【正文】 the sum of probabilities for the events in a set must equal one. 重慶大學制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING The third kind of node is a terminal node, representing the final result of a bination of decisions and events. Terminal nodes are the endpoints of a decision tree, shown as the end of a branch on handdrawn diagrams and as a triangle or vertical line on putergenerated diagrams. 重慶大學制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING In general, ?Decision nodes and branches represent the controllable factors in a decision problem。 decision rule throughout the remainder of the chapter. 重慶大學制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING DECISION MAKING WITH EXPERIMENTATION Frequently, additional testing (experimentation) can be done to improve the preliminary estimates of the probabilities of the respective states of nature provided by the prior probabilities. These improved estimates are called posterior probabilities. 重慶大學制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING We first update the Goferbroke Co. example to incorporate experimentation, then describe how to derive the posterior probabilities, and finally discuss how to decide whether if is worthwhile to conduct experimentation. 重慶大學制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING Continuing the Prototype Example As mentioned at the end of Sec. , an available option before making a decision is to conduct a detailed seismic survey of the land to obtain a better estimate of the probability of oil. The cost is $30,000. 重慶大學制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING A seismic survey obtains seismic soundings that indicate whether the geological structure is favorable to the presence of oil. We will divide the possible findings of the survey into the following two categories: USS: Unfavorable seismic soundings。 which is given as one of the entries in a payoff table. 4. This payoff table should be used to find an optimal action for the decision maker according to an appropriate criterion. 重慶大學制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING One additional element needs to be added in the decision analysis framework. The decision maker generally will have some information that should be taken into account about the relative likelihood of the possible states of nature. Such information can usually be translated to a probability distribution, acting as though the state of nature is a random variable, in which case this distribution is referred to as a prior distribution. Prior distributions are often subjective in that they may depend upon the experience or intuition of an individual. The probabilities for the respective states of nature provided by the prior distribution are called prior probabilities. 重慶大學制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING kinds of Decision Analysis 1. Deterministic Decision Analysis 2. Indeterminable Decision Analysis 3. Probability Decision Analysis 重慶大學制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING Characteristics of Decision Analysis 1. Deterministic Decision Analysis 2. Indeterminable Decision Analysis 3. Probability Decision Analysis (1) Goal (2) Actions (3) Certain Nature (4) Payoff (1)Goal (2) Actions (3) Uncertain Nature (4) No knowledge about probability of nature(5) Payoff (1) Goal (2) Actions (3) Nature (4) Payoff (5)Probability 重慶大學制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING Formulation of the Prototype Example in This Framework As indicated in Table , the Goferbroke Co. has two possible actions under consideration: drill for oil or sell the land. The possible states of nature are that the land contains oil and that it does not, as designated in the column headings of Table by oil and dry. Since the consulting geologist has estimated that there is 1 chance in 4 of oil (and so 3 chances in 4 of no oil), the prior probabilities of the two states of nature are and , respectively. Therefore, with the payoff in units of thousands of dollars of profit, the payoff table can be obtained directly from Table , as shown in Table . 重慶大學制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING State of Nature Alternative Oil Dry 1. Drill for Oil 700 100 2. Sell the Land 90 90 Chance of Status 重慶大學制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING State of Nature Alternative Oil Dry 1. Drill for Oil 700 100 2. Sell the Land 90 90 We will use this next to find the optimal action according to each of the four criteria described below. (Indeterminable Decision Analisys) 重慶大學制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING (1) The MaxiMax Payoff Criterion Maximax payoff criterion: For each possible action, find the maximum payoff over all possible states of nature. Next, find the maximum of these maximum payoffs. Choose the action whose maximum payoff gives this maximum. 重慶大學制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING State of Nature Maximax payoff Maximux Savage Alternative Oil Dry 1. Drill for Oil 700 100 700 2. Sell the Land 90 90 90 700 Action : Drill for Oil 重慶大學制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING (2) The Maximin Payoff Criterion Maximin payoff criterion: For each possible action, find the minimum payoff over all possible states of nature. Next, find the maximum of these minimum payoffs. Choose the action whose minimum payoff gives this maximum. Thus, since the minimum payoff for selling (90) is larger than that for drilling (100), the former alternative (sell the land) will be chosen as the action to take. 重慶大學制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING State of Nature Maximin payoff Maximux Savage Alternative Oil Dry 1. Drill for Oil 700 100 100