Model
• Randy Kitchell is a NCAA t-shirt vendor. The
fixed cost of any order is $750, the variable cost
is $6 per shirt.
• Randy’s selling price is $10 per shirt, until a
week after the tournament when it will drop to
$4 apiece. The expected demand at full price is
1500 shirts.
• He wants to build a spreadsheet model that will
let him experiment with the uncertain demand
and his order quantity.
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Building a Model
The logic behind the model is simple. An Excel IF function
will be used.
The profit is calculated
with the formula
Profit = Revenue – Cost
and the Cost = 750 + 6*B4
Revenue Case 1:
Demand outstrips order (B3 > B4)
In that case everything gets sold for 10 dollars
Revenue is then simply 10*B4
(since B4 is the number ordered)
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Building a Model
Revenue Case 2:You have ordered too many.
That is order (B3) is less than peak demand
Then you can only sell B3 at 10 dollars and the rest (B4-B3) at
4 dollars
Revenue = 10*B3+4*(B4-B3)
Revenue = IF(B3>B4,10*B4,10*B3+4*(B4-B3))
Profit = IF(B3>B4,10*B4,10*B3+4*(B4-B3)) – (750 + 6* B4)
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Building a Model
The formula can be rewritten to be more flexible.
=-B3-B4*B9+IF(B8>B9,10*B8+B6*(B9-B8))
It can be made more readable by using range names. The
formula would then read
=-Fixed_order_cost-Variable_cost*Order + IF(Demand >
Order, Selling_price*Order, 10*Demand+Salvage_value*
(Order-Demand)
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Spreadsheet for Loan problem
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END Part 2
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Decision Making without Probabilities
Three commonly used criteria for decision making
when probability information regarding the
likelihood of the states of nature is unavailable are:
– the optimistic approach
– the conservative approach
– the minimax regret approach.
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Decision Making with Probabilities
Expected Value Approach
– If probabilistic information regarding the states of
nature is available, one may use the expected
value (EV) approach.
– Here the expected return for each decision is
calculated by summing the products of the payoff
under each state of nature and the probability of
the respective state of nature occurring.
– The decision yielding the best expected return is
chosen.
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Expected Value of a Decision Alternative
• The expected value of a decision alternative is the sum
of weighted payoffs for the decision alternative.
• The expected value (EV) of decision alternative di is
defined as:
N
EV( d i )   P( s j )Vij
j 1
where:
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N = the number of states of nature
P(sj ) = the probability of state of nature sj
Vij = the payoff corresponding to decision
alternative di and state of nature sj
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Brainstorming Support Tools
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