İŞLETME KARAR MODELLERİ - Deneme Sınavı - 4

Events are environmental factors that influence the choice of the decision maker. However, they are uncontrollable.

The first step in the decision-making process is to define the problem. Perhaps this is the most important and most difficult part of the process. At this step, it is very important to describe the problem statement clearly and concisely.

Once the decision problem has been identified, in the second step the objective of the problem must be clearly stated. Therefore, "Establishing objectives" is the second step.

When the decision maker does not know
the probabilities of occurrence of events, the
decision-making is called “decision making
under uncertainty”. In this sense, the correct answer is B.

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.

The third step in the decision making process is "Listing all possible decision alternatives."

The fourth step in the decision-making process is "Identifying the possible outcomes for each decision alternative."

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 fifth step in the decision making process is "Identifying the pay-off matrix for each combination of alternatives."In this step, the matrix for each alternative and event combination is generated and the outcomes are written to the matrix.

In decision making under certainty, the decision maker knows outcomes of events for each decision alternative. In this case, because the decision maker knows everything about the problem, it is easier to make the best decision.

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.

In decision making under uncertainty, there is more than one event and these may not be identified or measured. Decision maker has no information and knowledge about outcomes of the events or probability of occurrence of the events. In cases where there is no level of information or knowledge about the outcomes of events, the decision is given under uncertainty.

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.

In decision making under risk, decision makers have information about the probability of occurrence of each events. The probability value can be known precisely or predicted. These possibilities can be obtained from the personal opinions of the decision-maker, from the statistical records held in the enterprise, from expert opinions, from market research.

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.