Chapter 4

Dr. Fadi FayezUpdated by: Ola A.Younis

Problem Identification. Environmental analysis. Variable Identification. Forecasting. The Use of multiple models. Model categories. Model management. Knowledge-based modeling.

The perception of a difference between the current state of affairs and the desired state of affairs.

The problem statement contains (3) components:◦ Current state of affairs.◦ Desired state of affairs.◦ Central of objectives that distinguishes the two.

A common error in the formation of the problem is a premature focus on the choice set of solutions rather than the problem itself.

Problem Scope Once the problem is defined, the decision maker

must examine the scope of the problem, i.e. available resources, cognitive limitation, time constraints, etc

Decision-making under certainty: assumed that complete knowledge is available so that

decision maker knows exactly what the outcome of each course of action will be.

Decision-making under Uncertainty:Several outcomes are possible for each course of action. Decision maker does not know, or can't estimate the

probability of occurrence of the possible outcome. Decision-making under Risk: Several possible (random) outcomes for each action with

several probabilities. Risk analysis must calculated.

Influence Diagrams A method of modelling a decision

Sales volume

low

medium

high

A B

BA

A B

BA

A outcome is relevant to the probability of event B

Decision A is necessary to estimate probability of event B

Outcome of event A is known when making decision B

Decision A is made prior to decision B

Single Goal Situations

Decision tables

Decision trees

Investment example

One goal: maximize the yield after one year

Yield depends on the status of the economy (the state of nature)◦ Solid growth◦ Stagnation◦ Inflation

1. If solid growth in the economy, bonds yield 12%; stocks 15%; time deposits 6.5%

2. If stagnation, bonds yield 6%; stocks 3%; time deposits 6.5%

3. If inflation, bonds yield 3%; stocks lose 2%; time deposits yield 6.5%

Decision variables (alternatives) Uncontrollable variables (states of economy) Result variables (projected yield)

States of Nature

Solid Stagnation Inflation

Alternatives Growth

Bonds 12% 6% 3%

Stocks 15% 3% -2%

CDs 6.5% 6.5% 6.5%

10

Optimistic approach

Pessimistic approach

Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th editionCopyright 2001, Prentice Hall, Upper Saddle River, NJ

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Use known probabilities (Table 5.3)

Risk analysis: compute expected values

Can be dangerous

Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th editionCopyright 2001, Prentice Hall, Upper Saddle River, NJ

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Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th editionCopyright 2001, Prentice Hall, Upper Saddle River, NJ

Decision Tree A more detailed method of modelling a

decision

Enter contest

win contest win large

return of wager

Lose wager

Lose/gain nothing

loose contest

Do not enter contest

Basic Risky Decision Problems faced by the decision maker that

require a choice selection in the face of some uncertainty

Blasters soft drink example

uncertainty

Decision

Basic risky decision

Objective

Objective 1

Objective 2

Objective n

Total satisfactionDecision

uncertainty

Basic risky decision with multiple objectives

Certainty Decision Structure It involves situation in which the trade-off among the various

objectives and risk is not significant A variation of this structure is the multiple objectives and no-

risk decision It arises in situation that are so broad and complex

Objective 1

Objective 2

Objective n

Total satisfactionDecision

multiple objectives, no-risk decision

Sequential Decision Structure Conditions during the decision process may change over time,

and a choice made earlier may not be appropriate any more It represents a series of basic risky decisions in a successive

time period with arrows to indicate the relationship between each temporal set

Objective 1 Objective 2 Objective n

Total satisfactionDecision 1

multiple period sequential decision

Decision 2 Decision n

Uncertaintyt1

Uncertaintyt2

Uncertaintyt3

A model is a simplified representation of a real situation. modeling is the process of developing, analyzing and interpreting a model in order to help make better decisions.

Decision models can be classified in a number of ways, i.e. time, mathematical or logical focus.

A problem can be thought as a set of subsystems that are functionally decomposable at the desire of the decision maker

Abstract Model characteristics:1.It focuses on the mathematical precision with which various

outcomes can be predicted. 2.Since each subsystem of the problem context is modelled and

further decomposed, some detail of the information is lost to the decision maker

Abstract Model can be divided into four subsystems:

Deterministic Models: Stochastic Models Simulation Models Domain Specific Models

The construction of a simulation model for discrete events goes through the following steps:

State the objective of the model Define the scope and boundary of the system Define the state of the system Define all events that can effect the system state

and their individual impact on each state variable Define the unit of time used by the system Create statistical definition for each event in the

model Determine, a priori, the metrics desired from the

model Define the starting state of the model

A formal mathematical approach to a problem may not be the most appropriate strategy? Check out the disadvantages of Abstract Models ? Page 116.

Conceptual model can be thought as an analogies to the problem context

Experience from a past problem context can be used to assist in forecasting events and outcomes in a new context

Conceptual model often criticized as a subjective and individually biased toward the beliefs of the decision maker

Steve Hornik Drive up mail example (pages 118-119)◦ Strong acceptance◦ Poor acceptance◦ Moderate acceptance

A decision is not much of a decision unless some uncertainty is present

Uncertainty must be quantified in some manner in order for a decision to be made with any degree of success

Three requirement of probability:◦ All probability must be within the range of 0 to ◦ The probabilities of individual outcomes of an event must add

up to the probability of their union◦ The total probability of a complete set of outcomes must be

equal to 1

Types of probability◦ Long-run frequency◦ Subjective◦ Logical

Direct Forecasting

Odds Forecasting◦ It focuses on gambling prospective◦ The goal is to find a specific amount of money to

win or lose

Comparison Forecasting◦ Similar to the odds forecasting method◦ It presents the decision maker with a choice

between of one of lottery-like events

Graduation

Science related college

Remain at university

Non-science related college

fails

IT

Medicine related practical college

Basic science

literature

Languages and admin.

IT jobs

teaching

Hospitals and labs

teaching

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