ISE 562; Dr. Smith
Decision Problems – 2: Practice
Decision Theory
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ISE 562; Dr.
• Problem structuring practice (inputs and trees)
• Identifying states of nature and their uncertainty
• Define the decision tree with probabilities and payoffs; find the optimal decision.
• See if you can work the following problems (at least set them up before class.
• (If you are viewing the lecture later, hit “pause” and try the exercises.)
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ISE 562; Dr. 1:
The management of First Bank was concerned about the potential loss that might occur in the event of a physical catastrophe such as a power failure or fire. The bank estimated the loss from one of these incidents could be as much as $100M, including losses due to interrupted service and customer relations. One project the bank is considering is the installation of an emergency power generator at its operations headquarters. The cost of the emergency generator is $0.8M, and if it is installed no losses from this type of incident will be incurred. However, if the generator is not installed, there is a 10% chance that a power outage will occur during the next year. If there is an outage, there is a 0.05 probability that the resulting losses will be very large, or approximately $80M in lost earnings. Alternatively, it is estimated there is a 0.95 probability of only slight losses of around $1M. Using decision tree analysis should the bank install the generator?
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ISE 562; Dr. 2: SC is playing UCLA in a major conference game of the season. SC is trailing UC 21 to 14, with 7 seconds left in the game, when SC scores a touchdown. Still trailing 21 to 20, SC can either go for 2 points and win or go for 1 point to send the game into overtime. The conference championship will be determined by the outcome of the game. If SC wins it will go to the with a payoff of $7.2M; if it loses it will go to the Sun Bowl with a payoff of $1.7M. If SC goes for 2 points, there is a 33% chance it will be successful and win (and a 67% chance it will fail and lose). If it goes for 1 point, there is a 0.98 probability of success and a tie and a 0.02 probability of failure. If the teams tie, they will play overtime, during which SC believes it has only a 20% chance of winning because of fatigue.
Should SC go for 1 or 2 points? What would SC’s probability of winning in overtime have to be to make SC indifferent to going for 1 or 2 points?
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ISE 562; Dr. 3: The company has 3 health care plans for staff to choose from:
Plan 1: monthly cost of $32 with a $500 deductible; participants pay the first $500 of medical costs for the year; the insurer pays 90% of all remaining expenses.
Plan 2: monthly cost of $5 but a deductible of $1200 with the insurer paying 90% of medical expenses after the insurer pays the first $1200 in a year.
Plan 3: monthly cost of $24 with no deductible; the participants pay 30% of all expenses with the remainder paid by the insurer.
estimates her annual medical expenses
are defined by the following probability distribution: 9/17/2022 5
ISE 562; Dr. Smith
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