### Sensitivity Analysis and Value of Perfect Information

The oil wildcatter learned that the optimal decision changed when his attitude toward risk changed. Since risk attitude is difficult to express quantitatively, the oil wildcatter wanted to learn more about the uncertainties in his problem. Before spending any money on information-gathering procedures, he would like to know the benefit of knowing, before the 'Drill' or 'Not_Drill' decision, the amount of oil or the cost of drilling. The simplest approach is to calculate the value of perfect information for each uncertainty. This quantity gives an upper limit on the amount that could be spent profitably on information gathering. The expected value of information for the amount of oil is calculated by the following statement:

```      vpi Oil_Deposit;
```

The result of the previous statement is written to the SAS log as

```   NOTE: The currently optimal decision yields 140000.
NOTE: The new optimal decision yields 295000.
NOTE: The value of perfect information of stage Oil_Deposit
yields 155000.
```

This means that the wildcatter could spend up to \$155,000 to determine the amount of oil in the deposit with certainty before losing money. There are several alternative ways to calculate the expected value of perfect information. For example, the following statement

```      vpi Cost;
```

is equivalent to

```      save;
move Cost before Drill;
evaluate;
recall;
```

The messages, which appear on the SAS log, show that if there is some way that the wildcatter knows what the cost to drill will be before his decision has to be made, it will yield an expected payoff of \$150,000. So, the expected value of perfect information about drilling cost is \$150,000 - \$140,000 = \$10,000.

```   NOTE: The current problem has been successfully saved.

NOTE: Present order of stages:

Cost(C), Drill(D), Oil_Deposit(C), _ENDST_(E).

NOTE: The currently optimal decision yields 150000.

NOTE: The original problem has been successfully recalled.
NOTE: Present order of stages:

Drill(D), Cost(C), Oil_Deposit(C), _ENDST_(E).
```