Decision Analysis Flashcards
what is a decision tree
shows decision problems in a graphical format
How can manager make decisions quickly and without complete information
manage risk and uncertainty
what are the two factors to balance downside risks and upside rewards?
use data and common sense
do good decisions always result in good outcomes
not always! BUT WE try to use structured approach to decision making so it is more LIKELY to have a good outcome
why does good decision not always lead to good outcome
cuz you may not have all the info at hand
situation may change
MOST LIKELY: UCNERTAINTY
What decision do you make?
the best deciison. based on your analysis and the information you have at the time but
1) you may not have all the info
2) the situation might have uncertainty
WHAT are 3 common characterisitcis of decision problems
1) set of alternatives (Strategies) available to the deciison maker
2) criteria (factors that are important to the decision maker/ basis of making decisions about the alternatives)
-> PAYOFF= dollar value
3) states of nature (future events that are not under the decision makers control)
Payoff matrix elements
-top left
-rows
-columns
-cell values
Decision
alternatives
states of nature/outcomes
payoff values
are the possible outcomes (under the states of nature) mutuallyy exclusive and colelctively exhaustive?
meaning
yes
mutuual exclusive: if one occurs the other cant occur
collectively exhaustive: these are the ONLY options that can occur
What are non-probablistic methods?
-no decision rule works best in every situation
- so you have rules to help enhace insight and sharpen intution about decision problems
Rules like: MAXIMAX, MAXIMIN,MINIMAX
Maximax is
optimistic criteria
Maximin is
conservative criteria
Minimax is
regret
Maximax definition
selecting the best (max) payoff in each row (alternative) of the payoff table, and then select the alternative w largest payoff
MAXimizing the MAXimium best case
is the maximiax decision rule high risk
yes! because no guarantee that max payoff will happen
when would you use maximax
when decision maker can survive even the worst case payoff
MAXIMIN defiiniton
maximizing the minimum payoff, PESSIMISTIC APPROACH
tryign to minimize the loss and get the best results in a worst case scenario
LOW RISK
maximin process
-determine the minimum possible payoff for each alternative
-select alternative with the largest minmum payoff
MAX of the minimum of the rows
why is it called the pessimistic approach
ALSO what is the criteria for making this decision
Because you are making decisions with the lower reward, but you have a lower risk
lower reward is the criteria, but since its also lower risk you cant lose money
Minimax definition
-this rule is based on the concept of regret, or opptunity loss
-EXAMINES THE REGRET WE WILL FEEL IF WE MAKE THE WRONG CHOICE GIVEN WHAT THE STATE OF NATURE occurs
How do you use the minimax regret decision rule?
1) first convert our payoff matrix into a regret matrix
2) summarizes the possible opportunity cost of each decision alternative
how to do maximax in excel
- get the max of the rows (use MAX)
- MAXIMAX get the max of the columnes (use MAX)
- USE VLOOKUP to get the deciison (VLOOKUP (MAXIMAX, TABLE, 2, FALSE)
probabilistic methods meaning
probablistic decision rules can be used if the states of nature are assigned probabilites that represent their likelihood of occurrence.
when can we use probabilistic methods?
when problems occur more than once, possible to estimate these from historical data
Many decision problems represent one-time
decisions so data for estimating probabilities are
unlikely to exist. In these cases, probabilities are
often assigned subjectively
sometimes you gotta estimate the values
What is expected monetary value
decision rule that selects the decision alternative with the largest EMV, average payoff based on the probabilites
how to calculate EMV
EMV= sum of probabilites x payoff
where payoff is the payoff for the alternative
EMV is calculated for each state of nature
in xl: sumproduct (look at slide 25), and then max in the EMV box, then decision use VLOOKUP
Expected value of perfect information
-MEANING
-how od u work with this
->what do probabilities mean
-imagine if u knew perfect info, that would be valuable!!
-we can make the right deciison if we know the outcome (not posisble irl)
-what u can do is take the largest value in each state of nature and multiply it by its probability, this will give you EV with PI
-they do not tell us which state of nature will occur, they only indicate the likehood of the various states of nature
EV of PI formula? evpi
EV with PI - EVwithout PI
What is a decision tree
shows decision problems in a graphical format
when can decisions trees be used?
for any decision problem, but they are particularly useful for the more complex types
2 types of decision trees
1) multistage
2) contingent
Decision tree- nodes
squares - decision node= “choice”
circles - event node= “state of nature” (out of
control
triangles- terminal node= “problem has been completed” (all payoffs have been incurred)
Where are probabilities listed on decision trees
probability branches
probabilities are conditional on the events that have already been observed (those to the left)
!!!
