BUS104 CH#13: Decision Analysis

Decision tree: branches

-Branches leaving each round node represent different states of nature -Branches leaving each square node represent difference decision alternatives

What is the step-by-step calculation for EVPI?

1) Determine the optimal return corresponding to each state of nature 2) Compute expected value of these optimal returns 3) Subtract the EV of the optimal decision from the amount determined in Step 2

What is the "decision problem" characterized by?

1) decision alternatives 2) states of nature 3) resulting payoffs

How do you define states of nature?

1) mutually exclusive (no more than one can occur) 2) collectively exhaustive (at least one must occur) -thus one and only one of the possible states of nature will occur

What are the 3 commonly used criteria for decision making when probability information regarding the likelihood of the states of nature is *unavailable*?

1) optimistic approach (the risk taker) 2) conservative approach (the risk averse) 3) minimax regret approach (in between)

Decision tree:

A chronological (aka time dependent) representation of the decision problem.

Influence diagram:

A graphical device that shows the relationship among decisions, chance events, and consequences for a decision problem

Decision strategy:

A strategy involving a sequence of decisions and chance outcomes to provide the optimal solution to a decision problem.

Payoff table:

A table showing payoffs for all combinations of decision alternatives and states of nature

Influence diagram: nodes

An intersection or junction point of an influence diagram or a decision tree

Decision analyis:

Can be used to develop an optimal strategy when a decision makes is faced with several decision alternatives and an uncertain or risk-filled pattern of future events

How do you find the expected value of a decision alternative?

Find the sum of the weighted payoffs for the decision alternative P(sj) = probability of each state of nature Vij = payoff of decision di under state of nature (sj) N = number of states of nature

How can payoffs be expressed?

In profit, cost, time, distance, or any other appropriate measure

What can sensitivity analysis be used to determine?

It can determine how changes to probabilities of the states of nature and values of payoffs will have of the chosen decision alternatives

Influence diagram: decision nodes

Nodes indicating points where a decision is made. -Squares or rectangles

Influence diagram: chance nodes

Nodes indicating points where an uncertain event will occur (aka states of nature). -Circles or ovals

Influence diagram: consequence nodes

Nodes of an influence diagram indicating points where a payoff will occur. -Diamonds

Decision alternatives:

Options available to the decision maker that they can employ

Payoff:

The consequence resulting from a specific combination of a decision alternative and a state of nature

expected value of perfect information (EVPI):

The expected value of information that would tell the decision maker exactly which state of nature is going to occur (i.e., perfect information -it is the increase in expected profit that would result if we knew which state of nature were to occur -this provides an "upper bound" on the expected value of any survey or sample info

Influence diagram: arcs

The lines connecting the nodes that show the direction of influence that the nodes have on one another -Lines

What lies at the end of each branch of a decision tree?

The payoffs!

States of nature:

The possible outcomes for chance events that affect the payoff associated with a decision alternative -These are future events that are not in the control of the decision maker, but may occur

Posterior probabilities:

The probabilities of the states of nature after revising the prior probabilities based on sample information.

Prior probability:

The probabilities of the states of nature prior to obtaining sample information -To make the best decision, the decision maker must seek out additional info about the states of nature

Risk analysis:

The study of the possible payoffs and probabilities associated with a decision alternative or a decision strategy -Good decision analysis always includes this. It provides probability info about the favorable as well as unfavorable consequences that may occur

Decision tree: square nodes

These correspond to decision alternatives

Decision tree: round nodes

These correspond to states of nature

Decision strategy steps?

This decision is based on a backward pass through the decision tree: 1) At chance nodes, compute the expected value by multiplying the payoff at the end of each branch by the corresponding branch probabilities. 2) At decision nodes, select the decision branch that leads to the best expected value. This expected value becomes the expected value at the decision node.

Expected value of sample information (EVSI):

This is the additional expected profit possible through knowledge of the sample or survey information. -It is the difference between the expected value of an optimal strategy based on sample information and the "best" expected value without any sample information.

Efficiency of sample information:

This is the ratio of EVSI to EVPI -The EVPI provides an upper bound for EVSI -This number is always between 0 and 1 EVSI/EVPI

Minimax regret approach:

This requires the construction of a regret table or an opportunity lost table -First, you calculate the difference between each payoff and the largest payoff for each state of nature -Second, using the regret table, the maximum regret for each possible decision is listed -Third, the decision chosen is the one corresponding to the minimum of the maximum regrets

Risk profile:

This shows the possible payoffs for a decision alternative along with their associated probabilities -sometimes decision makers change their minds after analyzing these

How do decision makers get additional info?

Through sample information (obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities)

T/F: Even when a careful decision analysis has been conducted, the uncertain future events make the final consequence uncertain

True! Future events cause uncertainly

T/F: The risk associated with any decision alternative is a direct result of uncertainty associated with the final consequence

True! Risk comes from uncertainty

Conservative approach:

Used by a conservative decision maker -For each decision the minimum payoff is listed and then the decision corresponding to the maximum of these minimum payoffs is selected (aka the minimum possible payoff is maximized) -If the payoff was in terms of costs, the maximum costs would be determined for each decision and then the decision corresponding to the minimum of these maximum costs is selected -Maximin approach

Optimistic approach:

Used by an optimistic decision maker -The decision with the largest possible payoff is chosen -If the payoff table was in terms of costs, the decision with the lowest cost would be chosen -Maximax approach

Expected value apprach:

Used when probabilities are available. -The expected return for each decision is calculated by summing the products of the payoff under each state of nature and the probability of the respective state of nature occurring -The decision yielding the best expected return is chosen

Regret:

the difference between the payoff associated with a particular decision alternative and the payoff associated with the decision that would yield the most desirable payoff for a given state of nature.