CHAPTER 4: MODELING AND ANALYSIS
Chapter 4 in “DECISION SUPPORT AND BUSINESS INTELLIGENCE SYSTEMS”
Chapter 17 part4 in “OPERATION MANAGEMENT. HEIZER, RENDER”
1
MSS Modeling
2


Modeling is a key element in most DSS/business
intelligence (also business analytics) and a
necessity in a model-based DSS.
There are many classes of models, and there are
often many specialized techniques for solving each
one
MSS Modeling
3

DSS Models

Algorithm-based models
Example: To make cost estimation. This model is programmed directly in the DSS.

Statistic-based models
Example :demand forecasting

Linear programming models
Example : A transportation model to determine the best shipping from product sources to
distribution centers (fed to it from the previous model) and hence to customers.

Graphical models
Example :A geographic information system

Qualitative models
Example :A financial and risk simulation model

Simulation models

Quantitative models (mathematical Models)
MSS Modeling
(Cont.)
4

There are some major modeling issues include:
Problem identification and environment analysis
 Variable identification
 Forecasting
 The use of multiple model
 Model categories
 Model management
 KNOWLEDGE-BASED modeling

Problem Identification
5

Environmental scanning and analysis, which is the
monitoring, scanning and interpretation of collected
information.

It is important to analyze the scope of the domain and forces
and dynamics of the environment.

A decision maker need to identify the organizational culture
and the corporate decision-making processes.

The problem must be understood, and everyone involve
should share the same frame.
MSS Modeling
(Cont.)
6

There are some major modeling issues include:
Problem identification and environment analysis
 Variable identification
 Forecasting
 The use of multiple model
 Model categories
 Model management
 KB modeling

Variable identification
7

Identification of the model variables, which are decision, result and
uncontrolled variables, and their relationships.

Influence diagrams : are graphical models of mathematical models, can
facilitate this process.

Cognitive maps is more general form of influence diagram which help a
decision maker to develop a better understanding of the problem.
Cognitive map
8
Influence diagram
9
MSS Modeling
(Cont.)
10

There are some major modeling issues include:
Problem identification and environment analysis
 Variable identification
 Forecasting
 The use of multiple model
 Model categories
 Model management
 KB modeling

Forecasting
11


Predicting the future.
Essential for constructing and manipulation of the
models.
E-commerce need forecasting
 Predictive analytics systems attempt to predict the most
profitable customers, the worst customers, and focus on
identifying products and services at appropriate prices to appeal
to them

MSS Modeling
(Cont.)
12

There are some major modeling issues include:
Problem identification and environment analysis
 Variable identification
 Forecasting
 The use of multiple model
 Model categories
 Model management
 KB modeling

Multiple model
13

A decision support system can include several
models, each represent a different part of decision
making problem.
MSS Modeling
(Cont.)
14

There are some major modeling issues include:
Problem identification and environment analysis
 Variable identification
 Forecasting
 The use of multiple model
 Model categories
 Model management
 KB modeling

Model category
15
MSS Modeling
(Cont.)
16

There are some major modeling issues include:
Problem identification and environment analysis
 Variable identification
 Forecasting
 The use of multiple model
 Model categories
 Model management
 KB modeling

Model management
17

Models must be managed to maintain their integrity
and thus their applicability.

Such management is done with the aid of model
base management systems
Knowledge Base Modeling
18


DSS uses mostly quantitative models, whereas
expert systems use qualitative, knowledge-based
models in their applications.
knowledge is necessary to construct solvable
models especially when considering expert systems
Static and Dynamic Models
19
DSS models can be classified as static or dynamic.
1. Static Models:
 Take
Single snapshot of situation
 Single interval
 Time can be rolled forward.
 Usually repeatable
 Stability in relevant data can is assumed
Static and Dynamic Models
20
2.
Dynamic Model:
 Is
Represent scenarios that change over time
 Time dependent
 Varying conditions
 Generate and use patterns

They also show averages per period, moving averages, and
comparative analyses .
CERTAINTY, UNCERTAINTY, AND RISK
21
Customary, we classify this knowledge into three
categories, ranging from complete knowledge to total
ignorance. These categories are
1-Certainty
2-Risk
3- Uncertainty
 When we develop models, any of these conditions
can occur, and different kinds of models are
appropriate for each case.

Decision Making Environment
22
Certainty, Uncertainty and Risk
Decision-Making Under Certainty
23

A condition under which it is assumed that future values are
known for sure and only one result is associated with an
action.

It occurs most often with structured problem with short time.

Certainty models are easy to develop and solve
Decision-Making Under Uncertainty
24

The decision maker consider situations in which
several outcomes are possible for each course of action

Probability of occurrence of each outcome unknown

It is more difficult than decision making under
certainty because there is insufficient information

Instead of dealing with uncertainty, the decision
makers attempt to obtain more information so that the
problem can treated:
Under certainty
 Under calculate risk.

