Construct a decision tree and calculate the probabilities and EMV for each decision using the information given.
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Construct a decision tree and calculate the probabilities and EMV for each decision using the information given. Your company has identified and purchased a plot of land suitable to develop a small lithium mine. Lithium is in high demand due to its use in lightweight batteries, including for electric vehicles. Lithium is found in three kinds of deposits, which we will call type type and type While you are sure that the site contains lithium, you do not know for certain what kind of deposit it holds. Based on the geological work you have already done, you estimate a chance of a type deposit, a chance of a type deposit, and a chance of a type deposit.
There are two kinds of mines you could build on the site, a bore mine or a pit mine The payoffs in millions of dollars for each kind of mine and deposit are as follows:Type of Deposit
Type Type Type
Bore mine
Pit mine
For example, if construct a bore mine and the deposit turns out to be of type your profit would be $ million.
You also have standing offer from a competing company to buy the site for $ million, which you may accept instead of developing the site.
Before making any other decisions, you have the option of performing a seismic reflection study of the site, which would be more detailed than your prior geological work and cost $ million. This study will predict the type of the deposit to be of type or The vendor that would perform the seismic reflection study has provided the following historical data:.
Seismic prediction probabilities conditional on deposit type
Type Type Type
Predict
Predict
Predict
That is for what turned out to be type deposits, seismic reflection studies have made the correct prediction in of past cases, have incorrectly predicted type in of past cases, and also incorrectly predicted type in of past cases. For what turned out to be type deposits, past reflection seismic studies have correctly predicted a type deposit in out of cases, incorrectly predicted a type deposit in out of cases, and incorrectly predicted a type deposit in out of cases. The type column of the table is interpreted similarly.
If you perform the seismic reflection study, you may still accept the offer to sell the site to your competitor after getting the study results, no matter what they turn out to be
Using a Bayes analysis and a decision tree, find course of action that optimizes your EMV in this situation. State the optimal policy and its EMV.
What is the EVSI of the seismic reflection survey?
What is the EVPI in this situation?
Related Book For
Quantitative Analysis for Management
ISBN: 978-0133507331
12th edition
Authors: Barry Render, Ralph M. Stair, Michael E. Hanna, Trevor S. Ha
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