The probabilites on branches leading out of any proability node must have a sum of
1.0
Monetary values are shown where
to the right of the terminal nodes
Where are intermediate costs and revenues shown?
on the other branches
How to calculate EMVs on a decision tree (how to solve a decision tree)
“ROLLING BACK”, starting on the right of the tree and working backwards
What are the two type of calcualtions that need to be done in solving a decision tree
1) Square= at each decision node the alternative with the highest EMV is selected
2) Circle= EMV is calculated and written above the node
How do you choose which tree to prune?
the one with the lower EMV
WHAT is a multistage decisions?
a multistage problem is one where decisions must be made at several different stages of the process!!
perfect vs sample information
perfect info= not realistic
sample info= both economical and also feasible
what is EVSI
expected value of sample information
definition of EVSI
-sample information is often expensive to obtain
EX: seismic testing, market survey, credit rating
EVSI formula
1) calculate expected value if sampling test was free
EX: This will be an addition equation
(Add cost of test to the value at the test node circle)
2) Take the difference between the two nodes, (equal value at both nodes)
(new sum - other node value)
this is up to how much u willing to pay for the test
what is the EVSI meaning
the most a person would be willing to pay for the test
how to calculate evpi
1) take the branch with no survey
2) you are GOING TO BE FLIPPING THIS PART OF THE TREE!! Make the state of nature consideration (the circle) first
3) Then make the two lines coming out of the circle be the states of nature, then draw squares and put the choices leading out of the two squares
4) Fill out the terminal nodes for the appropriate value
5) Solve the tree!!! the value you get will be the EV with PI!
6) EV with PI- EV without PI= EVPI
*NOTE: ev without pi is the unused emv value from the start
EV with PI meaning
what values we would acceptt,
higher than ev with pi value is good
lower than ev with pi value is bad
DO YOU ACTUALLY EVER MAKE THE EMV $$$$$ VALUES?
NO!!!! this is like a weighted avg of this outcome (you may make more or less)
steps to do minimax
1) get max of each state of nature ( columns)
2) Max value for the column- value in the cell= regret matrix
NOW YOU HAVE A REGRET MATRIX
3) the smallest value you calulcate is the value with the lowest regret, and this is the one we should choose
in xl: just do maxes first, then maxes- cell values, then maxes of all alts, then lowest of the alt values, then vlookup for decision
SLIDE 26- sensitivity analysis
What if the probabilities of low and high demand (0.4 & 0.6) change?
Would your decision (small plant / large plant) change?
Some of the quantities in a decision analysis, particularly the probabilities and payoffs, are often intelligent guesses at best.
Sensitivity analysis could analyze the impact of a change in the probability.
Try changing the probabilities in the Excel sheet to determine when or if the decision would change to build a small plant.
you always start a decision tree with this shape
EXCEPT FOR WHEN U DO EV WITH PI
square
evpi: circle
how to draw out a decision tree for sample info
the top half is regular without any data
the obttom half, start with the branch that you get analytics data, and two separate branches predicting high and low
have the other alts coming out of that and repeat the original branches
why do people still buy insurance if expected value of insurance is less than font buy insurance
dont wanna take risk
why do people go against expected value when they buy lottery?
cost is very low!! PEOPLE LIKE THE POTENTIAL OF HIGH PAYOFF
When the possible negative payoffs get large enough that you cease to be willing to play, you are indicating that you are “risk averse” for that level of loss. EMV might not be the best criterion to use here!
EXACTLY
Most people (and companies) are “risk averse” when the dollar values are sufficiently high.
Risk Aversion: Attitude Toward Loss
A big loss is “more bad” than a gain of the same magnitude is “good”
E.g., the loss of $1000 is worse than the good of gaining $1000
However, “small” losses are proportionate to “small” gains. This is why most people are willing to gamble “small” amounts of money.
Most people (and companies) are “risk averse” when the dollar values are sufficiently high.
Risk Aversion: Attitude Toward Loss
A big loss is “more bad” than a gain of the same magnitude is “good”
E.g., the loss of $1000 is worse than the good of gaining $1000
However, “small” losses are proportionate to “small” gains. This is why most people are willing to gamble “small” amounts of money.
For making multiple decisions, EMV is an excellent decision criterion because you will get the highest total return over the long run.
E.g. repeated purchases of petroleum quantities
For one-off decisions with “large” negative outcome values* EMV may not be the best decision criterion.
*those you are risk-averse to
It might be better to consider one of the non-probabilistic methods and/or the risk profile of each alternative and choose an alternative that you are comfortable with.
For making multiple decisions, EMV is an excellent decision criterion because you will get the highest total return over the long run.
E.g. repeated purchases of petroleum quantities
For one-off decisions with “large” negative outcome values* EMV may not be the best decision criterion.
*those you are risk-averse to
It might be better to consider one of the non-probabilistic methods and/or the risk profile of each alternative and choose an alternative that you are comfortable with.
when doing maximax,, maximin, and mini max regret remember what
YOU ARE CHOOSING BETWEEN ALTERNATIVES!!! SO DO UR MATH HORIZONTALLY (OR FOCUSED ON THE ORDERING DECISIONS~~~~~~~) DO NOT THINK OF THEM VERTICALLY IN ACCORDANCE OF STATE OF NATUER!!!! SEE Q2 ON REVIEW PCKG
