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项目管理实战利器之八——决策树分析和EMV

更新时间:2023-05-14 11:31:09 阅读：评论：0

作者: 楼政

一、决策者的工具包

“决策就是从多种方案中选择一个行动方针的认知过程。每一个决策过程都会产生一个最终选择。”这是在维基百科所阐述的。但它没有说的是，有些决策必须为未来发生的结果而做出。有数种工具可以用来帮助做出复杂的决策，即决策树分析和预期货币价值。

二、预期货币价值（EMV，Expected Monetary Value）

EMV是一种对概率和各种可能情景影响所做的平衡。以下两种方案，哪一种会提供更大的潜在收益呢？drupal

Scenario 1 方案1

Best ca provides a 20% probability of making $180,000最好的情景(Best ca)：盈利$180,000的概率为20%。	BC=20%X $180,000= $36,000*$180,000=$36,000
Worst ca provides a 15% probability of loosing [-$20,000]最坏的情景(Worst ca)：损失- $20,000的概率为15％。	WC= 15%* X(-$20,000) =(-$3,000)（- $ 20,000）=-$3,000
Most likely ca provides a 65% probability of making $ 75,000最可能的情景(Most likely ca)：盈利$75,000元的概率为65％。	X $75,00MLC= 65%*$75,000 = $48,750

Total Expected Monetary Value 100% $81,750Total EMV = BC+WC+MLC = $36,000+（-$3,000）+$48,750=$81,750

Scenario 2 方案2

mbo是什么

Best ca provides a 15% probability of making $200,000最好的情景(Best ca)：盈利$200,000的概率为15%。	X $200,000BC=15%X $180,000= $36,000*$200,000=$30,000
Worst ca provides a 25% probability of making $15,000最坏的情景(Worst ca)：盈利$15,000的概率为25％。	WC= 25%*$X $ 15,000 = $ 3,75015,000 = $ 3,750
Most likely ca provides a 60% probability of making $45,000最可能的情景(Most likely ca)：盈利$45,000元的概率为60％。	X $45,000 = $27,000MLC= 60%*$ 45,000 = $ 27,000

Total EMV = BC+WC+MLC = $30,000+$3,750+$27,000=$60,750

Which scenario do you choo?你选择哪种方案？当然选Number one, becau it has the highest EMV, or $81,750方案一，因为它具有更高的EMV为$81,750。

位置英文三、决策树分析（Decision Tree Analysis）

In decision tree analysis, a problem is depicted as a diagram which displays all possible acts, events, and payoffs (outcomes) needed to make choices at different points over a period of time.在决策树分析中，一个问题被描述为一个图表，这个图表显示了所有可能行动、事件和回报（成果），在一段时期内不同的时间点对上述内容必须作出的选择。

Example of Decision Tree Analysis: A Manufacturing Proposal制造业的一个实例

Your corporation has been prented with a new product development proposal.你的公司已经提交了新产品开发的建议。 The cost of the development project is $500,000.该项目的开发成本是50万元， The probability of successful development is projected to be 70%.开发成功的概率预计为70％。 If the development is unsuccessful, the project will be terminated.如果开发不成功，该项目将被终止。 If it is successful, the manufacturer must then decide whether to begin manufacturing the product on a new production line or a modified production line.如果成功，制造商必须决定是在一个新的生产线还是在经改造的生产线上制造该产品。 If the demand for the new product is high, the incremental revenue for a new production line is $1,200,000, and the incremental revenue for the modified production line is $850,000.如果产品需求高的话，新生产线增加的收入为120万元，而经改造生产线增加的收入为85万元。 If the demand is low, the incremental revenue for the new production line is $700,000, and the incremental revenue for the modified production line is $150,000.如果产品需求低的话，新生产线增加的收入为70万美元，而经改造生产线增加的收入为15万元。All of the incremental revenue values are gross figures, ie, before subtracting the $500,000 development cost, $300,000 for the new production line and $100,000 for the modified production line.所有这些收入增量，未减去50万元开发成本，新生产线30万美元，改造生产线10万美元。The probability of high demand is estimated as 40%, and of low demand as 60%.高需求概率估计为40％，低需求概率估计为60％。
The development of a decision tree is a multi step process.决策树的运用包括以下步骤：

The first step is to structure the problem using a method called decomposition, similar to the method ud in the development of a work breakdown structure.期盼英文第一步是运用分解的技术（类似于工作分解结构中运用的分解技术）将问题结构化。 This step enables the decision-maker to break a complex problem down into a ries of simpler, more individually manageable problems, graphically displayed in a type of flow diagram called a decision tree.这一步使决策者将一个复杂的问题分解成一系列更简单、更为单独管理的问题，并用流程图的形式体现出来。The are the symbols commonly ud:一下是常用的符号：

