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1、1 决策建模与严格不确定决策问题,学习目标： （1）掌握两种常用的决策建模方法： 决策表 决策树（2）掌握五种严格不确定决策问题的决策准则： 1 .乐观准则 2. 悲观准则 3. Hurwitz准则 4. 等概率准则(Laplace) 5. 后悔值极小化极大(Savage),1 决策建模与严格不确定决策问题,1.1 决策建模方法 1.2 严格不确定决策问题,1.1 决策建模方法,1.1.1 Example: a decision problem 1.1.2 Modeling the decision with decision tree 1.1.3 Modeling the decision
2、with pay-off table (or decision matrix) 1.1.4 Decision making under uncertainty 1.1.5 Decision making using probability information,1.1.1 Example: a decision problem,The Hewlett-Packard (HP) company specializes in assembling and selling PC systems for use by family doctor practices throughout the U.
3、S.A. The company is developing a new PC-based system. At present the company is trying to decide on the manufacturing and assembly process to be used. One aspect of this relates to the keyboard that will be used in the system, which will have specially labeled function keys. The company has decided
4、that it faces three alternatives: It can manufacture/assemble the keyboard itself. It can buy the keyboards from a domestic manufacturer. It can buy the keyboards from a manufacturer in the Far East.,1.1.1 Example: a decision problem (continued),The problem is that each of these options has differen
5、t costs and benefits associated with it. To manufacture/assemble the keyboard itself, the company would require major investment in new production equipment as well as extensive training of the work force. It is felt that such an investment is only likely to be cost-effective if sales of the new pro
6、duct are particularly good.Buying the keyboard from a domestic supplier will involve the company in less up-front expense and will be safer if large sales do not materialize in the future.Buying from an overseas supplier offers better quality but with the risk of disruptions in supply if there are p
7、roblems in the delivery system.,1.1.1 Example: a decision problem (cont.),Uncertainty in the decision problem There is uncertainty as to which decision to take because there is uncertainty over future sale. To help simplify the situation, the company is planning for one three possible sales levels i
8、n the future: Low Medium high,1.1.1 Example: a decision problem (cont.),What is under control and what is outside of control The company is faced with a range of alternative decisions over which it has control (i.e. it can choose among them) And it also faces an uncertain future in terms of sales. T
9、his future position is generally referred to as the possible states of nature: future sale levels, are outside the direct control of the company but they do include all the possibilities and only one of them can actually occur.,1.1.1 Example: a decision problem (cont.),Statement of the decision So,
10、the basic decision to be made is: which of the three supply options shall we choose, given the uncertainty we face as to the state of nature that will actually occur?,1.1.2 Modeling the decision with decision tree,It is also possible - and frequently useful - to represent the type of problem we have
11、 been examining in graphical form by constructing what is known as a decision tree. The tree diagram shows the logical progression that occurs over time in terms of decisions and outcomes and is particularly useful in sequential decision problems - where a series of decisions need to be made with ea
12、ch, in part, depending on earlier decisions and outcomes.,1.1.2 Modeling the decision with decision tree (cont.),The decision tree starts from the left-hand side and gradually moves across to the right. A box is used to indicate that at this point we must take a decision (the box is technically know
13、n as a decision node) The three alternatives branch out from this node: to manufacture (M) to buy domestically (BD) to buy abroad (BA) Each of these branches leads to a outcome node (indicated by a circle), which presents the possible states of nature: Low (L) Medium (M) High (H),1.1.2 Modeling the
14、decision with decision tree (cont.),Information for Decision making: In order to make decision we clearly need additional information to help us assess the alternatives. The key pieces of information would relate to the financial consequences of each combination of decision (called pay-off) state of
15、 nature (call probability),Decision tree with pay-off,With the pay-off information, which of the three alternative decisions would you recommend? The answer has to be: it depends. How reliable you think the information is? How risky the various options are? How critical the decision is to the compan
16、ys future?The key factor will depend on your own attitude to these future sates of nature.,Complete decision tree,Let us assume that the company has been able to quantify the likelihood of each of the states of nature occurring by attaching a probability to each. Such probabilities may have been derived from market research, from sales forecasting, or may simple be guesstimate based on some hard evidence and the experience of the decision maker. The probability of low sale is assessed at 0.2, medium at 0.5 and high at 0.3. Note that, they must sum to 1 to include all possible outcomes.,
