Decision Analysis Models
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1 Decision Analysis Models 1 Outline Decision Analysis Models Decision Making Under Ignorance and Risk Expected Value of Perfect Information Decision Trees Incorporating New Information Expected Value of Sample Information 2 Decision Analysis Models A set of decision alternatives We can choose only one alternative A set of possible states of nature We don t know which one will occur in advance A set of payoffs Each payoff is associated with an alternative action and a state of nature Value can be monetary or otherwise 3 Sec# 5442, 5447,
2 Certainty Decision Situations Categories Decision maker knows with certainty which state of nature will occur Ignorance Decision maker knows all of the several possible states of nature, but does not know the probability of occurrence for any of the states Risk Decision maker knows all of the several possible states of nature, and can assign probability of occurrence for each state 4 Decision Making Under Ignorance Decision Rules LaPlace-Bayes Select alternative with best average payoff MaxiMax Select alternative which will provide highest payoff if things turn out for the best MaxiMin Select alternative which will provide highest payoff if things turn out for the worst MinMax Regret Select an alternative that will minimize the maximum regret 5 EVPI Expected Value Under Imperfect Information (EVUII) EVUII = max(er i ) Expected Value Under Perfect Information (EVUPI) EVUPI = Σ max(r ij ) P(S j ) Expected Value of Perfect Information (EVPI) measures how much better we expect we could do if we had the perfect knowledge of the future EVPI = EVUPI EVUII Expected Regret 6 Sec# 5442, 5447,
3 Step 1: Study the Environment Diagnose problem and organize facts: Global Oil has a lease that gives them the right to explore in western Oklahoma The payoff from drilling will depend on the existence of oil/gas and current market conditions Prescot Oil offers to buy the lease for a single lump sum Frame management situation Decision needs to be made to either drill or sell the lease without knowing the actual levels (or existence) of oil/gas deposits 7 Step 2: Model Formulation Create a selective representation of reality Estimate cash flows for each decision alternative and state of nature Estimate probabilities for each state of nature Identify decisions and objectives Decision: to drill or sell the lease Objective: maximizing expected return 8 Step 3: Model Construction Construct the model Tabular format Calculate expected return for each of the decisions Find the maximum expected return and use it to make the decision Calculate EVPI Decision tree Graphical device for analyzing decisions under risk and calculating maximum expected returns Effective for sequential decision problems 9 Sec# 5442, 5447,
4 Initial Decision Tree ($1,).2.4 $4,.3 $9,.1 $2, Sell the Lease $15, 1 Decision Tree Elements Decisions Decision (square) nodes Branches leaving a decision node represent alternative actions The value of a decision node is the maximum of all decision branch values Events Event (circular) nodes Branches leaving an event node represent states of nature The value of an event node is the ER of the event branch values 11 Solving Decision Tree Start at the terminal nodes at the end of the tree and work backward Fold back the event node by calculating expected return for the event Prune (remove) the branches leaving decision node that do not yield the highest expected return When completed, the remaining branches will form the sequential decision rules for the problem 12 Sec# 5442, 5447,
5 Initial Tree Solved ($1,).2.4 $4, $43,.3 $9,.1 $2, $43, Pruning Sell the Lease $15, 13 Terrain Testing Terrain configuration is an indicator of the possible gas and oil deposits DRI will perform tests for $1, to determine the underground formation of the terrain The result is going to be one of the following terrain configurations Plate higher likelihood of a dry well Varied higher likelihood of gas well Ridge higher likelihood of oil well 14 Incorporating New Info Global considers conducting a new test in order to make a better decision If the test is done, it is no longer possible to sell the lease Global needs to pay for the test before it knows its outcome Use historical testing results to help assess the probabilities of drilling outcomes given different test results This will also help assess the upper limit on the amount Global should be willing to pay for testing 15 Sec# 5442, 5447,
6 Calculating Probabilities Prior probabilities ex: probability that the well contains gas Reliabilities ex: probability that the terrain is varied given that the gas was found Marginal probabilities ex: probability that the terrain is varied Posterior probabilities ex: probability that the well will contain gas given the terrain is varied 16 Final Tree Solved Plate $(82,).2 No Varied $43,125 Test $47,4 $43,125 No.25 Ridge $136, $136,25 No.625 ($11,) $3, $8, $19, ($11,) $3, $8, $19, ($11,) $3, $8, $19, 17 Expected Value of Sample Information If DRI did the testing for free, the maximum return Global can expect is $57,4 If Global decides NOT to do the testing, the maximum expected return is $43, Expected Value of Sample Information (EVSI) = $57, - $43, = $14,4 EVPI is $23, Testing moderately effective 18 Sec# 5442, 5447,
7 To Test or Not To Test If DRI testing costs $1, < EVSI of $14,4 do the test Global s decision sequence Test for the underground terrain structure If terrain plate, do not proceed with drilling If terrain varied or ridge, proceed with drilling If DRI testing costs more than EVSI of do not test and proceed with drilling 19 Bayes Theorem State of nature: event Information source: predictor Prior probabilities P(event) Initial belief about likelihood of states of nature (subjective) Reliabilities P(predictor event) Predictive power of the information source Marginal probabilities P(predictor) Likelihood with which predictions occur Posterior probabilities P(event predictor) Likelihood that state of nature occurs given a particular prediction 2 Sec# 5442, 5447,
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