The cond step requires the payoff values to be developed for each end-position on the decision tree.第二步是在决策树的每一个末端位置得到收益价值。 The values will be in terms of the net gain or loss for each unique branch of the diagram.这些值将在图型的每一个单独的分支上体现为净收益或净损失。 The net gain/loss will be revenue less expenditure.净增益/损失将用收入减去支出。 If the decision to not develop is made, the payoff is $0.如果决定不开发的情况下，收益为0元。 If the product development is unsuccessful, the payoff is - $500,000.如果产品的开发是不成功的，其回报是- 50万美元。 If the development is successful, the decision is to build a new production line (NPL) or modify an existing production line (MPL).如果开发成功，将做建立一个新的生产线（NPL）或改造现有的生产线（MPL）的决策。

建新的生产线，The payoff for the NPL high demand is ($ 1,200,000 - $500,000 development cost -$300,000 build cost) or $400,000.需求高时，收益为（120万美元- 50万美元的开发成本- 30万美元建造成本）或40万美元。 For a low demand, the payoff is ($700,000 - $500,000 development cost -$300,000 build cost) or -$100,000.需求低时，其收益是（70万美元美发- 50万美元的开发成本- 30万美元建造成本）或- 10万美元。

改造现有的生产线，The payoff for the MPL high demand is ($850,000 -$500,000 development cost - $100,000 build cost) or $250,000.需求高时，收益为（85万美元- 50万美元的开发成本- 10万美元建设费用）或25万美元。需求低时，其收益For a low demand, the payoff is ($720,000- $500,000 development cost - $100,000 build cost) or $120,000.是（720 000美元- 50万美元的开发成本- 10万美元建造成本）或12万美元。

The third step is to asss the probability of occurrence for each outcome:第三步是评估每种结果的发生概率：
开Development Successful = 70% NPL High Demand = 40% MPL High Demand = 40%发成功= 70％
开Development Unsuccessful = 30% NPL Low Demand = 60% MPL Low Demand = 60%发不成功= 30％

新生产线高需求= 40％

新生产线低需求60％

改造生产线高需求= 40％

改造生产线低需求= 60％

Probability Totals* 100% 100% 100%概率合计为（概率之和必须等于100％）： 100％，100％，100％
*Probabilities must always equal 100%, of cours

The fourth step is referred to as the roll-back and it involves calculating expected monetary values (EMV) for each alternative cour of action payoff.第四步是被称为Roll-back。计算采取行动后，每条分支的预期货币价值（EMV汽车涉水）。 The calculation is (probability X payoff) = EMV This is accomplished by working from the end points (right hand side) of the decision tree and folding it back towards the start (left hand side) choosing at each decision point the cour of action with the highest expected monetary value (EMV).计算公式为（概率×收益）= EMV，依照终点（右侧）往起点（左侧）方向顺序，在决策点处选择最高预期货币价值（EMV）决策作为行动依据。

Decision D2: 决策D2： New Production Line vs. Modified Production Line新建生产线还是改造生产线
计算新建生产线的EMV：high demand + low demand = EMV high demand + low demand = EMV
(4 0% X $400,000) + (60%X -$100,000) (40% X $250,000)+(60% X $120,000)（4 0％×$ 400,000）+（60％× - $ 100,000）= $100,000

计算改造生产线的EMV:

（40％×$ 250,000）+（60％×$120,000flaw）= $172,000
$100,000 $172,000
Decision Point 2 Decision: Modified Production Line with an EMV of $172,000D2决策：决定改造生产线。因为改造生产线的EMV $172,000，大于新建生产线的假腿EMV $100,000。

萌菌物语下载决策D1Decision 1: Develop or Do Not Develop：开发还是不开发

计算开发的EMV：Development Successful + Development Unsuccessful
(70% X $172,000) (30% x (- $500,000)) 70％× $172 000 + 30％×（- $500，platform是什么意思000） = -$29,600
$120,400 + (-不开发的EMV：0Development Successful + Development Unsuccessf

D1Decision: DO NOT DEVELOP the product becau the expected value is a negative number.决策：不开发此产品。因为开发此产品的EMV预期值是负数。

When doing a decision tree analysis, any amount greater than zero signifies a positive decision.在做决策树分析时，任何金额大于零的决策标志着一个积极的决策。 This tool is also very uful when there are multiple cas that need to be compared.决策树是非常有用的工具，尤其在有多个情景需要进行比较时，应该选择其中The one with the highest payoff should be picked.收益最高的一个。

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