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CHAPTER 4: MODELING AND ANALYSIS

Chapter 4 in “DECISION SUPPORT AND BUSINESS INTELLIGENCE SYSTEMS”

Chapter 17 part4 in “OPERATION MANAGEMENT. HEIZER, RENDER”

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MSS Modeling

DSS Models Algorithm-based models Statistic-based models Linear programming models Graphical models Quantitative models Qualitative models Simulation models

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MSS Modeling (Cont.)

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

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Problem Identification

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.

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MSS Modeling (Cont.)

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

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Variable identification

Identification of the model variables, which are decision, result and uncontrolled variables, and their relationships. Influence diagrams Cognitive maps is more general form of

influence diagram which help a decision maker to develop a better understanding of the problem.

Influence diagramCognitive map

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MSS Modeling (Cont.)

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

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Forecasting

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

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MSS Modeling (Cont.)

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

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Multiple model

A decision support system can include several models, each represent a different part of decision making problem.

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MSS Modeling (Cont.)

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

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Model category

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MSS Modeling (Cont.)

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

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Model management & Knowledge Base Modeling

Models must be managed to maintain their integrity

Some knowledge is necessary to construct solvable models especially when considering expert systems

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Static and Dynamic Models

1. Static Models: Single snapshot of situation Single interval Time can be rolled forward. Usually repeatable Stability in relevant data can is assumed

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Static and Dynamic Models

2. Dynamic Model: Represent scenarios that change over time Time dependent Varying conditions Generate and use patterns Show averages.

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Decision Making Environment

Certainty, Uncertainty and Risk

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Decision-Making Under Certainty 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

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Decision-Making Under Uncertainty

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.

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Decision-Making Under Risk

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 Diagrams4-21

Graphical representation of model: a model of a model

It depicts 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 Diagrams4-22

Decision Variables

Result or outcome variables (intermediate or

final)

Certainty

Uncertainty

Arrows indicate type of relationship and direction of influence

Amount in CDs

Interest earned

PriceSales

Uncontrollable

or intermediate

variables

Influence Diagrams4-23

Random (risk)Place tilde above variable’s name

~ Demand

Sales

Preference(double line arrow)

Graduate University

Sleep all day

Ski all day

Get job

Arrows can be one-way or bidirectional, based upon the direction of influence

Profit Model Example 4-24

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.

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An Influence Diagram for the Profit Model

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MSS Modeling with Spreadsheets

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 analysis

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MSS Modeling with Spreadsheets (cont.)

Other important spreadsheet features include what-if analysis, goal seeking, data management, and programmability.

Most spreadsheet packages provide fairly seamless 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

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Introduction to Decision Analysis

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

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Decision problem

The basic elements of decision making in decision analysis:

alternatives

State of nature ( event)

payoff

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Decision problem

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

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Payoff Table Analysis

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.

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Payoff Table Analysis

States of nature

alternatives State 1 State 2

Attentive 1 Outcome 1 Outcome 2

Alternative 2 Outcome 3 Outcome 4

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Decision tree

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.

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Decision tree (cont.)

A decision tree is a chronological 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.

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Decision tree (cont.)

1

2

State 1

State 2

State 1

State 2

Alte

rnat

ive

1

Alternative 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

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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.

SolutionSupplement 2-38

= (.5)($200,000) + (.5)(-$180,000)EV for node 1= $10,000

EV for node 2= $40,000 = (.5)($100,000) + (.5)(-$20,000)

Payoffs

$200,000

-$180,000

$100,000

-$20,000

$0

Construct la

rge plant

Construct small plant

Do nothing

Favorable market (.5)

Unfavorable market (.5)1

Favorable market (.5)

Unfavorable market (.5)2

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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.

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Example: Tom Brown Investment Decision(cont.)

State of Nature DJA Correspondence

S.1: A large rise in the stock market Increase over 1000 pointsS.2: A small rise in the stock market Increase between 300 and 1000S.3: No change in the stock market Change between -300 and +300S.4: A small fall in stock market Decrease between 300 and 800S5: A large fall in the stock market Decrease of more than 800

State of Nature DJA Correspondence

S.1: A large rise in the stock market Increase over 1000 pointsS.2: A small rise in the stock market Increase between 300 and 1000S.3: No change in the stock market Change between -300 and +300S.4: A small fall in stock market Decrease between 300 and 800S5: A large fall in the stock market Decrease of more than 800

The States o

f Natu

re

are M

utually

Exclusiv

e

and Collecti

ve

Exhaustive

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)

Tom has to make the investment decision

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Solution

Construct a Payoff Table.

