BMGT332 Chapter 14

general principles for constructing a decision tree

- begin with a decision node, and then, alternate between chance and decision nodes - a "compound" decision (chance) node may be better represented by consecutive decision (chance) nodes: tradeoff between number of branches and number of nodes - create a tree that is as general as possible--do not eliminate certain branches from consideration because of the specific values of the inputes as presented in the case

rolling back

- determine EMV at each leaf-node - work backword from the leaf-nodes and use rules to compute EMV at each node - write the computed EMV on the node - for each decision node, put an arrow on the optimal decision and an X on each of the other alternatives - continue rolling back until EMV of root node is computed - at each leaf node, write the probability of reaching that leaf node

causes that make decision making a difficult task

- uncertainty regarding the future - conflicting values or objectives

alternative

a course of action intended to solve a problem

decision node

a square node that represents a decision

a risk profile

a table that shows the chances associated with possible outcomes in the optimal decision

payoff matrix (payoff table)

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

event nodes

circular nodes in a decision tree that represent uncertain events

decision tree

composed of a collection of nodes (represented by circles and squares) interconnected by branches (represented by lines)

minimax regret decision rule

convert the payoff matrix into a regret matrix that summarizes the possible opportunity losses that could result from each decision alternative under each state of nature. determine the maximum regret under each alternative and select the alternative with the minimum regret

the states of nature in a decision problem

correspond to future events that are not under the decision maker's control

branches eminating from event nodes

correspond to the possible states of nature or the possible outcomes of an uncertain event

EMV at a leaf node =

cumulative payoff at that node

probabilistic methods

decision rules that assume that probabilities of occurrence can be assigned to the states of nature in a decision problem - EMV, EOL

nonprobabilistic methods

decision rules that assume that probabilities of occurrence can't be assigned to the states of nature in a decision problem - maximax, maximin, minimax regret

the values assumed by the various decision crtieria under each alternative

depend on the different states of nature that can occur

maximin decison rule

determine the minimum possible payoff for each alternative and then select the alternative with the largest minimum payoff - more conservative approach

maximax decision rule

determines the maximum payoff for each alternative and then selects the alternative associated with the largest payoff

good decisions

do not always result in good outcomes

expected value of perfect information (EVPI) =

expected value with perfect information (EVwPI) - maximum EMV

EMV at a decision node =

highest EMV among EMV's on decision branches

the EMV for a given decision alternative

indicates the average payoff we would receive if we encounter the indentical decision problem repeatedly and always select this alternative

the minimum expected opportunity loss (EOL)

is equivalent to the expected value of perfect information (EVPI)

the impact of the alternatives on the criteria

is of primary importance to the decision maker

a good decision

is one that is in harmony with what you know, what you want, what you can do, and to which you are committed

the goal of decision analysis

is to help individuals make good decisions

selecting the alternative with the highest EMV

makes sense in situations where the identical decision problem will be faced reeatedly, but can be very risky in decision problems encountered only once

a decision

must involve at least two alternatives for addressing or solving a problem

leaves (terminal nodes)

objects where the various branches in a decision tree end

alternatives are evaluated

on the basis of the value they add to one or more decision criteria

single-stage decision problems

problems in which a single decision must be made

multistage decision problems

problems in which multiple decisions must be made

concept of regret

related to opportunity loss in decision making

many decision problems

represent one-time decisions for which historical data for estimating probabilities are unlikely to exist

branches eminating from a decision node

represent the alternatives for a particular decision

the criteria in a decision problem

represent various factors that are important to the decision maker and influenced by the alternatives

the expected monetary value (EMV) decision rule

selects the decision alternative with the largest EMV

expected regret (expected opportunity loss)

selects the decision alternative with the minimum expected opportunity loss

the decision with the smallest EOL will also have the largest EMV

so the EMV and EOL decision rules always result in the selection of the same decision alternative

expected monetary value (EMV) =

sum of the payoff for the alternative under a state of nature * the probability of the state of nature

expected value of perfect information (EVPI)

the expected value obtained with perfect information minus the expected value obtained without perfect information (given by the maximum EMV)

probabilities do not tell us which state of nature will occur

they only indicate the likelihood of the various states of nature

EMV at a chance node =

weighted average of EMV's on outcome branches