Decision-Making Under Risk
25

It also known as a probabilistic, stochastic decision
making.

The decision maker must consider several possible
outcomes for each alternative, each with given
probability of occurrence.

Risk analysis
A decision-making method that analyzes the risk (based on
assumed known probabilities) associated with different
alternatives. Also known as calculated risk
 Can be performed by calculating the expected value of each
alternative and selecting the one with best expected value

Influence Diagrams
4-26





Graphical representation of model: a model of a model
It shows the key elements, including decisions,
uncertainties, and objectives as nodes
It also shows dependencies among variables &
provides relationship framework
It could be drawn in any level of detail
It can demonstrate the dynamic nature of the problem

The simplest way to extend an static ID into a dynamic one
is by including multiple instances (time slices)
Influence Diagrams
4-27
Decision
Variables
Result or outcome
variables (intermediate or
final)
Uncontrollable
or intermediate
variables
Arrows indicate type of relationship and direction of influence
Certainty
Amount
in CDs
Interest
earned
Sales
Uncertainty
Price
Influence Diagrams
4-28
Random (risk)
~
Demand
Sales
Place tilde above
variable’s name
Preference
(double line arrow)
Sleep all
day
Graduate
University
Get job
Ski all
day
Arrows can be one-way or bidirectional, based upon the
direction of influence
Profit Model Example
4-29
Consider the following profit model:
Profit = income – expenses
Income = units sold * unit price
Units sold = 0.5 * amount used in ads
Expenses = unit cost * unit sold + fixed cost
The influence diagram is shown next.
30
An Influence Diagram for the Profit
Model
MSS Modeling with Spreadsheets
31

Models can be developed and implemented in a variety
of programming languages and systems

With their strength and flexibility, spreadsheet
packages were quickly recognizes as easy-to-use
software.

The spreadsheet is clearly the most popular end-user
modeling tool because it incorporates many powerful
financial, statistical, mathematical, and other functions.

Allows linear programming and regression(failure)
analysis
MSS Modeling with Spreadsheets
(cont.)
32

Other important spreadsheet features include what-if
analysis, goal seeking, data management, and
programmability.

Most
spreadsheet
packages
provide
fairly
seamless(easy) integration because they read and write
common file structures and easily interface with
databases and other tools.

Microsoft Excel is the most popular spreadsheet
package.

Static or dynamic models can be built in a spreadsheet
Introduction to Decision Analysis
33

The field of decision analysis provides framework for making
important decisions.

Decision analysis allows us to select a decision from a finite, and
usually not too large, number of possible decision alternatives when
uncertainties regarding the future exist.

The goal is to optimized the resulting payoff in terms of a decision
criterion.

Single-goal situations can be modeled with:


decision tables
decision trees
Decision problem
34

The basic elements of decision making in decision analysis:
Alternatives
State of nature
(event)
Payoff
Decision problem
35

A decision problem is characterized by decision
alternatives, states of nature, and resulting payoffs.

The decision alternatives are the different possible
strategies the decision maker can employ.

The states of nature refer to future events, not
under the control of the decision maker, which will
ultimately affect decision results
Payoff Table Analysis
36
Payoff
Table analysis can be applied when There is a finite set of discrete decision alternatives.
The outcome of a decision is a function of a single future event.
In a Payoff Table The rows correspond to the possible decision alternatives.
The columns correspond to the possible future events.
Events (States of Nature) are mutually exclusive and collectively
exhaustive.
The body of the table contains the payoffs.
 Payoffs can be expressed in terms of profit, cost, time, distance or
any other appropriate measure.
Payoff Table Analysis
37
States of nature
alternatives
State 1
State 2
Attentive 1
Outcome 1
Outcome 2
Alternative 2
Outcome 3
Outcome 4
Decision tree
38

The Payoff Table approach is useful for a single
decision situation.

Many real-world decision problems consists of a
sequence of dependent decisions.

Decision Trees are useful in analyzing multi-stage
decision processes.
Decision tree
(cont.)
39

A decision tree is a chronological(sequential) representation of the
decision problem.

Each decision tree has two types of nodes:



round nodes correspond to the states of nature
square nodes correspond to the decision alternatives.
The tree is constructed outward into the future with branches
emanating from the nodes.


