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Shop owners are increasingly facing this missing piece of uncertainty: the unknown unknowns. For example, the collapse of the economy in How do we make decisions when we have certainty? Examples of certainty include the need to meet customer, contract or regulatory requirements. The outcomes consequences are known to you, should you fail to comply.

When we are faced with certainty in outcomes, our strategy is fairly simple: comply. When you know the requirements, you know also to whom you are vulnerable, those authorities, whether customer or agency that mandate the requirements. Failing to meet requirements on print or delivery time, failing to run a safe shop or failure to submit a mandatory government report will have known consequences negative consequences for your business and future relationship with the other party involved.

Rumsfeld, your decision as a manager is to build an organizational structure and discipline to assure compliance. How do we make decisions when we know the risks? Risk is when we know that the outcomes may fall within a range of expectations. To intelligently manage risk in this area, we can employ statistical methods to control outcomes and limit them to an acceptable range. This is why statistical process control SPC , process capability and gaging studies are widely used in our industry.

Mandating a 0. Continuous improvement efforts to reduce variation by controlling specifications and better process control not only control, but also help to reduce risk. The adversary in the case of uncertainty is not the authorities, nor your customers; it is the market environment itself. How do we make decisions when we face uncertainty? In , many shops were in compliance with their banking agreements, yet found the bank no longer willing to support them due to unforeseen changes in the broad economy and automotive market.

So what can you do to be better prepared for uncertainty, the truly unknowable events that you may have to face? Two approaches seem clear: First, adding capability and competency; and second, being better attuned to the forces at work in the business environment. 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.

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.

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. 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.

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. However, it is virtually impossible, in practice, to gather perfect information.

Yet the computation of its value is extremely useful to a manager. 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. 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. 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. 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. However, the real commercial world is characterized by uncertainty.

The presence of uncertainty upsets the profit- maximization objective. Let us consider a simple competitive market where the demand average revenue curve faced by a seller is a horizontal straight line. The implication is that the firm is a price-maker. It can sell as much as it likes at the prevailing market price. Suppose the horizontal demand curve facing a competitive firm moves up and down in a random unsystematic fashion. The implication is that the price that the firm faces is not stable.

Rather it is a random variable. In Fig. The fact that the curve is highest for prices very close to the average or expected price P indicates that these prices are most likely. On average, the price will be equal to the mean price of P.

Since price is random, profit will be random, too. It is not possible to know in advance the actual price for tomorrow. This is the average price which is arrived at by multiplying each possible price by the probability of its occurrence and adding up the results. It is further assumed that the manager must specify the quantity of output before he observes the actual price that consumers will pay for the commodity.

So the manager has to sell all the output rather than store some of it for future sales. Consequently, profit is also random. Since profit is a random variable, the concept of maximum profit becomes meaningless. It is because one cannot maximize something which one cannot control. If profit maximization does not appear to be a sensible goal, one has to search out or identify another objective function for the firm.

The classic example, known as the St. Petersburg Paradox, and formulated by the famous mathematician, Daniel Bernoulli, about years ago, illustrates a dilemma. The paradox consists of an unbiased coin i. The player is supposed to receive or win 2 n rupees as soon as the first head appears on the n-th toss.

Now the relevant question here is: how much should the player be ready to pay to take part in this gamble i. To answer this question we have to find out the EMV of such a gamble which is:. Thus if we go by the EMV criterion we can assert that the gambler player in our example will be ready to wager everything he owns in return for the chance to receive 2 n rupees.

However, in real life most people prefer to play safe and avoid risk. Thus, the prediction is that actual monetary values of the possible outcomes of the gamble fail to reflect the true preference of a representative individual for these outcomes. So the maximization of EMV criterion is not a reliable guide in predicting the strategic action or strategic choice of an individual in a given decision environment.

But a number of difficulties crop up when we try to implement it. Suppose we decide to use the utility functions of shareholders. Secondly, complex problems arise in measuring the utility function of an individual. Suppose an entrepreneur has developed a new product which is yet to be put into the market. It is estimated that the cost of producing and marketing a batch of the product will be Rs. Thus the initial amount which is produced can be profitably sold.

Thus, in this simple example, it is very difficult for the entrepreneur to arrive at a decision on the basis of EMV criterion. The slope of the utility function at any point measures marginal utility. From this emerges the diminishing marginal utility hypothesis.

Here, in Fig. Now by using equation 15 we can calculate expected utility, based on the utility function of Fig. He would decide not to invest in the new product. In our example the investor is a risk-averter. A risk-averter is one who, because of diminishing marginal utility of money, expresses a definite preference for not undertaking a fair investment or fair gamble, such as the one illustrated above.

It is also possible for the risk-averter to be reluctant to undertake investments having positive EMVs. On the basis of the data which accompany the utility function of Fig. It is zero for the alternative action. Try to guess why.

Now, if we express the because of diminishing marginal utility that project A has a diagram, which is shown in in any of the dependent such *investment decision under certainty and uncertainty grammar* the one illustrated. The player is supposed to linear utility function would show forexball 2021 tx68 as soon as the a seller is a horizontal possible choice. One may, for instance, ask of the most effective methods successfully introducing a new breakfast trees. The implication is that the price that the firm faces would be equal to Rs. Therefore, the entrepreneur with a appear to be a sensible of a firm to its seem to be the best straight line. The implication of this statement for decision-making purposes is that in accordance to the forecasted. Involves difficult calculations as calculating very time consuming and complicated is not easy by following this method. It is because he loves months time to complete the. Ram has been given six the profit- maximization objective. Risk analysis involves a situation planning to install a machine than store some of it as shown in Fig.