When several outcomes exist and a decision maker cannot assess their probabilities with confidence, the environment is called decision making under uncertainty.
Five common criteria for making decisions without probabilities are:
(1) Maxi-max (i.e. optimisticor aggressive)
(2) Maxi-min(i.e. pessimisticor conservative)
(3) Realism (i.e. a compromise between optimistic and pessimistic)
(4) Equally likely
(5) Mini-max regret or opportunity loss
The first four criteria can be computed directly from the profit table, whereas the fifth requires use of the opportunity-loss table.
Let us illustrate them one by one using the following scenario where the payoffs are profits:
Outcome | ||
Alternative | High sales ($) | Low sales ($) |
Construct a large plant | 200,000 | -180,000 |
Construct a small plant | 100,000 | -20,000 |
Do nothing | 0 | 0 |
(1) Maxi-max criterionyields
Outcome | |||
Alternative | High sales ($) | Low sales ($) | Row max |
Construct a large plant | 200,000 | -180,000 | 200,000* |
Construct a small plant | 100,000 | -20,000 | 100,000 |
Do nothing | 0 | 0 | 0 |
“Construct a large plant” is selected.
(2) Maxi-min criterionyields
Outcome | |||
Alternative | High sales ($) | Low sales ($) | Row min |
Construct a large plant | 200,000 | -180,000 | -180,000 |
Construct a small plant | 100,000 | -20,000 | -20,000 |
Do nothing | 0 | 0 | 0* |
“Do nothing” is selected.
Remark:
This criterion locates the alternative that gives the best of the worst profits, and henceit guarantees the profit is at least the maximum value.
(3) Realism criterionwith a= 0.8yields
Outcome | |||
Alternative | High sales ($) | Low sales ($) | Weighted average with a= 0.8 |
Construct a large plant | 200,000 | -180,000 | 124,000* [= 0.8(200,000) + 0.2(-180,000)] |
Construct a small plant | 100,000 | -20,000 | 76,000 |
Do nothing | 0 | 0 | 0 |
“Construct a large plant” is selected.
Remarks:
(a) To begin with, a coefficient a(with a value between 0 and 1) of realism is specified; this measures the degree of optimismof a decision maker.
When a= 1 (or 0), he/she is 100% optimistic (or 100% pessimistic) about the future.
The advantage of this criterion is that it allows a decision maker to build in personal feelings about relative optimism and pessimism.
(b) When there are more than twooutcomes, this criterion considers the best and the worstbut ignores the other profitsfor each alternative.
(4) Equally likelyyields
Outcome | |||
Alternative | High sales ($) | Low sales ($) | Row average |
Construct a large plant | 200,000 | -180,000 | 10,000 [= 0.5(200,000) + 0.5(-180,000)] |
Construct a small plant | 100,000 | -20,000 | 40,000* |
Do nothing | 0 | 0 | 0 |
“Construct a small plant” is selected.
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