Operations research knowledge: decision-making analysis technology-optimistic criteria, pessimistic criteria, regretful criteria
Max-max (max) criterion
The maximum maximum standard is also called the optimistic standard. It finds the best result for each action and then finds a better choice from the best result:
u(Ai*) = maxi maxj aij
Max-min (max-min) criterion:
The maximum and minimum criterion is also called the pessimistic criterion, also called the small and the middle to the big. It finds the worst result of each action, and then finds the best one from the worst result as its choice:
u(Ai*) = maxi minj aij
Minimum Opportunity Loss Criteria (min-max)
Also known as the minimum maximum regret criterion, it uses the concept of opportunity cost to make decisions. The first thing to do is to make a decision is that the computer will lose (regretvalue) matrix;The concept of opportunity loss is the loss of income when an event occurs because you do not choose the optimal decision.
Also known as the minimum maximum regret criterion, it uses the concept of opportunity cost to make decisions. The first thing to do is to make a decision is that the computer will lose (regretvalue) matrix;The concept of opportunity loss is the loss of income when an event occurs because you do not choose the optimal decision.
Minimum maximum regret value method: also known as Savanci decision accuracy, decision makers do not know the probability of any of the various natural states, and the decision goal is to ensure that large loss of opportunity is avoided. When using the minimum maximum regret value method, the decision matrix must first be transformed from the profit matrix to the opportunity loss matrix; then determine the maximum opportunity loss of each optional solution; again, among the maximum opportunity loss of these solutions, select a minimum value, and the optional solution corresponding to the minimum value is the decision-making choice.
In order to clarify the concept, the following is an example to explain in detail:
A company needs to decide its investment strategy based on the forecast of the growth trend of the macro economy in the next year. There are three types of macroeconomic growth trends: recession, unchange and prosperity, and three types of investment strategies: positive, stable and conservative. The returns of various states are shown in the table below.
| Estimated earnings |
Economic trend forecast |
Test |
||
| recession |
constant |
Prosperity |
||
| Investment Strategy |
positive |
50 |
150 |
500 |
| steady |
100 |
200 |
300 |
|
| keep |
400 |
250 |
200 |
|
The so-called decision-making is simply to make a decision. In detail, in order to determine the goals of a future action, based on one's own experience, on the basis of possessing certain information, and using scientific methods and tools to analyze, calculate and evaluate the factors of the problem that need to be decided, and choose an optimal solution from more than two feasible plans.
Depending on the number of decision outcomes, decisions can be divided into definite decisions (only one outcome per scheme) and uncertain decisions (only multiple outcomes per scheme). This question is an uncertain decision-making problem.
Since the several natural states faced by uncertain decision-making problems are uncertain and completely random, this makes uncertain decisions always accompanied by a certain degree of blindness, and the experience and personality of decision makers often play a leading role in decision-making. Decision-making criteria include optimism, pessimism, and regret value criteria.
Since the several natural states faced by uncertain decision-making problems are uncertain and completely random, this makes uncertain decisions always accompanied by a certain degree of blindness, and the experience and personality of decision makers often play a leading role in decision-making. Decision-making criteria include optimism, pessimism, and regret value criteria.
one,
| Optimism Code MaxMax (Get big and big) |
| 500 300 400 |
| positive |
two,
The maxmin pessimistic criterion refers to the fact that any action plan is believed to be the worst state, that is, the state with the smallest return value. Then, compare the results after the implementation of each action plan, and take the action with the maximum benefit value as the decision-making principle, also known as the maximum minimum criterion.
The three investment strategies given in the question table are the smallest returns: 50 when the positive is 100 when the stable is 200 when it is conservative, so the maximum returns is 200, that is, the action corresponding to the best decision based on the maxmin pessimistic criterion is conservative investment.
The three investment strategies given in the question table are the smallest returns: 50 when the positive is 100 when the stable is 200 when it is conservative, so the maximum returns is 200, that is, the action corresponding to the best decision based on the maxmin pessimistic criterion is conservative investment.
| Pessimism Code MaxMin (Small and medium to large) |
| 50 100 200 |
| keep |
three,
| Regret value criteria MinMax (Large and medium to small) |
First transform into regret matrix:
That is, for each economic trend, find the losses, such as: recession (400 -50), (400-100), (400 -400), and so on.
| Regret matrix |
| Estimated earnings |
Economic trend forecast |
Test |
||
| recession |
constant |
Prosperity |
||
| Investment Strategy |
positive |
350 |
100 |
0 |
| steady |
300 |
50 |
200 |
|
| keep |
0 |
0 |
300 |
|
| Regret value criteria MinMax (Large and medium to small) |
| 350 300 300 |
| Stable or conservative |