Chapter 4 Dr. Fadi Fayez Updated 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 AB B A A B B A 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 Bonds12%6% 3% Stocks15% 3% -2% CDs6.5% 6.5% 6.5%

10  Optimistic approach  Pessimistic approach Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

11  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 edition Copyright 2001, Prentice Hall, Upper Saddle River, NJ

12 Table 5.3: Decision Under Risk and Its Solution Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson, 6th edition Copyright 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 satisfaction Decision 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 satisfaction Decision 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 1Objective 2Objective n Total satisfaction Decision 1 multiple period sequential decision Decision 2Decision n Uncertainty t 1 Uncertainty t 2 Uncertainty t 3

 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 ) ◦ 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

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