MCom I Semester Statistical analysis Decision Theory Study Material Notes ( Part 2 )

MCom I Semester Statistical analysis Decision Theory Study Material Notes ( Part 2 ): Decision criteria Decision Making Environment Decisions Criteria Under Uncertainty Expected Monetary value Criteriaon Expected Opportunity Loss Table Pay of Table Expected Pat of Table Values in Rs Expected Profits Presuming Certainty of Demand Expected Assuming that you Have Perfect Knowledge  :

MCom I Semester Statistical Analysis Test Significance Small Samples Study Material Notes

Decision Criteria or Decision-Making Environment

Decision theory mainly deals with helping the decision-maker in selecting the best course of action among the available courses of action. The decision models have been classified on the type of information that is available about the occurrence of the various states of nature as well as upon the decision environment. Basically, there are four different states of decision environments: certainty, risk, uncertainty and conflict

(1) Decision-making under Certainty : This is the simplest form of decision-making. In this environment, the decision-maker knows with certainty the consequence of selecting every course of action i.e., the outcome resulting from the selection of a particular course of action is known with certainty. There is just one state of nature for each course of action and has probability one. There is complete and accurate knowledge of the consequence of each choice. Since the decision-maker has perfect knowledge of the future and the outcome, therefore, he simply selects that course of action where the pay-off is optimum. For example, suppose a person desires to invest Rs. 50,000 for a certain period. Bank deposits gives 6%, Unit Trust of India offers 7% and Government bond’s rate is 5% per annum. All the investments are fully secured. Hence, investment in UTI is the best choice. The various important techniques for taking decisions under conditions of certainty are : (i) linear programming, (ii) input-output analysis, (iii) techniques used in transportation and assignment problems, (iv) queuing models, (v) inventory models, (vi) break-even analysis etc.

(2) Decision-making under Risk : Under this condition, the various states of mature can be enumerated and the long-run relative frequency of their occurrence is assumed to be known. The information about the states of nature is probabilistic Te decision-maker cannot predict as to what outcome (pay-off) will occur as a result of his selecting a particular course of action. Since each course of action results in more than one outcome, therefore, it is not simple to calculate the exact monetary pay-offs or outcomes for the several combination of courses of action and States of nature. However, past experience, or past records often enable the decision-maker to assign probability values to the likely possible occurrence of each state of nature. Knowing the probability distribution of the states of nature, the best decision is to select that course of action which has the largest expected pay-off value.

The most widely used criterion for evaluating the alternative courses of action, in this case is the Expected Monetary Value (EMV) or expected utility. The objective of decision-making under this condition is to optimize the expected pay-off, which may mean either maximization of expected profit or minimization of expected regret.

(3) Decision-making under Uncertainty : The decision situations where there is no way in which the decision-maker can assess the probabilities of the various states of nature are called decisions under uncertainty. Thus, under this condition, the probabilities associated with occurrence of different states of nature are not known i.e., there is no historical data available or no relative frequency which could indicate the probability of the occurrence of a particular state of nature. In such a case, the decision-maker has no way of calculating the expected pay-off for his courses of action or strategies. Such situations arise when a new product is introduced in the market or a new plant is setup. In business situations there are many problems of this nature and here the choice of a course of action is very largely depend on the personality of the decision-maker and the policy of an organisation. A number of decision criteria have been provided for decision-making under the condition of uncertainty. The decision-maker may choose any one of the following: (i) maximin criterion, (ii) maximax criterion, (iii) minimax regret criterion, (iv) Hurwitz criterion and (v) Laplace criterion.

It may be pointed out that sometimes a distinction is made between decision-making under “risk” and decision-making under “uncertainty”. When the state of nature is unknown, but objective or empirical data is available so that the decision-maker can use these data to assign probabilities to the various states of nature, the procedure is generally referred to as decision-making under ‘risk’. When the state of nature is unknown and there is no objective information on which probabilities can be based, the procedure is referred to as decision-making under “uncertainty’. It may, however, be noted that even when no objective information is available, the decision-maker may, in Bayesian decision theory, assign subjective probability to the states of nature to help in taking a decision. Once probabilities are assigned, regardless of the manner in which they were obtained, the decision procedure that follows is exactly the same. Hence, for practical purposes risk and uncertainty are essentially the same and decision-making under both circumstances will be referred to as decision-making under uncertainty.

(4) Decision-making under Conflict Competitive Situation : Many practical Problems require decision-making in a competitive situation where there are two for more) opposing parties with conflicting interests and the action of one depends upon the action which the opponent takes. For example, candidates for an election, advertising and marketing campaigns by rival business firms, countries involved in military battles, etc., face situation of this type. Game theory technique is widely used for taking decisions under conflict competitive situation.

Decision Theory Study Material

Decisions Criteria Under Uncertainty

For the sake of convenience, decisions criteria under uncertainty can be divided into two parts:

(a) decision-making under uncertainty when event-probabilities are known

(b) decision-making under uncertainty when event-probabilities are not known.

(a) Decision-making Under Uncertainty When Event-Probabilities are known

When event-probabilities are known then following criterion are mainly used for taking decisions under the condition of uncertainty :

(1) Expected Monetary Value Criterion (EMV)

(2) Expected Opportunity Loss Criterion (EOL)

(1) Expected Monetary Value Criterion (EMV)

The ‘Expected Monetary Value Criterion’ is widely used to evaluate the alternative course of action (or act). The EMV for given course of action is just sum of possible pay-offs of the alternative, each weighted by the probability of that pay-off occurring. In short, the expected monetary valu, criterion requires the decision-maker to compute the expected pay-off for each decision alternative and then select the course of action that yields the highest EMV.

Steps for Calculating EMV : The various steps for calculating EMV are as follows:

(i) The decision-maker should clearly state all possible actions and also the possible outcomes of the actions.

(ii) The decision-maker must state the probability distribution concerning each possible action for which purpose he may use either a priori or empirical methods of calculating probabilities. In simple words, the decision-maker should assign a probability weight to each of the possible actions (or the states of nature).

(iii) The decision-maker must finally use some yardstick (usually rupees) that measures the value of each outcome.

(iv) Calculate the EMV for each course of action by multiplying the conditional pay-offs by the associated probabilities and add these weighted values for each course of action. Symbolically

EMV (A) = (, XP;)

where A; = course of action, i

P = probability of occurrence of state of nature e,

V = pay-off associated with course of action i and state of nature i (v) Choose, as the optimal act, that act with the highest EMV. This is known as Bayes decision rule.

Using the minimum EOL as the decision criterion, the best decision would be the second course of action i.e., do not develop the product.

Decision Theory Study Material

The Expected Value of Perfect Information (EVPI) : EVPI is an important concept in decision analysis. Expected Monetary Value (EMV) and Expected Opportunity Loss (EOL) criterion of statistical decision theory are based on prior analysis. Prior analysis uses subjective probabilities. These probabilities are based on the current information together with the business expertise, experience and judgement of the decision-maker. After making prior analysis the decision-maker must decide either to collect additional information regarding the states of nature or to take action as suggested by the prior analysis. Prior distribution is not always a perfect predictor regarding the states of nature. This is more so in business decision problems. However, if somehow the decision-maker finds a perfect predictor, he would prefer actions based on perfect predictor for it would enable him to maximize his profits or minimize his losses. The highest expected profits resulting in the presence of perfect predictor is called the expected pay-offs of perfect information (EPPI). EPPI is often called the expected value of pay-off under certainty. It is also known as ‘Expected Profits with Perfect Knowledge (EPPK)’. The perfect prediction reduces the opportunity losses due to uncertainty to zero. The highest pay-off in the absense of perfect predictor is expected pay-off (EMV) of the optimal action. The difference between EPPI and EMV of the optimal action is called the expected value of perfect information (abbreviated EVPI).

The expected value of perfect information (EVPI) may now be defined as the maximum amount, one would be willing to pay to obtain perfect information as to which state of nature (event) would occur. Since EMV represents the maximum attainable expected monetary value given only the prior outcome probabilities, with no information as to which state of nature will actually occur. Therefore, perfect information would increase profit from EMV (max) upto the value of EPPI. This increased amount is termed as expected value of perfect information (EVPI), i.e..

EVPI = EPPI – EMV (max.)

Thus, the main objective of the preposterous analysis is to determine whether or not it is profitable to gather additional information regarding the states of nature before taking the final action. Additional information may be gathered by conducting survey, by carrying out an experiment or by some other means. The objective of

Decision Theory Study Material