Decision Analysis and Management Final Exam Chapter 13

influence diagram

-A graphical device that shows the relationship among decisions, chance events, and consequences for a decision problem. -nodes: represent the decisions, chance events, and consequences -rectangles or squares depict decision nodes (complex size) -circles or ovals depict chance nodes (demand) -diamonds depict consequence nodes (profit)

Expected Value Approach

-An approach to choosing a decision alternative based on the expected value of each decision alternative. The recommended decision alternative is the one that provides the best expected value.

Influence diagram with sample information

-Research study becomes a decision node -research study results becomes a chance node -demand both influences research study results and profit

States of Nature

-The possible outcomes for chance events that affect the payoff associated with a decision alternative. -mutually exclusive and collectively exhaustive (at least one must occur)

Decision Analysis

-Used to develop an optimal strategy when a decision maker is faced with several decision alternatives and an uncertain set of future events

Problem Formulation

-decision alternatives -chance events: uncertain future events -consequences associated with each combination of decision alternative and chance event outcome

Characteristics of a decision problem

-decision alternatives -state of nature -payoffs

sensitivity analysis

-determines how changes in the probabilities for the states of nature or changes in the payoffs affect the recommended decision alternative - =P(s1) + (1-p)(s2) -the range in the graph of where the lines intercept demonstrate the highest EV. We determine these values by setting the equations equal to each other and then solving

Laplace table

-equal likelihood -Find the average and choose the highest average value

Optimistic Approach

-evaluates each decision alternative in terms of the best payoff that can occur -the decision alternative that is recommended is the one that provides the best possible payoff

Conservative Approach

-evaluates each decision alternative in terms of the worst payoff that can occur -decision alternative recommended is the one that provides the best of the worst possible payoffs.

Decision tree with sample information

-first decide if market research should be conducted -then decide favorable versus unfavorable -then decide size of condominiums -then branch for strong or weak demand -no market research, jump straight to condominium size because there will be no favorable or unfavorable report

Risk Analysis

-helps the decision maker recognize the difference between the expected value of a decision alternative and the payoff that may actually occur -provides info on favorable and unfavorable consequences

prior probability

-preliminary assessments for the states of nature that are the best probability values available at the time

What are the two categories of decision situations?

-probabilities can be assigned to future occurrence (risk) -probabilities cannot be assigned to future occurrences (uncertainty)

Minimax Regret Approach (opportunity loss)

-regret: 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. -choose the decision alternative that minimizes the maximum state of regret that could occur over all possible states of nature. -choose minimum of the maximum regret

Decision tree nodes

-round: states of nature -square: decision alternatives

payoff table

-table showing the expected payoffs for each alternative in every possible state of nature

Three commonly used criteria for decision making when probability information regarding the likelihood of the states of nature is unavailable are:

-the optimistic approach -the conservative approach -minimax regret approach

Calculating EV nodes in decision tree

-we select the large complex decision alternative branch the expected value that comes with it. -when choosing optimal decision, we choose the largest EV

Expected Value of Perfect Information (EVPI)

=| EVwPI-EVwoPI | -max we are willing to pay -also = expected opportunity loss -expected value w/out perfect information = total of expected values calculated with assumed outcomes. -EVwPI is always less than or equal to the expected value without perfect information

The expected value and expected opportunity loss criterion result in

the same decision

As the EVPI provides an upper bound for the EVSI efficiency is

always between 0 and 1

payoff

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

Decision Tree

graphical representation of the process underlying decisions and it shows the resulting consequences of making various choices

Difference between payoff table and sequential decision tree

payoff table is limited to a single decision

posterior probabilities

revised probabilities of events based on additional information

risk profile

shows the possible payoffs along with their associated probabilities