■ Definition: The maximin is the term given to the largest (the maximum) of the smallest outcomes (the minimums) associated with each decision alternative.
Example: Using the large-machine/small-machine decision outlined earlier, there are nine possible outcomes after two years for each alternative, depending upon whether demand was heavy-heavy, heavy-medium, heavy-light, and so forth. The nine possible outcomes were shown in column 8 in Table 2-2 for the large machine and in Table 2-3 for the small machine. The minimum outcomes are expected to be —$2,083 for the large machine and $861 for the small machine. The maximin outcome is, thus, $861, the larger of the smallest outcomes.
Rule: The maximin decision criterion is to select the alternative containing the maximin outcome. Thus the maximin criterion also selects the small machine in preference to the large machine.
In effect, the maximin criterion rules out every decision alternative except the one with the best of the worst outcomes. This is a risk averter’s decision criterion in the sense that it avoids alternatives which contain worse “downside” outcomes. But note that it also ignores the probability distribution and would have chosen the small machine even if its worst outcome probability was high and the large plant’s worst outcome probability was very low. Note also that the maximin criterion ignores all other
outcomes. 1 he large machine shows several relatively high outcomes, yet these don’t enter into consideration at all.
When is the maximin criterion appropriate? For repeated decisions it is clearly too pessimistic, always expecting the worst to happen, when, in fact, the law of averages should cause the EPV to be attained (on average) over many trials. For a one-shot deal, however, where the firm simply cannot afford to suffer the worst outcomes associated with some of the decision alternatives, the maximin criterion may be appropriate.
Example: In the large-machine/small-machine decision, suppose that any loss over $1,000 would cause the firm to go bankrupt and be liquidated by its creditors. The decision maker might then be unwilling to take the risk of the $2,083 loss associated with the large machine and choose the small machine to avoid to possibility of a loss exceeding $1,000.
Similarly, a decision maker looking for a promotion in the near future may reason that a loss resulting from one of his or her decisions will most likely prevent that promotion, and may decide to apply the maximin criterion. Thus, in particular situations, usually involving relatively short time horizons in which the law of averages cannot be relied on and in which the firm or the decision maker cannot afford the outcomes associated with some of the decision alternatives, the maximin criterion may be appropriate.