1. The concept of meaning
1.1. Basic Concepts
Also known as probabilistic analysis and decision tree analysis method, it refers to the relevant factors will form the decision-making program, a tree graphically demonstrated, and according to a system analysis to analyze programs and selection decisions. It is one of the most common risk decision making process, in particular type courageous in analyzing complex problem. She gains and losses based on the value, Expected Profit and Loss comparison of different schemes (referred to as the expected value), the decision to choose the program, its most important feature is the ability to vividly show the entire decision-making process on issues on time and at different stages, clear and logical thinking , structured, very intuitive.
2. The main contents
2.1. Structure
A decision tree is made up of different pattern tree nodes and program branches. Decision tree image as shown in FIG.
In FIG DESCRIPTION OF REFERENCE NUMERALS 1 below:
□ represents a decision point. Once a decision is needed, there is a decision point. Branch from decision point is referred to as lead-out program branch, the program branches to branch count represents the number of possible options.
○ represents the state of the node program (also called natural state point). Drawn from the branch node is called a branch state, the number of branches represents the natural state of the state branches may occur.
△ represents the result point (also known as peripheral). Listed value gains or losses in the value of the results of different states in the next point for policy-making of.
2.2. Species
According to the decision tree problem can be divided into:
Single-stage decision tree
Single-stage decision tree is just one decision (decision point) you can select the optimal scheme of the decision.
Multi-level decision trees
Need twice or more than twice the decision to elect called multi-level decision-optimal solution. Its decision-making principles and the same single-level decision-making, but to grade computing earnings expectations.
3. Tools Application
3.1. Draw step
Rendering decision tree follows:
First determined decision point, decision point generally as "I" represents, then decision point extraction number of straight, representatives of the various alternatives.
The program is called straight sticks, behind a program branch connection "○" called chance points, from the opportunity to stipple
The probability of each straight line is called branches, representing different states in the future, after the value representative of the probability of branch-offs different schemes in different states may be obtained. For ease of calculation, the decision tree "mouth" (decision points), and "○" (point opportunity) are numbered, are sequentially numbered from left to right, top to bottom.
After the draw decision trees, decision trees in accordance with the program draws the opposite, namely the gradual retreat from right to left, make decisions based on the expected value of the stratification.
3.2. Painted tree basic rules
1. A decision on the issue must be chosen - the end of the evaluation time point. That is, all strategies should be evaluated the same point in time. The value of all receipts and expenditures should be on the same point of time, otherwise the analysis ignores the time value of money.
2. And ending sequences of decision nodes may be expanded into various branches in chronological order starting from a decision node, each branch should not have a junction point (except starting point) In other words, a node can have only instrument a slip to enter.
3. From a decision point or drilling end node imitation emitted branch are mutually exclusive, and must include all possible.
3.3. Decision step
(1) picture from left to right to make the decision tree, the decision of a problem in the future development possibilities and the results are reflected in a tree graphic. Painting process decision tree, which is the process to develop a variety of programs. In the mapping process, the decision to have the entire sequence, from left to right, top to bottom, each node on the standard number.
(2) the respective values, standard state probabilities in the trees and, with particular attention to the accuracy of state probability.
(3) calculating gains or losses of a desired value of the programs. Beginning from the tip of the tree, to right to left direction of each point of the expected value, the calculation result above the marked nodes.
Expectation status point = Σ (loss probability value × value) × operation duration
(4) make decisions according to criteria desired value, the desired value scale loss preferred embodiment of the above decision point. Computing programs operating period of validity of the overall net effect in that final expectations. The formula is:
The net effect of the program = expected value of the program status point - the investment program
(5) to unsuccessful program, the program branches in the painting "//" symbol indicates a deleted branch.
If it is a multi-stage or multi-stage decision-making, the need to repeat the second, third and fourth steps work. as shown in picture 2:
3.4. The generation process
Typically, the method comprising the steps of decision trees, but in practical applications, which can skip a step or steps.
(1) made the decision problem, clear decision-making goal
(2) establish a decision tree model - selective growth, decision-tree index consists of two basic steps:
① put forward all possible branches rule that the possible decision of the index and its sub-categories (classified information) or classification threshold C (level or measurement data);
② select the best candidate by the branching rules of the above, the selection criterion is the maximum degree of similarity that the two child nodes generated between individuals, even if the two child nodes "purity" is maximized. Way to achieve this goal are: reducing the amount of entropy (ie, entropy) of, Gini index, X2 test, analysis of variance, variance to reduce the amount of calculation.