Select a Decision Making Criterion.

Apply the Criterion to the Payoff table.

Identify the Optimal Decision.

Evaluate the Solution.

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Solution (cont.)

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.

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The Payoff Table

States of Nature

Decision AlternativesLarge Rise Small Rise No Change Small Fall Large Fall

Gold -100 100 200 300 0Bond 250 200 150 -100 -150Stock 500 250 100 -200 -600C/D Account 60 60 60 60 60Stock 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

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Decision Making Criteria

One way of categorizing such criteria involves decision maker’s knowledge of which state of nature will occur:

Decision making under certainty The future state of nature is assumed known

Decision making under uncertainty.( no probabilities) 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.

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Decision Making Under Uncertainty 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 or conservative approach. Minimax Regret Criterion - pessimistic or conservative

approach. Maximax criterion - optimistic or aggressive approach. Principle of Insufficient Reasoning.

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Decision Making Under Uncertainty (cont.)

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.

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Decision Making Under Uncertainty (cont.)

To find an optimal decision

Record the minimum payoff across all states of

nature for each decision.

Identify the decision with the maximum

“minimum payoff”. The Maximin Criterion Minimum

Decisions LargeRrise Small Rise No change Small Fall Large Fall Payoff

Gold -100 100 200 300 0 -100Bond 250 200 150 -100 -150 -150Stock 500 250 100 -200 -600 -600C/D account 60 60 60 60 60 60

TOM BROWN - Continued

The Optimal

decision

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Decision Making Under Uncertainty (cont.)

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 incurs regret by failing

to choose the “best” decision.

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Decision Making Under Uncertainty (cont.)

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”.

The Payoff TableDecision Large rise Small rise No change Small fall Large fallGold -100 100 200 300 0Bond 250 200 150 -100 -150Stock 500 250 100 -200 -600C/D 60 60 60 60 60

Let us build the Regret Table

The Regret Table MaximumDecision Large rise Small rise No change Small fall Large fall RegretGold 600 150 0 0 60 600Bond 250 50 50 400 210 400Stock 0 0 100 500 660 660C/D 440 190 140 240 0 440

Investing in Gold incurs a regretwhen the market exhibits

a large rise 500

500

500

-100

-100

-(-100) = 600

The Optimal decision

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Decision Making Under Uncertainty (cont.)

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)

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Decision Making Under Uncertainty (cont.)

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 MaximumDecision Large rise Small rise No changeSmall fall Large fall PayoffGold -100 100 200 300 0 300Bond 250 200 150 -100 -150 200Stock 500 250 100 -200 -600 500C/D 60 60 60 60 60 60

The Optimal decision

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Decision Making Under Uncertainty (cont.)

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).

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Decision Making Under Uncertainty (cont.)

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.

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Decision Making Under Risk

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

(Probability)(Payoff)

Over States of NatureExpected Payoff = S Select the decision with the best expected

payoff or expected value EV

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Decision Making Under Risk (cont.)

The Expected Value Criterion ExpectedDecision Large rise Small rise No changeSmall fall Large fall ValueGold -100 100 200 300 0 100Bond 250 200 150 -100 -150 130Stock 500 250 100 -200 -600 125C/D 60 60 60 60 60 60Prior Probability0.2 0.3 0.3 0.1 0.1

(0.2)(250) + (0.3)(200) + (0.3)(150) + (0.1)(-100) + (0.1)(-150) = 130

The Optimal decision

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Decision Making Under Risk (cont.)

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.

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Decision Making Under Certainty 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 ?

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Decision Making Under Certainty (con.)

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)

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Decision Making Under Certainty (cont.)

The Expected Value of Perfect Information Decision Large Rise Small Rise No change Small Fall Large FallGold -100 100 200 300 0Bond 250 200 150 -100 -150Stock 500 250 100 -200 -600C/D 60 60 60 60 60Probab. 0.2 0.3 0.3 0.1 0.1

If it were known with certainty that there will be a “Large Rise” in the market

Large rise

... the optimal decision would be to invest in...

-100

250 500 60

Stock

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

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Decision Making Under Certainty (cont.)

Yes, Tom should purchase the forecast.

His expected return is greater than the forecast cost.