Scientific merit example

Bounded rationality The limitations on decision making caused by costs, human abilities, time, technology, and availability of information.

Suboptimization The result of different departments each attempting to reach a solu- tion that is optimum for that department.

Certainty Environment in which relevant parameters have known values.

Risk Environment in which cer- tain future events have probable outcomes.

Uncertainty Environment in which it is impossible to assess the likelihood of various future events.

EXAMPLE 55-1

Supplement to Chapter Five Decision Theory

to earth. Other managers seem oblivious to negative results and continue the process they associate with their previous successes, not recognizing that some of that success may have been due more to luck than to any special abilities of their own. A part of the problem may be the manager's unwillingness. to admit a mistake. Yet other managers demonstrate an inability to make a decision; they stall long past the time when the decision should have been rendered .

Of course, not all managers fall into these traps-it seems safe to say that the majority do not. Even so, this does not necessarily mean that every decision works out as expected. Another factor with which managers must contend is bounded rationality, or the limits imposed on decision making by costs, human abilities, time, technology, and the availability of information. Because of these limitations, managers cannot always expect to reach deci- sions that are optimal in the sense of providing the best possible outcome (e.g., highest profit, least cost). Instead, they must often resort to achieving a satisfactory solution.

Still another cause of poor decisions is that organizations typically departmentalize deci- sions. Naturally, there is a great deal of justification for the use of departments in terms of overcoming span-of-control problems and human limitations. However, suboptimization can occur. This is a result of different departments' attempts to reach a solution that is optimum for each. Unfortunately, what is optimal for one department may not be optimal for the orga- nization as a whole. If you are familiar with the theory of constraints (see Chapter 16), subop- timization and local optima are conceptually the same, with the same negative consequences.

5S.3 DECISION ENVIRONMENTS Operations management decision environments are classified according to the degree of cer- tainty present. There are three basic categories: certainty, risk, and uncertainty.

. Certainty means that relevant parameters such as costs, capacity, and demand have known values.

Risk means that certain parameters have probabilistic outcomes.

Uncertainty means that it is impossible to assess the likelihood of various possible future events.

Consider these situations:

1. Profit per unit is $5. You have an order for 200 units. How much profit will you make? (This is an example of certainty since unit profits and total demand are known.)

2. Profit is $5 per unit. Based on previous experience, there is a 50 percent chance of an order for 100 units and a 50 percent chance of an order for 200 units. What is expected profit? (This is an example of risk since demand outcomes are probabilistic.)

3. Profit is $5 per unit. The probabilities of potential demands are unknown. (This is an example of uncertainty.)

The importance of these different decision environments is that they require different anal- ysis techniques. Some techniques are better suited for one category than for others.

5S.4 DECISION MAKING UNDER CERTAINTY When it is known for certain which of the possible future conditions will actually happen, the decision is usually relatively straightforward: Simply choose the alternative that has the best payoff under that state of nature. Example 5S-1 illustrates this.

Determine the best alternative in the payoff table on the previous page for each of-the cases: It is known with certainty that demand will be (a) low, (b) moderate, (c) high.

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Supplement to Chapter Five Decision Theory

Choose the alternative with the highest payoff. Thus, if we know demand will be low, we would elect to build the small facility and realize a payoff of : 10 million. If we know demand will be moderate, a medium factory would yield the highest payoff ($12 million versus either $10 million or $2 million). For high demand, a large facility would provide the highest payoff.

Although complete certainty is rare in such situations, this kind of exercise provides some perspective on the analysis. Moreover, in some instances, there may be an opportunity to con- sider allocation of funds to research efforts, which may reduce or remove some of the uncer- tainty surrounding the states of nature, converting uncertainty to risk or to certainty.

5S.5 DECISION MAKING UNDER UNCERTAINTY At the opposite extreme is complete uncertainty: 0 information is available on how likely the various states of nature are. Under those conditions, four possible decision criteria are maximin, maximax, Laplace, and minimax regret. These approaches can be defined as follows:

Maximin-Determine the worst possible payoff for each alternative, and choose the alternative that has the "best worst." The maximin approach is essentially a pessimistic one because it takes into account only the worst possible outcome for each alternative. The actual outcome may not be as bad as that, but this approach establishes a "guaranteed minimum."

Maximax-Determine the best possible payoff, and choose the alternative with that pay- off. The maximax approach is an optimistic, "go for it" strategy; it does not take into account any payoff other than the best.

Laplace-Determine the average payoff for each alternative, and choose the alternative with the best average. The Laplace approach treats the states of nature as equally likely.

Minimax regret-Determine the worst regret for each alternative, and choose the alter- native with the "best worst." This approach seeks to minimize the difference between the payoff that is realized and the best payoff for each state of nature.

The next two examples illustrate these decision criteria.

Referring to the payoff table on page 217, determine which alternative