A branch emanating from a decision node corresponds to a decision
alternative. It includes a cost or benefit value.
A branch emanating from a state of nature node corresponds to a particular
state of nature, and includes the probability of this state of nature.
Decision tree (cont.)
40
State 1
1
State 2
State 1
2
State 2
State of nature node
Decision Making Strategy Using Decision Tree
 Work
backward from the end of each branch.
 At a state of nature node, calculate the expected
value of the node.
 At a decision node, the branch that has the highest
ending node value is the optimal decision.
 The highest ending node value is the value for the
decision node.
Let us illustrate by the following example
42
Example :Getz Products New Plant
Construction Decision
•
Getz Products Company is investigating the possibility of
producing and marketing backyard storage sheds.
•
Starting this project would require the construction of either
a large or a small manufacturing plant.
•
The market for the storage sheds could either be favorable or
unfavorable. Each state of nature has .50 chance of
occurring.
•
With a favorable market a large facility will give Getz
Products a net profit of $200,000. If the market is
unfavorable, a $180,000 net loss will occur.
•
A small plant will result in a net profit of $100,000 in a
favorable market, but a net loss of $20,000 will be
encountered if the market is unfavorable.
Supplemen
t 2-43
Solution
EV for node 1
= $10,000
= (.5)($200,000) + (.5)(-$180,000)
Payoffs
Favorable market (.5)
1
Unfavorable market (.5)
Favorable market (.5)
Construct
small plant
2
EV for node 2
= $40,000
Unfavorable market (.5)
$200,000
-$180,000
$100,000
-$20,000
= (.5)($100,000) + (.5)(-$20,000)
$0
44
Example: Tom Brown Investment
Decision

Tom Brown has inherited $1000.

He has decided to invest the money for one year.

A broker has suggested five potential investments.
 Gold.
 Junk
Bond.
 Growth Stock.
 Certificate of Deposit.
 Stock Option Hedge.
45
Example: Tom Brown Investment
Decision(cont.)
The return on each investment depends on the (uncertain) market behavior
during the year. Tom considers several stock market states (expressed by
changes in the DJA)
S.1:
S.2:
S.3:
S.4:
S5:
State of Nature
DJA Correspondence
A large rise in the stock market
A small rise in the stock market
No change in the stock market
A small fall in stock market
A large fall in the stock market
Increase over 1000 points
Increase between 300 and 1000
Change between -300 and +300
Decrease between 300 and 800
Decrease of more than 800
Tom has to make the investment decision
Solution
46

Construct a Payoff Table.

Select a Decision Making Criterion.

Apply the Criterion to the Payoff table.

Identify the Optimal Decision.

Evaluate the Solution.
Solution (cont.)
47

Construct a Payoff Table
 Determine

the set of possible decision alternatives.
for Tom this is the set of five investment opportunities.
 Defined
the states of nature.
The Payoff Table
48
States of Nature
Decision Alternatives
Large Rise Small Rise No Change Small Fall Large Fall
Gold
-100
100
200
300
0
Bond
250
200
150
-100
-150
Stock
500
250
100
-200
-600
C/D Account
60
60
60
60
60
Stock Option Hedge200
150
150
-200
-150
The Stock Option Alternative is dominated by the Bond Alternative
because the payoff for each state of nature for the stock option  the payoff
for the bond option. Thus the stock option hedge can be eliminated from any
consideration
Decision Making Criteria
49

One way of categorizing such criteria involves
decision maker’s knowledge of which state of nature
will occur:

Decision making under certainty


Decision making under uncertainty.( no probabilities)


The future state of nature is assumed known
There is no knowledge about the probability of the states of nature
occurring.
Decision making under risk (with probabilities)

There is some knowledge of the probability of the states of nature
occurring.
Decision Making Under Uncertainty
50

The decision criteria are based on the decision maker’s
attitude toward life.

These include an individual being pessimistic or optimistic,
conservative or aggressive.

Criteria




Maximin Criterion - pessimistic (negative)or conservative approach.
Minimax Regret Criterion - pessimistic or conservative approach.
Maximax criterion - optimistic or aggressive approach.
Principle of Insufficient Reasoning.
Decision Making Under Uncertainty
(cont.)
51
1.
The Maximin Criterion

This criterion is based on the worst-case scenario.

It fits both a pessimistic and a conservative decision maker.

A pessimistic decision maker believes that the worst
possible result will always occur.
 A conservative
decision maker wishes to ensure a
guaranteed minimum possible payoff.
Decision Making Under Uncertainty
(cont.)
52
 To
find an optimal decision
 Record
the minimum payoff across all states of nature for
each decision.
 Identify the decision
TOM BROWN - Continued
Decisions
Gold
Bond
Stock
C/D account
with the maximum “minimum payoff”.
The Maximin Criterion
LargeRrise Small Rise No change Small Fall
-100
250
500
60
100
200
250
60
200
150
100
60
300
-100
-200
60
Minimum
Large Fall Payoff
0
-150
-600
60
-100
-150
-600
60
Decision Making Under Uncertainty
(cont.)
53
2.
The Minimax Regret Criterion
 This
criterion fits both a pessimistic and a conservative
decision maker.
 The
payoff table is based on “lost opportunity,” or
“regret”.
 The decision maker acquire regret by failing to choose
the “best” decision.
Decision Making Under Uncertainty
(cont.)
54

