İŞLETME KARAR MODELLERİ - Deneme Sınavı - 3

Equally likely method indicates that all events occur equally likely if the probability of occurrence of events is unknown. The mathematical representation of the method is as follows: n: number of events related to the problem. Possibility of occurrence of each event = P (O_j ) = 1/n ,  j = 1, 2, 3 …n.

In a decision problem, the decision maker is aware of various possible events but has insufficient information to assign any probabilities of occurrence to them. This kind of a decision problem is termed as decision making under uncertainty. There are many unknowns and no possibility of knowing what could occur in the future to change the outcome of a decision in decision making under uncertainty. For firms launching a new product, an important change in marketing strategy or opening first branch can be given examples of decision making under uncertainty.

Generally, five different methods can be used for decision making under uncertainty. These methods are: Equally Likely (Laplace), Criterion of Optimism (Plunger), Criterion of Pessimism (Wald), Criterion of Realism (Hurwicz), Minimax Regret (Savage).

If decision maker has a pessimistic approach, this method can be used. The decision maker thinks that the worst outcomes for each alternative will be realized. However, when choosing from alternatives, it selects the best alternative for the objective of the problem. If the problem is maximization, the worst outcome is the lowest value. However, the best alternative (maximum value) of these worst outcomes is chosen.

Criterion of realism allows the decision maker to use both criterion of pessimism and criterion of realism approaches together. There is a coefficient indicating the level of optimism of the decision maker. This coefficient is symbolized by alpha (α). When decision maker is pessimistic, the 1- α coefficient is used. If the problem is minimization, the best value is the smallest value and this value is multiplied by alpha coefficient. The worst value is the highest value and this value is multiplied by 1-α coefficient. Then, these values are sum up. Finally, the alternative with the best value (minimum value) is selected. The mathematical representation of the method is as follows: Min_i {α*Min (0_ij)_j + (1 – α)*Max (0_ij)_j}.

In the criterion of realism approach there is a coefficient indicating the level of optimism of the decision maker. This coefficient is symbolized by alpha (α). When decision maker is pessimistic, the 1- α coefficient is used. When the objective function is maximization, the highest values of the alternatives are multiplied by alpha and the smallest values of the alternatives are multiplied by 1– α.

The Minimax Regret (Savage) method is based on opportunity loss, also called regret. It is defined as the difference between the optimal and the actual pay-off. Regret is the amount lost when the best alternative is not selected.

Criterion of realism allows the decision maker to use optimism and pessimism approaches together. There is a coefficient indicating the level of optimism of the decision maker. This coefficient is symbolized by alpha (α). When decision maker is pessimistic, the 1- α coefficient is used. The alpha is between 0 and 1. When the alpha is equal to 1, the decision maker is optimistic. When it is equal to 0, the decision maker is pessimistic. The alpha coefficient is determined by the decision maker.

Minimax regret method is based on opportunity loss, also called regret. It is defined as the difference between the optimal and the actual pay-off. Regret is the amount lost when the best alternative is not selected.

In decision making under risk, there exist more than one state of nature and the decision maker has sufficient information to assign probabilities to the occurrence of each of these states. Such decision-making is also known as probabilistic or stochastic decision making.

In the decision making process under risk, a probability value must be determined for the chance of realization of all states of nature in the strategy table and the sum of all probabilities of states of nature must be equal to 1. After these possibilities are added to the strategy table, the decision maker should determine which approach will be used to select the best course of action. These approaches are Expected Value (EV) (or Expected Monetary Value (EMV)), Expected Opportunity Loss (EOL), and the Maximum Probability.

As known, the probability values change from 0 to 1, where 0 means the event occurrence probability is low and 1 means this probability is high. The process of determining probabilities for states of nature is very important. In the decision making process under risk, a probability value must be determined for the chance of realization of all states of nature in the strategy table and the sum of all probabilities of states of nature must be equal to 1.

In maximum probability criterion, the decision maker confronts the various possible states of nature in a decision under risk and; he or she chooses the alternative that is best for the most likely state of nature, rather than calculating in all states of nature. With another saying, it states that the decision maker should ignore all possible events except the one most likely to occur, and should select the best possible result (maximum gain or minimum loss) in the given circumstances.

While maximum probability criterion has the advantage of simplicity, ignoring substantive information related to the less likely states of nature makes it a weaker decision making criterion. Because it does not mean that the state of nature which has a low probability will not occur. On the contrary, it indicates that there is a possibility of occurrence of the event, but it has a low chance of occurring according to other alternatives.

The expected value of perfect information is used to place an upper limit on what you should pay for information that will aid in making a better decision. That is if we have perfect information about a state of nature before the decision is made, how much is this information worth? The expected value of perfect information (EVPI) is the difference between the expected value under certainty and the expected value under risk.

EVPI = EVwPI – EVwoPI, where EVwPI stands for expected value with perfect information and EVwoPI stands for expected value without perfect information. So  EVPI = 569 – 183 = 386.

A chance node, represented in a circle shape on the decision tree, indicates that one of a finite number of states of nature is expected to occur at this point in the process. The states of nature are shown on the tree as branches to the right of the chance nodes and the assumed probabilities of the states of nature are written above the branches.

The probability multiplication in the denominator of Bayes rule equality is called joint probability. In order to obtain any multiplication result in the denominator, the researcher needs to know what state of nature has emerged, as well as which B result is reached with this state of nature. The joint probabilities calculated in the denominator, correspond to each scenario mentioned in decision tree definitions in decision making problems.

With the formula used in Bayes’s theorem, while the result of a given event is certain, the possibility of the causes of this result is investigated. From the other perspective, in Bayes’ formula, the cause and result are displaced.

The foundation of operations research is mostly cited to studies and applications in the U.S. Army right before The World War II. However, Leonid V. Kantorovich is recognized as the first to explore this area. In 1939, Kantorovich published a paper on a method for a production plan which he claimed to be the optimal way. This study included a linear program without a systematic solution.