【正文】 ers? How much should be produced? Should the product be test marketed in a small region before deciding upon full distribution? How much advertising is needed to launch the product successfully? 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 博士 ?2022 SYSTEMS ENGINEERING 2. A financial firm investing in securities. Which are the market sectors and individual securities with the best prospects? Where is the economy headed? How about interest rates? How should these factors affect the investment decisions? 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 博士 ?2022 SYSTEMS ENGINEERING 3. A government contractor bidding on a new contract. What will be the actual costs of the project? Which other panies might be bidding? What are their likely bids? 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 博士 ?2022 SYSTEMS ENGINEERING 4. An agricultural firm selecting the mix of crops and livestock for the uping season. What will be the weather conditions? Where are prices headed? What will costs be? 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 博士 ?2022 SYSTEMS ENGINEERING 5. An oil pany deciding whether to drill for oil in a particular location. How likely is oil there? How much? How deep will they need to drill? Should geologists investigate the site further before drilling? 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 博士 ?2022 SYSTEMS ENGINEERING These are the kinds of decision making in the face of great uncertainty that decision analysis is designed to address. Decision analysis provides a framework and methodology for rational decision making when the outes are uncertain. 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 博士 ?2022 SYSTEMS ENGINEERING Frequently, one question to be addressed with decision analysis is whether to make the needed decision immediately or to first do some testing (at some expense) to reduce the level of uncertainty about the oute of the decision. 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 博士 ?2022 SYSTEMS ENGINEERING For example, the testing might be field testing of a proposed new product to test consumer reaction before making a decision on whether to proceed with fullscale production and marketing of the product. Therefore, decision analysis divides decision making between the cases of without experimentation and with experimentation. 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 博士 ?2022 SYSTEMS ENGINEERING The first section introduces a prototype example that will be carried throughout the chapter for illustrative purposes. Sections and then present the basic principles of decision making without experimentation and decision making with experimentation. We next describe decision trees, a useful tool for depicting and analyzing the decision process when a series of decisions needs to be made. 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 博士 ?2022 SYSTEMS ENGINEERING A PROTOTYPE EXAMPLE The GOFERBROKE COMPANY owns a tract of land that may contain oil. A consulting geologist has reported to management that she believes there is 1 chance in 4 of oil. Because of this prospect, another oil pany has offered to purchase the land for $90,000. However, Goferbroke is considering holding the land in order to drill for oil itself. The cost of drilling is $100,000. If oil is found, the resulting expected revenue will be $800,000, so the pany39。 decision rule: Using the best available estimates of the probabilities of the respective states of nature (currently the prior probabilities), calculate the expected value of the payoff for each of the possible actions. Choose the action with the maximum expected payoff. 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 博士 ?2022 SYSTEMS ENGINEERING For the prototype example, these expected payoffs are calculated as follows: E [Payoff (drill)] = (700) + (100) = 100. E [Payoff (sell)] = (90) + (90) = 90. Since 100 is larger than 90, the alterative action selected is to drill for oil. 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 博士 ?2022 SYSTEMS ENGINEERING The big advantage of Bayes39。 oil is fairly likely. 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 博士 ?2022 SYSTEMS ENGINEERING Based on past experience, if there is oil, then the probability of unfavorable seismic soundings is P(USS | State = Oil) = , so P(FSS | State = Oil) = 1 = . Similarly, if there is no oil , then the probability of unfavorable seismic soundings is estimated to be P(USS | State = Dry) = , so P(FSS | State = Dry) = 1 = . 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 博士 ?2022 SYSTEMS ENGINEERING We soon will use these data to find the posterior probabilities of the respective states of nature given the seismic soundings. Prior Probabilities Conditional Probabilities Joint Probabilities Posterior Probabilities 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 博士 ?2022 SYSTEMS ENGINEERING Fig probability tree diagram showing all the probabilities leading to the calculation of each posterior probability of the state of nature given the finding of the seismic survey 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 博士 ?2022 SYSTEMS ENGINEERING DECISION TREES Decision trees provide a useful way of visually displaying the problem and then anizing the putational work already described in the preceding two sections. These trees are especially helpful when a sequence of decisions must be made. 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 博士 ?2022 SYSTEMS ENGINEERING Decision trees model sequential decision problems under uncertainty. A decision tree describes graphically the decisions to be made, the events that may occur, and the outes associated with binations of decisions and events. Probabilities are assigned to the events, and values are determined for each oute. A major goal of the analysis is to determine the best decisions. Decision trees have three kinds of nodes and two kinds of branches. 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 博士 ?2022 SYSTEMS ENGINEERING Nodes and Branches A decision node is a point where a choice must be made