chapter 4 quantitative methods

decision making without probabilities

-optimistic -conservative -minimax

payoffs can be expressed in terms of

-profit -cost -time -distance -any other measure appropriate for the decision problem being analyzed

make the best possible decision?

-seek additional info, use it to revise/update prior prob so the final decision is based on more accurate probabilities for the state of nature (bays' theorem)

the probabilities 4 expected value approach has to satisfy ... (2)

1. P>=0 2. sum of Ps = 1

minimax regret approach how?

1. calculate regret 2. list maximum regret for each decision alternative (compare the payoff from state of nature) 3. select the decision alternative with the minimum of the maximum regret values

develop posterior probabilities tables

1. column 1 = states of nature; column 2=prior prob, column 3=conditional probabilities (favorable market research report given each state of nature) 2. column 4 = joint probabilities 3. sum the joint probabilities in column 4 4. divide each joint probability in column 4 by P(F) to obtain revised / posterior probabilities (P s1 | F)

optimistic approach how?

1. determine the max payoff for each decision alternative 2. select the decision alternative that provides the overall maximum payoff

methods to analyze more complex sequential decision problems

1. draw a decision tree consisting of decision and chance nodes and branches that describe the sequential nature of the problem *determine probs for all chance outcomes 2. work backward through the tree, compute EV at all chance nodes 3. select best decision branch at all decision nodes

conservative approach how?

1. identify the minimum payoff for each of the decision alternatives 2. select decision alternative that maximizes the minimum payoff

info gathered that is worth it the difference between EVwPI and EVwoPI

EVPI

at each decision node, ______ that is taken is based on the decision made

branch of tree *taken based on probability or chance

connect the nodes, leaving the decision node correspond to the decision alternatives -leaving the chance node correspond to the states of nature

branches

uncertain future events

chance events

circles

chance nodes

used to depict chance nodes

circles

research outcomes (sample info) GIVEN each state of nature

conditional probability

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

conservative approach

begin to study decision analysis, how?

consider problems that involve reasonably few decision alternatives ad reasonably few possible future events

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

decision analysis

decision making that do not require knowledge of the probabilities of the states of nature

decision making without probabilities *appropriate in situations

squares

decision nodes

sequence of decisions and chance outcomes where the decisions chosen depend on the yet to be determined outcomes of chance events

decision strategy

provides a graphical representation of the decision making process

decision tree *shows the natural/logical progression that will occur over time

main criticism to optimistic/conservative/minimax regret approach

do not consider any info about the probabilities of the various states of nature

express the value of market RESEARCH info

efficiency

special case of to states of nature, _____ can be used to determine how changes for the probe of the sattes of nature affect the recommended decision alternative

graphical procedure *p on horizontal axis *EV on vertical axis *linear equations--> straight lines

decision making without probabilities *appropriate in situations

in which the decision maker has little confidence in his or her ability to assess the probabilities *simple best-case/worst-case analysis is desirable

-give info about a state of nature (e.g. demand weak/strong) -indicate what's going on in the future

indicators

efficiency = 54% =??

info from market research study is 54%as efficient as perfect info

low efficiency ratings for sample info

lead the decision maker to look for other types of info

decision making is nether purely optimistic nor purely conservative

minimax regret approach

joint probabilities how?

multiply prior probability values in column 2 by the corresponding conditional probability vales in column 3

N=

number of states of nature

drawback to sensitivity analysis

numerous calculations required to evaluate the effect of several possible changes in the state-of-nature probabilities

difference between the payoff for the best decision alternative and the payoff for the decision for other alternatives

opportunity loss/ regret

evaluates each decision alternative in terms of the best payoff that can occur *recommend decision alternative that provides the best possible payoff *maximum profit=largest profit *minimization = smallest payoff

optimistic approach

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

payoff

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

payoff table

at the end of states-of-nature branches

payoffs

revised probabilities

posterior probabilities

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

prior probability

expected value with perfect info

prob of states of nature x max payoff

we can determine with certainty, prior to making a decision, which state of nature is going to occur

provide perfect info regarding the states of nature

high efficiency ratings

sample info is almost as good as perfect info and that additional sources of info would not yield significantly better results

additional info is obtained through experiments designed to provide ____ about the states of nature

sample information

helps decision maker by describing how changes in the state of nature probabilities and/or changes in the payoffs affect the recommended decision alternative

sensitivity analysis

used to determine how changes in the probabilities for the states of nature or changes in the payoffs affect the recommended decision alternative

sensitivity analysis

used to depict decision nodes

squares

possible outcomes for a chance event

states of nature

analysis of the decision tree and the choice of an optimal strategy requires

that we know the branch probabilities corresponding to all chance nodes

decision tree shows graphically

the sequences of decision alternatives and states of nature that provide all the possible payoffs

if a small change in the value of one of the inputs causes a change in the recommended decision alternative

the solute not the decision analysis problem is sensitive to that particular input

sensitivity analysis decision maker

understand which of inputs (prob for states of nature/changes in the payoffs) are critical to the choice of the best decision alternative

decision making with probabilities

use EXPECTED VALUE approach to identify the best decision alternative

sensitivity analysis can assist management in deciding

whether more effort/time should be spent obtaining better estimates of payoffs and probabilities

expected value of sample info (EVSI)=

|EVwSI - EVwoSI| *how much/max amount PDC should pay to conduct market research study