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Chapter 14 Decision Analysis. Problem Formulation Decision Making without Probabilities Decision Making with Probabilities Risk Analysis and Sensitivity Analysis Decision Analysis with Sample Information Computing Branch Probabilities Utility and Decision Making. Problem Formulation.

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Section 14 Decision Analysis Problem Formulation Decision Making without Probabilities Decision Making with Probabilities Risk Analysis and Sensitivity Analysis Decision Analysis with Sample Information Computing Branch Probabilities Utility and Decision Making

Problem Formulation A choice issue is described by choice options, conditions of nature, and coming about adjustments. The choice choices are the diverse conceivable systems the chief can utilize. The conditions of nature allude to future occasions, not under the choice's control producer, which may happen. Conditions of nature ought to be characterized so they are totally unrelated and on the whole thorough.

Payoff Tables The outcome coming about because of a particular mix of a choice option and a condition of nature is a result . A table demonstrating settlements for all blends of choice choices and conditions of nature is a result table . Settlements can be communicated as far as benefit , cost , time , separation or some other suitable measure.

Decision Trees A choice tree is a sequential representation of the choice issue. Every choice tree has two sorts of hubs; round hubs relate to the conditions of nature while square hubs compare to the choice choices. The branches leaving every round hub speak to the diverse conditions of nature while the branches leaving every square hub speak to the distinctive choice options. Toward the end of every appendage of a tree are the adjustments accomplished from the arrangement of branches making up that appendage.

Decision Making without Probabilities Three generally utilized criteria for choice making when likelihood data in regards to the states' probability of nature is occupied are: the hopeful approach the preservationist approach the minimax misgiving methodology.

Optimistic Approach (MaxiMax) The idealistic methodology would be utilized by a hopeful leader. The choice with the biggest conceivable result is picked. On the off chance that the result table was as far as expenses, the choice with the most minimal expense would be picked.

Conservative Approach (MaxiMin) The traditionalist methodology would be utilized by a moderate leader. For every choice the base result is recorded and after that the choice relating to the greatest of these base adjustments is chosen. (Consequently, the base conceivable result is boosted.) If the result was as far as expenses, the most extreme expenses would be resolved for every choice and after that the choice comparing to the base of these greatest expenses is chosen. (Subsequently, the greatest conceivable expense is minimized.)

Minimax Regret Approach The minimax misgiving methodology requires the development of a misgiving table or an open door misfortune table. This is finished by computing for every condition of nature the distinction between every result and the biggest result for that condition of nature. At that point, utilizing this misgiving table, the most extreme misgiving for every conceivable choice is recorded. The choice picked is the one comparing to the most extreme's base second thoughts.

Example Consider the accompanying issue with three choice options and three conditions of nature with the accompanying result table speaking to benefits: States of Nature s 1 s 2 s 3 d 1 4 - 2 Decisions d 2 0 3 - 1 d 3 1 5 - 3

Maximaxdecision Maximax result Example Optimistic Approach An hopeful chief would utilize the idealistic (maximax) approach. We pick the choice that has the biggest single worth in the result table. Most extreme Decision Payoff d 1 4 d 2 3 d 3 5

Maximin choice Maximin result Example Conservative Approach A traditionalist leader would utilize the preservationist (maximin) approach. List the base result for every choice. Pick the choice with the most extreme of these base settlements. Least Decision Payoff d 1 - 2 d 2 - 1 d 3 - 3

Example Minimax Regret Approach For the minimax subtracting so as to misgive methodology, first figure a misgiving table every result in a section from the biggest result in that segment. In this sample, in the first section subtract 4, 0, and 1 from 4; and so on. The subsequent misgiving table is: s 1 s 2 s 3 d 1 0 1 d 2 4 2 0 d 3 0 2

Minimax choice Minimax lament Example Minimax Regret Approach (proceeded with) For every choice rundown the greatest misgiving. Pick the choice with the base of these qualities. Greatest Decision Regret d 1 d 2 4 d 3

Decision Making with Probabilities Expected Value Approach If probabilistic data in regards to the conditions of nature is accessible, one may utilize the normal quality (EV) approach . Here the normal return for every choice is ascertained by summing the result's results under every condition of nature and the likelihood of the separate condition of nature happening. The choice yielding the best expected return is picked.

