The Maximin decision rule is used for a risk-averse manager, who wants to minimize the possibility of having a poor outcome. It is called Maximin because the manager will find the decision alternative that MAXImizes the MINimum payoff. In effect, the Maximin rule will determine the worst-case scenario for each decision alternative, and then choose the alternative that has the best worst-case. Again, this does not guarantee that the final result will be good. It just ensures that if bad things happen, you will have controlled your losses by choosing a decision whose worst-case scenario is not as bad as the worst-case scenarios of the other decision alternatives. To determine the decision under the Maximin decision rule, a column is added on the right side fo the payoff table, and the lowest (or worst) payoff for each row (decision alternative) is recorded. From these, identify the highest one, and that will be in the row of the decision alternative to be selected under this rule.  Since the decision alternative Do Nothing has the maximum payoff in the new Maximax column, it would be selected as the decision to implement. Note that this is clearly a risk-reducing decision. In this case, applying the Maximin rule will ensure that the business will not suffer a loss. However, it also won't have the possibility of gaining a profit, either. Notice also that a payoff of $0 is the largest payoff, as it is higher than either of the negative numbers. Signs count! Page 5 of 9 Page 2The Criterion of Realism decision rule is an attempt to make a tradeoff between complete risk indifference (as in the Maximax rule), and total risk aversion (as in the Maximin rule). With this procedure, the decision maker will decisde how much emphasis to put on each extreme. Tod do this, he must choose a Coefficient of Realism, called alpha (α), which is a decimal number between 0 and 1. This number provides the emphais on the optimistic view. The number (1-α), then, is the amount of emphasis that is placed on the most pessimistic outcome. For example, if a manager chose an alpha of 0.6, he would be placing 60% emphasis on a risky, high return (Maximax-type) outcome, and 40% emphasis (since 1-0.6 = 0.4 or 40%) on a low-risk, pessimistic, (Maximin-type) outcome. Explained another way, the Criterion of Realism calculates a weighted average of the best and worst outcomes for each alternative, using α and (1-α) as the weights, respectively. To determine the decision under the Criterion of Realism decision rule, a column is added on the right side of the payoff table. In this column the decision maker must calculate the factor by multiplying the best outcome in the row by α, multiplying the worst outcome in the row by (1-α),and adding the two result together. Note that the sign on the payoffs is important, and frequently the worst payoff in a row will be a negative number. Make sure you add positive and negative numbers correctly! From these calculated numbers in each row, identify the highest one, and that will be in the row of the decision alternative to be selected under this rule. In the example above, the manager decided to use an alpha of 0.8, meaning that he wanted to place 80% emphasis on a high-payoff alternative, and so only 20% emphasis on the low-risk alternative. Since the decision alternative Construct a Large Plant has the maximum payoff in the new Criterion of Realism column, it would be selected as the decision to implement. Do you see how Mr. Thompson got the $124,000 in the Construct a Large Plant row? He multiplied alpha (0.8) by the best row outcome of 200,000 and got 160,000. He then multiplied (1-α) (1 - 0.8 or 0.2) by the worst outcome in the row, which is -180,000 to get -36,000. 160,000 plus -36,000 gives 124,000. Now you do it for the Construct a Small Plant row as a check on your knowledge. Page 6 of 9 Page 3Below is a new payoff table for another situation. Use each of the decision rules to determine the best alternative under each rule. Feel free to back up to previous pages if you need to review a method, but don't move on to the next page until you have your answer for each. The rules we learned are:
It may help to redraw the payoff table on a piece of paper in landscape mode, then add the new columns on the right as needed. Page 7 of 9 Page 4Did you get your four decisions, one for each decision rule? If so, click on the link to see a PowerPoint presentation with a discussion of how each of them should be determined. Follow along with your solutions as a knowledge check.
Page 8 of 9 Page 5We have seen that different decision rules will sometimes give us different "best" decisions. How can that be? Isn't there one "best" or optimal decision for each scenario a company faces? Answer that question in your mind, and then roll your mouse over the graphic to check your understanding. Once again, here are the decision rules that we have covered when decision making under uncertainty:
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What is the best decision if you want to take the conservative approach also called maximin strategy
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