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