Which Criterion uses weighted average of maximum and minimum pay off in decision making
Maximin, maximax and minimax regret are three approaches to decision making under uncertainty. Show IllustrationPayoff tables show the payoff (profit or loss) for the range of possible outcomes based on two factors:
For example, suppose Geoffrey Ramsbottom is faced with the following pay-off table. He has to choose how many salads to make in advance each day before he knows the actual demand.
Probability 40 salads 50 salads 60 salads 70 salads 40 salads 0.10 $80 $0 $(80) $(160) 50 salads 0.20 $80 $100 $20 $(60) 60 salads 0.40 $80 $100 $120 $40 70 salads 0.30 $80 $100 $120 $140 The question is then which output level to choose. The maximax rule involves selecting the alternative that maximises the maximum payoff available. This approach would be suitable for an optimist, or 'risk-seeking' investor, who seeks to achieve the best results if the best happens. The manager who employs the maximax criterion is assuming that whatever action is taken, the best will happen; he/she is a risk-taker. So, how many salads will Geoffrey decide to supply? Looking at the payoff table, the highest maximum possible pay-off is $140. This happens if we make 70 salads and demand is also 70. Geoffrey should therefore decide to supply 70 salads every day. MaximinThe maximin rule involves selecting the alternative that maximises the minimum pay-off achievable. The investor would look at the worst possible outcome at each supply level, then selects the highest one of these. The decision maker therefore chooses the outcome which is guaranteed to minimise his losses. In the process, he loses out on the opportunity of making big profits. This approach would be appropriate for a pessimist who seeks to achieve the best results if the worst happens. So, how many salads will Geoffrey decide to supply? Looking at the payoff table,
The highest minimum payoff arises from supplying 40 salads. This ensures that the worst possible scenario still results in a gain of at least $80. Minimax regretThe minimax regret strategy is the one that minimises the maximum regret. It is useful for a risk-neutral decision maker. Essentially, this is the technique for a 'sore loser' who does not wish to make the wrong decision. 'Regret' in this context is defined as the opportunity loss through having made the wrong decision. To solve this a table showing the size of the regret needs to be constructed. This means we need to find the biggest pay-off for each demand row, then subtract all other numbers in this row from the largest number. For example, if the demand is 40 salads, we will make a maximum profit of $80 if they all sell. If we had decided to supply 50 salads, we would achieve a nil profit. The difference or 'regret' between that nil profit and the maximum of $80 achievable for that row is $80. Regrets can be tabulated as follows : Daily supply Daily Demand40 salads 50 salads 60 salads 70 salads 40 salads $0 $80 $160 $240 50 salads $20 $0 $80 $160 60 salads $40 $20 $0 $80 70 salads $60 $40 $20 $0 The maximum regrets for each choice are thus as follows (reading down the columns):
A manager employing the minimax regret criterion would want to minimise that maximum regret, and therefore supply 40 salads only. Note that the above techniques can be used even if we do not have probabilities. To calculate expected values, for example, we will need probabilities. Your FeedbackWe value your feedback on the topics or anything else you have found on our site, so we can make it even better.Give Feedback Which criterion uses weighted average?The Hurwicz criterion can be viewed as a weighted average of the best and the worst uncertainty realizations.
In which criterion the decision is to choose that course of action with maximum average payoff?It is called Maximax beacuse the manager will find the decision alternative that MAXImizes the MAXimum payoff for each alternative. Typically this would be a decision maker who has an optimistic outlook, and is looking for the highest possible gain, without considering how risky it could be for the company.
What is Maximax criterion in decisionMaximax is the criterion used by a decision maker who chooses the act which makes possible the maximum payoff. If the payoff table contains losses rather than profits, the maximax decision maker would choose the act which would make possible the minimum loss.
What is minimax criterion in decisionMinimax (sometimes MinMax, MM or saddle point) is a decision rule used in artificial intelligence, decision theory, game theory, statistics, and philosophy for minimizing the possible loss for a worst case (maximum loss) scenario.
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