CS3252 Management Science
Tutorial # 9, October 5 - October 10, 1998

  1. We have $1000 to invest. All the money must be placed in one of the 3 investments: gold, stock, or money market certificates. If $1000 is placed in an investment, the value of the investment one year from now depends on the state of the economy (see table below). Assume that each state of the economy is equally likely. For each of the following decision criteria, determine the optimal decision:
    1. maximin
    2. maximax
    3. minimax regret
    4. probabilistic expected value
    5. Hurwicz's (with )

  2. Oilco must decide whether to drill or not to drill for oil in the South China Sea. It costs $100,000 and if oil is found the value is estimated to be $600,000. At present, Oilco believes there is a 45% chance that the field contains oil. Before drilling, Oilco can hire (for $10,000) a geologist to obtain more information about the likelihood that the field will contain oil. There is a 50% chance that the geologist will issue a favorable report and a 50% chance of an unfavorable report. Given a favorable report, there is an 80% chance that the field contains oil. Given an unfavorable report, there is a 10% chance that the field contains oil. Determine the optimal course of action for Oilco. What are the EVPI (expected value of perfect information) and EVSI (expected value of sample information)?
  3. You have $1 million to invest in stocks or bonds. The percentage yield on each investment during the coming year depends on whether the economy has a good year or a bad year. It is equally likely that the economy will have a good or a bad year.

    1. If you are risk-neutral, how should the money be invested?
    2. For $5,000 you can hire a consulting firm to forecast the state of the economy. The consulting firm's forecasts have the following properties:
      P{good forecast|economy good} = 0.80.
      P{good forecast|economy bad} = 0.20.

      Should the consulting firm be hired? What are the EVSI and EVPI?


RUDY SETIONO
Fri Sep 25 09:59:48 SST 1998