MATH451-Unit 4 Intellipath - Decision Making Under Risk

MATH451 – Unit 4 Intellipath Decision Making Under Risk In decision making under risk, the decision maker usually has some idea to what the probabilities of occurrence of the different outcomes can be. Selecting the alternative with the highest expected monetary value (EMV) is one of the most popular methods of making decision under risk. In this section, you will determine the EMV as well as expected opportunity loss (EOL). You will use Excel program to calculate these values. Probability of Occurrence The probability of occurrence of each outcome can be obtained from:  survey  exports  personal feelings Decision Making Under Risk The problem environmental is called decision making under risk . Consider the alternative with the highest expected monetary value (EMV). Calculate the expected opportunity loss (EOL) and expected value of perfect information. The EMV is calculated by the weighted average of all possible payoffs for that alternative as: EMV for an alternative = Payoff (of first outcome) * P(of first outcome) + Payoff (of the second outcome) * P(of the second outcome) + … Expected Monetary Value and Expected Opportunity Loss Expected monetary value (EMV) represents the long-run average payoff. Expected opportunity loss (EOL), also called regret , is considered to be the difference between the optimal payoff and the actual payoff received. In all decision-making application under risk, the minimum EOL will always is equal to the decision alternative as the maximum EMV. Perfect Information

Having the right kind of information at the time of decision making is very critical. Therefore, perfect information can seriously help a company to make proper and correct decision and, therefore, it has a value so-called expected value of perfect information . Consider the following two types of perfect information:  Expected value with perfect information (EVwPI)  Expected value of perfect information (EVPI) Expected Value with Perfect Information The first one is the expected value with perfect information (EVwPI) which defines the expected payoff if you have perfect information before a decision has to be made. It is calculated as: EVwPI = (Best payoff of first outcome) * P(of the first outcome) + (Best payoff of the second outcome) * P(of the second outcome) + … Expected Value of Perfect Information The second perfect information is called expected value of perfect information (EVPI) which is the difference of EVwPI and the expected value without information which means maximum EMV. Example Consider a company’s outcomes for four different decision-making options they have. The following table shows the payoff of each alternative:

Q: Decision making under risk involves considering various choices and several possible outcomes. The learning materials provide an example of this using the choice of factory size and whether there is high, moderate, or low demand. The payoffs are shown in the following table: Payoffs Outcome O1 O2 O3 O4 O5 Choice C1 17 233 -131 231 107 C2 -137 155 248 29 -146 C3 311 61 -150 24 360 C4 185 298 86 297 12 C5 -119 330 85 353 -107 Probability 0.265 0.137 0.095 0.195 0.308 What is the expected opportunity loss (EOL) for choice 1? Round your answer off to the nearest tenth. A: 228.9 Q: Decision making under risk involves considering various choices and several possible outcomes. The learning materials provide an example of this using the choice of factory size and whether there is high, moderate, or low demand. The payoffs are shown in the following table: Payoffs Outcome O1 O2 O3 O4 O5 Choice C1 17 233 -131 231 107 C2 -137 155 248 29 -146 C3 311 61 -150 24 360 C4 185 298 86 297 12 C5 -119 330 85 353 -107 Probability 0.265 0.137 0.095 0.195 0.308 What is the expected value with perfect information (EVwPI)? Round your answer off to the nearest tenth. A: 330.9

Q: Decision making under risk involves considering various choices and several possible outcomes. The learning materials provide an example of this using the choice of factory size and whether there is high, moderate, or low demand. The payoffs are shown in the following table: Payoffs Outcome O1 O2 O3 O4 O5 Choice C1 154 -75 285 182 94 C2 -15 169 -27 -65 -18 C3 55 144 193 208 240 C4 263 223 305 91 345 C5 305 318 374 225 -125 Probability 0.031 0.208 0.166 0.174 0.421 Which of the following choices has the highest EMV, and what is its value when rounded off to the nearest integer? A: C4, 266 Q: Decision making under risk involves considering various choices and several possible outcomes. The learning materials provide an example of this using the choice of factory size and whether there is high, moderate, or low demand. The payoffs are shown in the following table: Payoffs Outcome O1 O2 O3 O4 O5 Choice C1 17 233 -131 231 107 C2 -137 155 248 29 -146 C3 311 61 -150 24 360 C4 185 298 86 297 12 C5 -119 330 85 353 -107 Probability 0.265 0.137 0.095 0.195 0.308 Each outcome admits a choice with no regret. Which of the following choices corresponds to no regret for each outcome? A: 3, 5, 2, 5, 3, which means choice 3 for outcome 1, choice 5 for outcome 2, and so on.

Let   be the  i th choice,   be the  j th outcome,   be the payoff for the  i th choice with the  j th outcome, and lastly, let   be the probability of the  j th outcome. Sometimes, the letters get changed around. Consider the following expressions: a.  b.  c.  d.  Which of the following is the correct expression for the expected monetary value? A: Only d for choice r Q: A company has outcomes for four different decision-making options they have. The following table shows the payoff of each alternative. What is the value of expected value with perfect information (EVwPI)? A: $104,000 Q: A company has outcomes for four different decision-making options they have. The following table shows the payoff of each alternative.

What is the value of expected monetary value for the median plant? A: $76,000 Q: A company has outcomes for four different decision-making options they have. The following table shows the payoff of each alternative. What is the value of expected opportunity loss (EOL) for the no plant option? A: $104,000 Q: The value of the best minimum expected opportunity loss (EOL) choice is always __________. A: equal to the expected value of perfect information (EVPI) Q: When the probability of occurrence of each outcome can be accessed, the problem environment is called __________. A: decision making under risk Q: Which of the following best calculates expected value of perfect information (EVPI)? A: Expected value with perfect information (EVwPI) − maximum of expected monetary value (EMV) Q: A: