Decision Making Under Certainty Pdf

Decision making under certainty pdf

In this article we will discuss about Managerial Decision-Making Environment:- 1. Concept of Decision-Making Environment 2. Decision-Making Environment under Uncertainty 3. Risk Analysis 4. Certainty Equivalents.

Decision making under certainty pdf

The distinction is drawn on the basis of the degree of knowledge or information possessed by the decision-maker. But there is a difference between the two concepts. Risk can be characterized as a state in which the decision-maker has only imperfect knowledge and incomplete information but is still able to assign probability estimates to the possible outcomes of a decision.

Risk is objective but uncertainty is subjective; risk can be measured or quantified but uncertainty cannot be. Modern decision theory is based on this distinction. In general, two approaches are used to estimate the probabilities of decision outcomes. With the priori method, the decision-maker is able to derive probability estimates without carrying out any real world experiment or analysis. For example, we know that if we toss an unbiased coin, one of two equally likely outcomes i.

Uncertainty does not seem to suggest that the decision-maker does not have any knowledge.

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These not only constitute a formal description of the problem but also provide the structure necessary for a solution:. The manufacturer of these has imposed a condition on you: You have to order in batches of But you cannot assign any probability estimate to the alternative levels of demand or sales.

It is not possible for you to wait for some time to study the nature or determine the level of demand, nor can you place more than one order.

Thus, a situation of complete uncertainty prevails. The three alternative strategies are to order shirts A 1 , A 2 or A 3. The states of nature which are external to and beyond the control of the inventory manager are the events and in this case are three levels of demand: D 1 , D 2 , or D 3. Since the inventory manager does not know which of the events will occur, he is forced to make his decision in the face of uncertain outcomes. Thus we can say that a payoff matrix provides the decision-maker with quantitative measures of the payoff for each possible consequence and for each alternative under consideration.

Positive payoff implies profit and negative pay-off implies loss.

For the T-shirts inventory and ordering problem, the payoff matrix is presented in Table 8. It may be noted that once subjective probabilities are introduced, the distinction between risk and uncertainty gets blurred.

The maximin or Wald criterion is often called the criterion of pessimism. That is, the decision-maker should choose the best of the worst. In our T-shirt example the minimum payoffs associated with each of the actions are presented below:.

Thus, the criterion is conservative in nature and is well-suited to firms whose very survival is at stake because of losses. An exactly opposite criterion is the maximax criterion. It is known as the criterion of optimism because it is based on the assumption that nature is benevolent kind. Thus, this criterion is suitable to those who are particularly venturesome extreme risk takers.

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The decision-maker would thus choose to order units because this offers the maximum possible payoff. The Hurwicz alpha criterion seeks to achieve a pragmatic compromise between the two extreme criteria presented above. The focus is on an index which is based on the derivation of a coefficient known as the coefficient of optimism.

If, for instance, we assume that the decision-maker has a coefficient of 0. He has implicitly assigned a probability of occurrence of 0. A value of alpha a equal to 0. The results of applying the Hurwicz criterion in Eq. Thus, the decision-maker would choose A1, i.

This criterion suggests that after a decision has been made and the outcome has been noted, the decision-maker may experience regret because by now he knows what event occurred and possibly wishes that he had selected a better alternative.

Decision making under certainty pdf

The implication is that the decision-maker would develop a regret opportunity loss matrix and then apply the minimax rule to select an action. The conversion of a payoff matrix to a regret matrix is very easy.

Decision-Making under Certainty, Risk and Uncertainty

All we have to do is to subtract each entry in the payoff matrix from the largest entry in its column. Table 8. The regret value in Table 8. For example, if T-shirts are ordered and demand is units, then regret is Rs.

Thus, if the decision-maker had known that demand was going to be T-shirts, his optimal decision would have been to order T-shirts; if he had ordered only T- shirts his opportunity loss would be Rs. If the original payoff table is stated in terms of losses or costs, the decision-maker will then select the smallest loss for each event and subtract this value from each row entry. These probability assignments can then be utilized to calculate the expected payoff for each action and to choose that action with the maximum smallest expected payoff loss.

Therefore, following the Laplace criterion, the decision-maker would order units because it has the highest expected value. This criterion is also based on the assignment of probabilities. However, the assumption that each event is equi-probable is not made. Suppose, for example, the inventory manager and the marketing manager reach a consensus of opinion that the applicable probabilities for these different states of nature are: sell units, 0.

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Therefore, by using the maximization of expected value criterion, the inventory manager would choose A 2 , i. The results of employing the six criteria to our T-shirt example are given in Table 8.

In the final analysis, the inventory manager can easily toss out the A 3 option, but he must still bear the burden of choosing A 1 or A 2 in the face of uncertain demand. For example, if the inventory manager knew, before arriving at the decision, that actual demand were going to be units, the optimal decision would be to order units with a payoff of Rs.

Therefore, in our example, the expected value of perfect information is to be computed as follows:. Thus, the inventory manager knows that the maximum amount that he would pay for a perfect prediction of demand would be Rs.

Decision making under certainty pdf

However, it is virtually impossible, in practice, to gather perfect information. Yet the computation of its value is extremely useful to a manager.

Decision making under certainty pdf

The basic point to note here is that they provide the decision-maker with a procedure for evaluating the benefits of obtaining additional information and comparing them with the costs of this information. Based on these probabilities the expected value of the three actions order , or would be Rs. The optimal decision would still be the same, viz. Here we drew a distinction between risk and uncertainty.

But the decision-maker is still able to assign probability estimates to the possible outcomes of a decision.

These estimates are either subjective judgments or may be derived from a theoretical probability distribution. This distinction was first drawn by F. Risk analysis involves a situation in which the probabilities associated with each of the payoffs are known. Risk analysis is based on the concept of random variable.

Decision making under certainty - Example 1

For example, when one rolls a die the number that comes up is a random variable. Now the values that a random variable can assume may not be equally likely i. In this case, the six possible outcomes are equally likely i. The concept may now be illustrated. Suppose we have the following pay-off matrix Table 8. In such a situation some criterion has to be tried to arrive at a relative measure of risk. The expected monetary value EMV criterion no doubt furnishes necessary and useful information to the decision-maker.

Here, for the sake of simplicity, we consider only two probability distributions. However, the distribution of possible outcomes is more closely concentrated around this expected payoff for alternative A than it is for alternative B, i.

Managerial Decision-Making Under Risk and Uncertainty

So according to our criterion, alternative A would be treated as less risky than alternative B. If we adopt the simple EMV criterion, a cursory glance would make project B apparently seem to be the best possible choice. However, a closer scrutiny of the cash flows also reveals that project A has a small expected value, but, at the same time, it shows less variation and according to our yardstick, appears to be less risky. The results of our calculations are shown in Table 8.

Thus, the project B has a higher EMV but it is risker since it has a higher standard deviation.

Decisions Making Environments: Certainty, Uncertainty and Risk

Hence, it involves more risk. If, however, two projects or alternatives have significantly different expected monetary values, we can use standard deviation to measure relative risk of the two projects. In such a situation, we cannot compare the two projects so easily by using the standard deviation measure.

In case of two or more projects alternatives having unequal costs or benefits payoffs the CV is undoubtedly a preferable measure of relative risk. In our example, the coefficients of variation for projects A and B are, respectively, 0. From Table 8.

For project A it is 0. So long we restricted ourselves to considerations of risk involving objective probabilities. In some cases, however, a relative frequency also known as the classical interpretation of probability does not work because repeated trials are not possible.

One may, for instance, ask what is the probability of successfully introducing a new breakfast food like Maggie. In such situations the decision-maker has to assign probabilities on the basis of his own belief in the likelihood of a future event. These probabilities are called subjective probabilities.

In reaching decisions he makes use of these subjective probabilities in precisely the same way the objective or relative frequency probabilities would be used if they were available.