Consider the example we discussed from class about the decision of whether to build a small, large, or very large plant. Recall that the payoff, in millions of dollars, was dependent upon the demand, which might be low, medium, or high. We did not know the probabilities that the demand would be in any of these three states.

We discussed various decision rules, such as the maximax, maximin, minimax regret, and Laplace rules. Consider a new decision rule:

The payoff of alternative i is equal to: (maximum payoff for alternative i) + (1-)(minimum payoff for alternative i)

where 0

1. Let =0.6. What alternative is the best?

2. For what level of would you be indifferent between building a small plant and a large plant?

3. Observe the answers you get when you set to 0 and to 1. What do you notice about the results?

Table 1: Payoff Table Low Medium High Small $50 -8 0 Large -10 64 12 Very Large -15 12 66