İŞLETME KARAR MODELLERİ

There are some different methods used in decision making under uncertainty. 

-Equally Likely (Laplace)
-Criterion of Optimism (Plunger)
-Criterion of Pessimism (Wald)
-Criterion of Realism (Hurwicz)
-Minimax Regret (Savage)

In this sense, the correct answer is option E.

The correct answer is given in option A. Because if decision maker has an optimistic approach, this method can be used. In this method, whether the objective of problem is maximization or minimization, the best outcome for each alternative is realized and decision maker select the best among these alternatives. If the problem is the minimization, the best outcome is the lowest value. In this case, the alternative which is the smallest value is chosen. The mathematical representation of the method is as follows:

The decision maker is a little optimistic, a little pessimistic and the method that involves both cases is called Criterion of Realism. This method allows the decision maker to use these two approaches together. So, the correct answer is A.

There are four events in the problem. So, the probability of occurrence of each event is 1/4.
District 1 = 10.000*1/4 + 12.500*1/4 + 15.000*1/4 + 16.500*1/4 = 13.500 TL
District 2 = 15.000*1/4 + 17.000*1/4 + 18.000*1/4 + 24.500*1/4 = 18.625 TL
District 3 = 12.000*1/4 + 13.000*1/4 + 20.000*1/4 + 32.000*1/4 = 19.250 TL
District 4 = 21.000*1/4 + 25.000*1/4 + 27.000*1/4 + 40.000*1/4 = 28.250 TL
Since the objective of this decision problem is maximization, decision maker chooses the highest value among the alternatives. The decision maker selects district 4 with 28.250 TL.

First, the maximum values are determined for each alternative. Then, the highest value (40.000 TL) and the alternative for that value (District 4) is selected. The correct answer is D.

The alpha coefficient is determined by the decision maker as 0.3. Then 1-alpha becomes 0.7. In this case, the decision maker is optimistic with a probability of 30%, and pessimistic with a probability of 70%.

First, the minimum values are determined for each alternative. These values are multiplied by the α coefficient. Then the maximum values are determined for each alternative. These values are multiplied by the (1- α) coefficient. These values of each alternative are sum up.
Product 1 = 3*0.3 + 12*0.7 = 9.3 days
Product 2 = 1*0.3 + 18*0.7 = 12.9 days
Product 3 = 5*0.3 + 15*0.7 =12 days
Product 4 = 4*0.3 + 11*0.7 = 8.9 days
Product 5 = 2*0.3 + 10*0.7 = 7.6 days
Then, because the objective is minimization the lowest value (7.6 days) and the alternative for that value (Product 5) is selected.

The method used for the loss of opportunities when the best alternative is not selected is “Minimax Regret”. This method is based on opportunity loss, also called regret. In this sense the correct answer is option B.

This 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.
This method proposed that maximum regret be minimized by choosing the best pay off for each event. The regret of each event for each alternative is calculated and regret matrix or opportunity loss table is created. This table shows the losses to be incurred if the alternative is not selected for the best outcomes of each event.
If the objective is maximization, the maximum value of each event is determined. All values of the relevant event are subtracted from this maximum value. If the objective is minimization, the minimum value of each event is determined. The smallest value of each event is subtracted from all values of relevant event. In this way, the regret matrix is obtained.
After the regret matrix has been constructed, the maximum opportunity loss (regret) for each alternative is located. Then the alternative with the smallest value
among these maximum regrets selected.

In this method, regardless of the objective function, the smallest value is always selected from the regret matrix.

According to these information, the correct answer is given in the option C.

For the values given in the Table, a regret matrix is created. Because the objective is
minimization, the minimum value of each event is selected. The smallest value of each event is subtracted from all other values in relevant column. Thus, a regret matrix is created. This table shows the regret matrix of the problem.

According to the results in Table, maximum regret of each alternatives are as follows:
Product 1 = maximum regret = 5 days
Product 2 = maximum regret = 8 days
Product 3 = maximum regret = 6 days
Product 4 = maximum regret = 4 days
Product 5 = maximum regret = 3 days
The alternative with the smallest value (product 5) is chosen among the maximum regrets. The correct answer is E.

Equally Likely (Laplace) method indicates that all events occur equally likely if the probability of occurrence of events is unknown. Therefore, calculation is made considering that the event’s possibility occur equally. The final decision is made according to the objective (maximum or minimum) of the problem.

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.

Equally Likely (Laplace) method indicates that all events occur equally likely if the probability of occurrence of events is unknown. Therefore, calculation is made considering that the event’s possibility occur equally. The final decision is made according to the objective (maximum or minimum) of the problem.