Recall Probability Concepts Probability of any occasion is somewhere around 0 and 1. An occasion with likelihood = 0 is an outlandish occasion. An occasion with likelihood = 1 is a certain thing. Likelihood of test space = 1. That is, likelihood of one of the occasions from the example space happens is 1. Which is arbitrary â State of Nature or Decisions?

Recall Probability Concepts Joint, Marginal and Conditional Probabilities Dem Rep Total Rich 100 700 800 Poor 1500 900 2400 Total 1600 1600 3200 Marginal Probability: P(Rich) = 800/3200 P(Democrat) = 1600/3200 Joint Probability: P(Rich and Rep) = 700/3200 P(Poor and Dem) = 1500/3200

Recall Probability Concepts Joint, Marginal and Conditional Probabilities Dem Rep Total Rich 100 700 800 Poor 1500 900 2400 Total 1600 1600 3200 Conditional Probability: | read as given . P( Dem | Rich) = 100/800 P (Poor | Rep) = 900/1600 P(Rep | Poor) = 900/2400

Expected Value of a Decision Alternative The normal estimation of a choice option is the whole of weighted adjustments for the choice option. The normal quality (EV) of choice option d i is characterized as: where: N = the quantity of conditions of nature P ( s j ) = the likelihood of condition of nature s j V ij = the result relating to choice elective d i and condition of nature s j

Summation Notation Ã is utilized to demonstrate including various things. In the event that we have a rundown of 20 things, every thing can be recorded by i and the rundown is spoken to by a variable x. speaks to the first thing and speaks to 15 th thing. To include every one of the things in the rundown . i is the record of summation. This says include numbers 1 through 20. To include number 4 through 18 compose If what is included is clear, for instance, every one of the numbers, the record may be discarded. , for instance says include every one of the numbers in the rundown

Example: Burger Prince Burger Prince Restaurant is mulling over opening another eatery on Main Street. It has three unique models, each with an alternate seating limit. Burger Prince evaluates that the normal number of clients every hour will be 80, 100, or 120. The result table for the three models is on the following slide. Choice: Model. Condition of Nature: Customers every hour What does the leader pick?

Example: Burger Prince Payoff Table Average Number of Customers Per Hour s 1 = 80 s 2 = 100 s 3 = 120 Model A $10,000 $15,000 $14,000 Model B $ 8,000 $18,000 $12,000 Model C $ 6,000 $16,000 $21,000

Example: Burger Prince Expected Value Approach Calculate the normal quality for every choice. The choice tree on the following slide can help with this count. Here d 1 , d 2 , d 3 speak to the choice choices of models A, B, C, and s 1 , s 2 , s 3 speak to the conditions of nature of 80, 100, and 120.

Example: Burger Prince Decision Tree Payoffs .4 s 1 10,000 s .2 15,000 s 3 .4 d 1 14,000 .4 s 1 8,000 d .2 1 3 s 2 18,000 s 3 d 3 .4 12,000 .4 s 1 6,000 4 s .2 16,000 s 3 .4 21,000

Example: Burger Prince Expected Value For Each Decision Choose the model with biggest EV, Model C. EMV = .4(10,000) + .2(15,000) + .4(14,000) = $12,600 2 d 1 Model An EMV = .4(8,000) + .2(18,000) + .4(12,000) = $11,600 d 2 Model B 1 3 d 3 EMV = .4(6,000) + .2(16,000) + .4(21,000) = $14,000 Model C 4

Expected Value of Perfect Information Frequently data is accessible which can enhance the likelihood gauges for the conditions of nature. The normal estimation of impeccable data (EVPI) is the increment in the normal benefit that would come about if one knew with assurance which condition of nature would happen. The EVPI gives an upper bound on the normal estimation of any example or study data .

Expected Value of Perfect Information EVPI Calculation Step 1: Determine the ideal return relating to every condition of nature. Step 2: Compute the normal estimation of these ideal returns. Step 3: Subtract the EV of the ideal choice from the sum decided in step (2).

Example: Burger Prince Expected Value of Perfect Information Calculate the normal quality for the ideal result for every condition of nature and subtract the EV of the ideal choice. EVPI= .4(10,000) + .2(18,000) + .4(21,000) - 14,000 = $