Section 8.


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Section 8 Choice Examination Choice Investigation A strategy for deciding ideal techniques when confronted with a few choice options and a questionable example of future occasions. The Choice Examination Approach Recognize the choice options - d i Distinguish conceivable future occasions - s j
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Section 8 Decision Analysis MT 235

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Decision Analysis A strategy for deciding ideal systems when confronted with a few choice options and a questionable example of future occasions. MT 235

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The Decision Analysis Approach Identify the choice choices - d i Identify conceivable future occasions - s j fundamentally unrelated - stand out state can happen thorough - one of the states must happen Determine the result connected with every choice and every condition of nature - V ij Apply a choice standard MT 235

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Types of Decision Making Situations Decision making under conviction condition of nature is known choice is to pick the option with the best result MT 235

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Types of Decision Making Situations Decision settling on under vulnerability The chief is not able or unwilling to gauge probabilities Apply a judgment skills model MT 235

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Decision Making Under Uncertainty Maximax Criterion (for benefits) - hopeful rundown greatest result for every option pick elective with the biggest most extreme result MT 235

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Decision Making Under Uncertainty Maximin Criterion (for benefits) - negative rundown least result for every option pick elective with the biggest least result MT 235

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Decision Making Under Uncertainty Minimax Regret Criterion figure the misgiving for every option and every state list the greatest misgiving for every option pick the option with the littlest greatest misgiving MT 235

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Decision Making Under Uncertainty Minimax Regret Criterion Regret - measure of misfortune because of settling on an off base choice - opportunity cost MT 235

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Types of Decision Making Situations Decision making under danger Expected Value Criterion register expected quality for every choice option select option with “best” expected worth MT 235

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Computing Expected Value Let: P(s j )=probability of event for state s j and N=the aggregate number of states MT 235

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Computing Expected Value Since the states are totally unrelated and comprehensive MT 235

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Types of Decision Making Situations Then the normal estimation of any choice d i is MT 235

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Decision Trees A graphical representation of a choice circumstance Most helpful for successive choices MT 235

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$200K P(S 1 ) = .3 2 Large $ - 20K P(S 2 ) = .7 $150K P(S 1 ) = .3 Medium 1 3 $ 20K P(S 2 ) = .7 Small $100K P(S 1 ) = .3 4 $ 60K P(S 2 ) = .7 MT 235

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EV 2 = 46 $200K P(S 1 ) = .3 2 Large $ - 20K P(S 2 ) = .7 EV 3 = 59 $150K P(S 1 ) = .3 Medium 1 3 P(S 2 ) = .7 $ 20K Small EV 4 = 72 $100K P(S 1 ) = .3 4 $ 60K P(S 2 ) = .7 MT 235

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Decision Making Under Risk: Another Criterion Expected Regret Criterion Compute the misgiving table Compute the normal misgiving for every option Choose the option with the littlest expected misgiving The normal misgiving basis will dependably yield the same choice as the normal worth foundation. MT 235

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Expected Regret Criterion The normal misgiving for the favored choice is equivalent to the Expected Value of Perfect Information - EVPI is the normal benefit of knowing which state will happen. MT 235

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EVPI – Alternative to Expected Regret EVPI – Expected Value of Perfect Information EVwPI – Expected Value with Perfect Information about the States of Nature EVwoPI – Expected Value without Perfect Information about the States of Nature EVPI=|EVwPI-EVwoPI| MT 235

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Mass. Narrows Production (MBP) is arranging another assembling office for another item. MBP is considering three plant sizes, little, medium, and expansive. The interest for the item is not completely known, but rather MBP accept two potential outcomes: 1. Popularity, and 2. Low request. The benefits (settlements) connected with every plant size and interest level is given in the table underneath. Investigate this choice utilizing the maximax (idealistic) approach. Break down this choice utilizing the maximin (preservationist) approach. Examine this choice utilizing the minimax lament measure. Presently expect the leaders have likelihood data about the conditions of nature. Expect that P(S 1 ) =.3, and P(S 2 ) =.7. Break down the issue utilizing the normal worth foundation. [1] How much would you be willing to pay in this sample for immaculate data about the genuine interest level? (EVPI) Compute the normal open door misfortune (EOL) for this issue. Look at EOL and EVPI. [1] Note that that P(S 1 ) and P(S 2 ) are supplements, so that that P(S 1 )+P(S 2 )=1.0. MT 235

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Bayes Law In this mathematical statement, P(B) is known as the earlier likelihood of B and P(B|A) is known as the back, or now and then the changed likelihood of B. The thought here is that we have some beginning assessment of P(B) , and after that we get some extra data about whether A happens or not, and afterward we utilize Bayes Law to process this updated likelihood of B. MT 235

