Advanced Operations Management (33:623:400)
Professor Eckstein
A Bayesian Decision Tree with Three "States of the World"
(Former Midterm Problem)
Your firm currently holds the mining rights to a plot of
land in southern
Alaska
, which is suspected to contain valuable cobalt deposits. You estimate there is 25% chance the plot of land will be an
“excellent” source of cobalt, in which case you would make a $24 million
profit from developing it. There is
a 50% chance it will be “good” source of cobalt, in which case you would
earn a profit of $9 million from developing it.
Otherwise, it will be a “poor” source of cobalt, and developing it
would yield a loss of $12 million. If
you do not develop the plot, you can sell it for $4 million.
Before deciding whether to develop or sell the plot, you may conduct a
test drilling program, which will cost $2 million.
The results of the program may be either “promising” or
“unpromising”. In the past, test
drilling has yielded a “promising” result for 96% of the tested plots that
turned out to be “excellent”, 60% of the tested plots that turned out to be
“good”, and 24% of the tested plots that turned out to be “poor”.
By law, the results of the test drilling program must be made public.
A “promising” result would increase the sales value of the plot, if
you don’t develop it yourself, to $10 million.
An “unpromising” result would lower the sales value of the plot to $1
million.
What should you do to maximize the expected value of the
plot of land? What is the EVSI of the test drilling program?