Ch 14 - Decision Analysis (QMB4702)

Decision Tree Analysis

A diagramming and calculation technique for evaluating the implications of a chain of multiple options in the presence of uncertainty.

Decision Making

A difficult task due to 1) uncertainty in the future 2) conflicting values or objectives

Payoff Matrix

A table that summarizes the final outcome (payoff) for each decision alternative under each possible state of nature

Utility Theory

A theory that allows decision makers to incorporate their risk preference and other factors into the decision-making process. So, it is not just monetary like EMV would be.

Certainty Equivalent

Amount equivalent to decision maker's mind to a situation involving risk What you receive with certainty in one alternative

Constructing Utility Functions

Assign utility values of 0 to worst payoff and 1 to best Assign probabilities to utilities

Branch

Decision alternatives

Square

Decision node

Multicriteria Decision Making

Decision problem involving conflicting criterion or objectives two techniques multi criteria scoring model and analytic hierarchy process

Maximin

Decision rule that identifies the minimum payoff for each alternative. Choose the alternative with the largest minimum payoff. Take all the minimums, then the max of the mins. Weakness: Does not consider states of nature, and sometimes there can only be marginal differences in the mins we select from

Maximax

Decision rule where you identify maximum payoff for each alternative. Choose the alternative with the largest maximum payoff. Get the maximum in the matrix, then the maximum of the maximums. Weakness: does not take into account different states of nature and always assumes the best outcome

Alternatives

Different courses of action intended to solve a problem

Risk Premium

EMV decision maker is willing to give up to avoid a risky situation (or, willing to pay to seek one) EMV - Certainty Equivalent

Circle

Event node

Criteria

Factors that are important to the decision maker and influenced by the alternatives

States of Nature

Future events not under the decision maker's control

Regret Matrix

In a column, pick the highest, then subtract it by everything in that column. Do the same for the next column. Then you get a regret matrix. It shows the OC.

Multi-Stage Decision Problems

Many problems involve a series of decisions. These can be analyzed via decision trees. Each intermediate decision branches off

Analytic Solver

Microsoft Excel tool to construct decision trees

Rolling Back a Decision Tree

Multiply payoff by probabilities of branches to get EMV. Highest is what we select

Analytic Hierarchy Process

Provides a structured approach for determining scores and weights. 1. Create a pairwise comparison matrix (1/preference of i to j) 2. Normalize a pairwise matrix by computing sum of column, then dividing each entry in matrix by column sum. Process is repeated for other criteria. 3. Make a matrix summarizing this info, then getting the weighted average score

Utility

Represents total worth, value, or desirability of the outcome of a decision alternative to the decision maker. Each decision maker has their own utility function.

Multicriteria scoring model

Scores each alternative on each criterion. The value of score is 0 or 1. These are subjective assessments of the utility. Assigns weights to reflect relative importance.

Expected Opportunity Loss/Regret (EOL)

Selects smallest expected regret/opportunity loss First build a regret matrix, then do the weighted average by probability outcomes, then select the MINIMUM. This tells us we will have the least amount of regret

EOL EMV relationship

Smallest EOL will always be the biggest EMV

Good decisions

Something carefully considered. Can sometimes result in bad outcomes.

Probabilistic Models

Sometimes states of nature are assigned probabilities to represent the likelihood of occurrence. We estimate these probabilities from historical data. If it is one time, we can't really do this, so instead we must assign subjective probabilities based on interviews from experts. These are expected monetary value and expected opportunity loss/regret

Expected Monetary Value (EMV)

The product of a risk event probability and the risk event's monetary value It selects the largest expected monetary value. Just multiply each outcome by state of nature probability, then select the max. Weakness: should not really be used for one-time decision problems since a) we are not totally sure about probability b) could be less risk involved in one state of nature over the other even if our EMV is considered

Regret

True payoff under the same state of nature

Exponential Utility Function

Used to model classic risk averse behavior U(x) = 1 - e^(-x/R) R = risk tolerance x = monetary payoff you want to find utility for

Terminal node

a place where the game ends, represents the payoff

Decision Analysis

a set of quantitative decision-making techniques for decision situations in which uncertainty exists

Radar Chart

compares aggregate values of three or more variables represented on axes starting from the same point

Minimax Regret

decision rule focused on how much we will regret a decision if we don't go for it. Compute the regret (opportunity cost) for each. You have to make a Regret Matrix first, then pick the maximums, and find the minimum of the maximums. Weakness: Adding another alternative could change the outcome

Risk Premium > 0

risk averse

Risk Premium = 0

risk neutral

Risk Premium < 0

risk seeking

Decision Rules

the basic rules governing how decisions are made. No single decision rule is always best and each has its own weaknesses. Maximax, maximin, minimax regret

Expected Value of Perfect Information

the difference between the expected payoff with perfect information and the expected payoff under risk EV of PI = EV with PI - max EMV (this will always be minimum EOL)

Non-Probabilistic Models

the use of subjective assumptions to estimate event impact without estimating likelihood Also called deterministic. These are maximax, maximin, and the minimax regret