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Now assume that MBP has the alternative of doing statistical surveying to show signs of improvement evaluation of the presumable level of interest. Statistical surveying Inc. (X-ray) has done significant examination around there and set up a reported reputation for guaging interest. Their exactness is expressed regarding probabilities, restrictive probabilities, to be correct. Let F be the occasion: MRI figures appeal (i.e., MRI conjectures S 1 ) Let U be the occasion: MRI gauges low request (i.e., MRI estimates S 2 ) The restrictive probabilities, which measure MRI’s exactness, would be: This would say that 80% of the time when interest is high, MRI conjectures popularity. Also, 75% of the time when the interest is low, MRI figures low request. In the estimations, which take after, in any case, we should reverse these restrictive probabilities. That would we say we is, should know: MT 235

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States of Nature Prior Probabilities Conditional Probabilities Joint Probabilities Posterior Probabilities Posterior Probabilities States of Nature Prior Probabilities Conditional Probabilities Joint Probabilities MT 235

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Now, utilizing Bayes Law, we can develop another choice tree, which will give us a choice procedure: Should we pay MRI for the statistical surveying? In the event that we don\'t do the statistical surveying, what ought to our choice be? In the event that we do the statistical surveying and get a sign of appeal, what ought to our choice be? In the event that we get a sign of low request, what ought to our choice be? We will utilize a choice tree as demonstrated underneath to focus this method. MT 235

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$200K P(S 1 |U)= .103 $-20K P(S 2 |U)=.897 P(S 1 |U)= .103 $150K $20K P(S 2 |U)=.897 $100K P(S 1 |U)=.103 $60K P(S 2 |U)=.897 EV 4 = $107.16K $200K P(S 1 |F)= .578 4 Large $-20K P(S 2 |F)=.422 EV 2 = 107.16 EV 5 = $95.14K $150K P(S 1 |F)= .578 Medium 5 2 $20K Favorable Forecast P(S 2 |F)=.422 EV 6 = $83.12K $100K P(S 1 |F)= .578 Small 6 $60K P(F)= .415 P(S 2 |F)=.422 EV 7 = $2.66K 1 EV 1 = $81.98K Large 7 P(U)= .585 Unfavorable Forecast EV 8 = $33.39K Medium 8 3 Do Survey EV 3 = 64.12 EV 9 = $64.12K Small 9 Don’t do Survey $72K MT 235

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Expected Value of Sample Information – EVSI – Expected Value of Sample Information EVwSI – Expected Value with Sample Information about the States of Nature EVwoSI – Expected Value without Sample Information about the States of Nature EVSI=|EVwSI-EVwoSI| MT 235

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Efficiency of Sample Information – E Perfect Information has a proficiency rating of 100%, the effectiveness rating E for test data is figured as takes after: Note: Low productivity appraisals for test data may lead the chief to search for different sorts of data MT 235

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Example 2: The LaserLens Company (LLC) is considering presenting another item, which to some degree will supplant a current item. LLC is uncertain about whether to do this in light of the fact that the money related results rely on the economy\'s condition. The result table beneath gives the benefits in K$ for every choice and each monetary state. Examine this choice utilizing the maximax (idealistic) approach. Investigate this choice utilizing the maximin (preservationist) approach. Break down this choice utilizing the minimax lament model. Presently accept the chiefs have likelihood data about the conditions of nature. Accept that P(S 1 )=.4. Examine the issue utilizing the normal worth basis. What amount would you be willing to pay in this sample for impeccable data about the real condition of the economy? (EVPI) Compute the normal open door misfortune (EOL) for this issue. Think about EOL and EVPI. MT 235

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Now assume that LLC has the choice of contracting with a monetary anticipating firm to show signs of improvement evaluation without bounds condition of the economy. Financial matters Research Inc. (ERI) is the estimating firm being considered. In the wake of researching ERI’s anticipating record, it is found that before, 64% of the time when the economy was solid, ERI anticipated an in number economy. Likewise, 95% of the time when the economy was powerless, ERI anticipated a feeble economy. Conditions of Nature Prior Probabilities Conditional Probabilities Joint Probabilities Posterior Probabilities States of Nature Prior Probabilities Conditional Probabilities Joint Probabilities Posterior Probabilities MT 235

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7a. Focus LLC’s best choice procedure. Should they procure ERI or proceed without extra data? On the off chance that they purchase the monetary conjecture, what ought to their ensuing choice methodology be? 7b. Decide the amount LLC ought to be willing to pay (most extreme) to ERI for a monetary conjecture. 7c. What is the data\'s effectiveness gave by ERI? MT 235

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EV 4 = $124.04K $140K P(S 1 |F)= .895 4 d 1 $ - 12K P(S 2 |F)=.105 2 Favorable Fore

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