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Unformatted text preview: Decision Analysis The last six chapters have dealt largely with the analysis of stochastic processes processes that evolve in a probabilistic manner.over time (e.g., Markov chains). Some of this analysis focused on decision making in the face of this uncertainty (e.g., Markov decision processes). We now turn to decision making in the face of uncertainty in a different context. Instead of making decisions over a long time, we now are concerned with making perhaps just one decision (or at most a sequ ence of a few decisions) about what to do in the immediate future. However, there still are random factors outside our control that create some uncertainty about the outcome of each of the alternative courses of action. Decision analysis provides a framework and methodology for rational decision making in this context. Frequently, one question to be addressed is whether to make the needed decision immediately or to first do some testing (at some expense) to reduce the level of uncer tainty about the outcome of the decision. For example, the testing might be field testing of a proposed new product to test consumer reaction before making a decision on 864 whether to proceed with full-scale production and marketing of the product. This test ing is referred to as performing experimentation. Therefore, decision analysis divides decision making between the cases of without experimentation and with experimenta tion. The first section introduces a prototype example that will be carried throughout the chapter for illustrative purposes. Sections 20.2 and 20.3 then present the basic principles of decision making without experimentation and decision making with exper imentation. Section 20.4 describes decision trees, a useful tool for depictin g and aria lyzing the decision process. We then conclude the chapter by introducing utility theory, which provides a way of calibrating the possible outcomes of the decision to reflect the true value of these outcomes to the decision maker. 20.1 A Prototype Example 865 20.2 / De cision Making without Experimentation The OOFERBROKE COMPANY owns a tract of land that may con tain oil. A consult ing geologist has reported to management that she believes the re is 1 chance in 4 of oil. Because of this prospect, another oil company has offered to purchase the land for $90,000. However, Goferbroke is considering holding the land in order to drill for oil itself. If oil is found, the companys expected profit will be approximately $700,000. A loss of $100,000 will be incurred if the land is dry (no oil). Table. 20.1 summarizes these data. Section 20.2 discusses how to approach the decision of whether to drill or sell based just on these data. However, another option prior to making a decision is to conduct a detailed seismic survey of the land to obtain a better estimate of the probability of finding i1. Section 20.3 discusses this case of decision making with experimentation, at which point the necessary additional data will be provided.point the necessary additional data will be provided....
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- Fall '09