To find an optimal decision
 For each state of nature.
 Determine the best payoff over all decisions.
 Calculate the regret for each decision alternative as
the difference between its payoff value and this best
payoff value.
 For each decision find the maximum regret over all states
of nature.
 Select the decision alternative that has the minimum of
these “maximum regrets”.
500 - (-100)
= 600
500
-100
The Payoff Table
Decision Large rise Small rise No change Small fall Large fall
Gold
-100-100 100 Investing
200in Gold incurs
300a regret 0
when
exhibits -150
Bond
250
200
150the market-100
500
Stock
500
250
100a large rise
-200
-600
C/D
60
60
60
60
60
The Regret Table
Maximum
Decision Large rise Small rise No change Small fall Large fall Regret
Gold
600
150
0
0
60
600
Let us build the Regret Table
Bond
250
50
50
400
210
400
Stock
0
0
100
500
660
660
C/D
440
190
140
240
0
440
Decision Making Under Uncertainty
(cont.)
56
3.
The Maximax Criterion
This criterion is based on the best possible scenario.
 It fits both an optimistic and an aggressive decision maker.
 An optimistic decision maker believes that the best
possible outcome will always take place regardless of the
decision made.
 An aggressive decision maker looks for the decision with
the highest payoff (when payoff is profit)

Decision Making Under Uncertainty
(cont.)
57

To find an optimal decision.
 Find the maximum payoff for each decision alternative.
 Select the decision alternative that has the maximum of
the “maximum” payoff.
The Maximax criterion
Maximum
Decision Large rise Small rise No changeSmall fall Large fall Payoff
Gold
-100
100
200
300
0
300
Bond
250
200
150
-100
-150
250
Stock
500
250
100
-200
-600
500
C/D
60
60
60
60
60
60
Decision Making Under Uncertainty
(cont.)
58
4.
The Principle of Insufficient Reason

This criterion might appeal to a decision maker who is neither
pessimistic nor optimistic.
It assumes all the states of nature are equally likely to occur.
 The procedure to find an optimal decision.

 For
each decision add all the payoffs.
 Select
the decision with the largest sum (for profits).
Decision Making Under Uncertainty
(cont.)
59

Sum of Payoffs
 Gold 500 Dollars
 Bond 350 Dollars
 Stock
50 Dollars
 C./D 300 Dollars

Based on this criterion the optimal decision alternative is to
invest in gold.
Decision Making Under Risk
60




Probabilistic decision situation
States of nature have probabilities of occurrence.
The probability estimate for the occurrence of each
state of nature( if available) can be incorporated in
the search for the optimal decision.
For each decision calculate its expected payoff by
S
(Probability)(Payoff)
Expected Payoff =
Over States of Nature
Select the decision with the best expected payoff or
expected value EV
61
Decision Making Under Risk
(cont.)
(0.2)(250) + (0.3)(200) + (0.3)(150) + (0.1)(-100) + (0.1)(-150) = 130
Decision Making Under Risk
(cont.)
62

When to Use the Expected Value Approach
 The
Expected Value Criterion is useful in cases where
long run planning is appropriate, and decision
situations repeat themselves.
Decision Making Under Certainty
63


Now suppose that Tom has been approached by an
economic forecasting firm that proposes to help
him in making the investment decision. The firm
claim that their analysts will tell Tom with
CERTAINTY how the future economic situation
will be for $50.
This will turn Tom’s decision environment to one
of decision making under certainty.
Should Tom purchase the forecast ?
Decision Making Under Certainty
(con.)
64

The gain in Expected Return obtained from knowing with
certainty the future state of nature is called:
Expected Value of Perfect Information (EVPI)

EVPI = Expected value with perfect information - Best EV

EV: Expected Return of the EV criterion .

EVwPI: Expected Return with Perfect Information =
(best outcome of 1st state of nature)*(Probability of 1st state of nature)
+ ….. +(best outcome of last state of nature)*(Probability of last state of
nature)
Decision Making Under Certainty
(cont.)
65
If it were known with certainty
that there will be a “Large Rise” in the market
-100rise
Large
250
Stock
500
60
... the optimal decision would be to invest in...
Similarly,
Expected Return with Perfect information =
0.2(500)+0.3(250)+0.3(200)+0.1(300)+0.1(60) = $271
EVPI = EVwPI - EV = $271 - $130 = $141
Decision Making Under Certainty
(cont.)
66
Yes, Tom should purchase the forecast.
His expected return is greater than the forecast
cost.