Components of Decision Making
A decision-making situation includes several componentsthe decisions themselves and the actual events that may occur in the future, known as states of nature . At the time a decision is made, the decision maker is uncertain which states of nature will occur in the future and has no control over them.
A state of nature is an actual event that may occur in the future .
Suppose a distribution company is considering purchasing a computer to increase the number of orders it can process and thus increase its business. If economic conditions remain good, the company will realize a large increase in profit; however, if the economy takes a downturn, the company will lose money. In this decision situation, the possible decisions are to purchase the computer and to not purchase the computer. The states of nature are good economic conditions and bad economic conditions. The state of nature that occurs will determine the outcome of the decision, and it is obvious that the decision maker has no control over which state will occur.
As another example, consider a concessions vendor who must decide whether to stock coffee for the concession stands at a football game in November. If the weather is cold, most of the coffee will be sold, but if the weather is warm, very little coffee will be sold. The decision is to order or not to order coffee, and the states of nature are warm and cold weather.
To facilitate the analysis of these types of decision situations so that the best decisions result, they are organized into payoff tables . In general, a payoff table is a means of organizing and illustrating the payoffs from the different decisions, given the various states of nature in a decision problem. A payoff table is constructed as shown in Table 12.1.
Table 12.1. Payoff table
Using a payoff table is a means of organizing a decision situation, including the payoffs from different decisions, given the various states of nature .
Each decision, 1 or 2, in Table 12.1 will result in an outcome, or payoff , for the particular state of nature that will occur in the future. Payoffs are typically expressed in terms of profit revenues , or cost (although they can be expressed in terms of a variety of quantities ). For example, if decision 1 is to purchase a computer and state of nature a is good economic conditions, payoff 1 a could be $100,000 in profit.
It is often possible to assign probabilities to the states of nature to aid the decision maker in selecting the decision that has the best outcome. However, in some cases the decision maker is not able to assign probabilities, and it is this type of decision-making situation that we will address first.