Select the best tree pruning and (3) of the tree
Try to achieve an extension of the "biggest tree" is often over-fitting, fitting the model may not only focus on the main features of the training branch of variables, which also fit the error, the "noise" and therefore needs to be trim the over-fitting can be corrected in order to obtain the best fit and relatively concise decision tree. After pressing tree pruning occurs before the growth arrest or into the front and rear pruning algorithm pruning algorithm. After pruning generally from the end of the tree, child nodes of each cut one by one, to give a series of sub-tree, and then choose the best in quality, there are several calculation methods, which are commonly used as a "cost-complexity" method.
(4) determine each endpoint and calculate the comprehensive index
Direction from the treetops to the roots, back to the use of multiplication, that expected utility for all outcomes in each decision node to its prior probability of the product of the sum to obtain the expected utility value of the policy-making schemes, and integrated with, according to the index value for each Sort program, carried out the merits of a choice.
(5) Evaluation of the tree
4. advantages and disadvantages
4.1. Advantages
Advantages make decisions with decision trees are:
(1) which constitutes a simple decision-making process, decision-makers can order step by step.
(2) there is an intuitive graphical decision tree to facilitate decision-makers to analyze scientific and careful thinking.
(3) After the decision tree to draw graphics, easy to brainstorm and common analysis, it is conducive to collective decision-making.
(4) decision tree method is more complex decision-making problems, particularly convenient for multi-stage decision problem was particularly even in the decision-making process, stepwise thinking by drawing a decision tree can go step by step, think twice.
4.2. Disadvantages
1) In the course of the analysis of some of the parameters are not included in the tree, it is not comprehensive;
2) If the rating too much or too many branches appear, it will not be easy to draw.
5. Examples Analysis
5.1 Case 1: A Hotel "single-stage decision tree" analysis
A resort hotel proposed a proposed A, B two programs, A to build upscale hotels, to invest 250 million yuan, B to build mid-range hotel, invested 130 million yuan, after the completion of the hotel requires 15 years to recover the investment. According to projections. The higher the probability of hotel occupancy rate in the region is 0.7, the lower the probability is 0.3.
If the construction of upscale restaurants, when the high occupancy rate, profitable every year 30 million yuan, while the occupancy rate is not high, the loss of 3 million yuan;
If the construction of mid-range hotels, the occupancy rate is high, it can profit 12 million yuan each year, when the occupancy rate is not high, the profit of 300 million.
It was also predicted that in 15 years, the situation will change, 15 years ago must be divided into six and nine years after the two were taken into account. If the first six years, the rapid development of tourism in the region, it can develop better after nine years, the probability of hotel occupancy rate may rise to 0.9, such as slow first six years of development, the corresponding case after nine years the poor, the probability of hotel occupancy rate was 0.9.
Make a decision which program should be used.
Solution: According to the known conditions, are listed in Table 1 as a decision table (first 6 years), in Table 2 (9 years) shown in FIG.
Press question is intended to draw the decision tree shown in FIG. 2.
After calculating the first nine years of earnings expectations:
Point ④: [3000 × 0.9 + (- 300) × 0.1] × 9 = 24030
Point ⑤: [3000 × 0.1 + (- 300) × 0.9] × 9 = 270
Point ⑥: [1200 × 0.9 + 300 × 0.1] × 9 = 9900
Point ⑦: [1200 × 0.1 + 300 × 0.9] × 9 = 3510
Then calculate the expected return all two programs:
Point ②: [3000 × 0.7 + (- 300) × 0.3] × 6 + 24030 × 0.7 + 270 × .3 = 28962
Point ③: (1200 × 0.7 + 300 × 0.3) × 6 + 9990 × 0.7 + 3510 × 0.3 = 13626
收益期望值由两个部分构成，前一部分是方案前6年的收益期望值，后一部分是加上后9年的收益期望值。但是，所有的两段的收益期望值不是简单的相加，获得后 9 年收益期望值的可能性是建立在前 6 年的基础上的，即点④的 24030 万元必须乘以获得此值的概率 0.7，点⑤的 270 万元乘以获得此值的概率 0.3，点 ⑥和点⑦也必须乘上各状态获得的概率。各方案实际收益期望值：
高档饭店 28962-25000(投资)=3962(万元)
中档饭店 13626-13000(投资)=626(万元)
结论：根据期望值准则进行决策，应采用建高档饭店的方案，净收益期望值为 3962 万元。将建中档饭店的方案删除。
5.2.案例 2：某饭店“多级决策树”分析
某饭店决定投资建饭店消耗品生产厂，提出三个方案：
一是建大厂，投资350万元；二是建小厂，投资170万元；三是建小厂，如果经营得好再扩建，扩建再投资150万元，管理人员对未来10年中前 4 年、后6年的损益值和概率进行了预测，其数据如决策树图3所示。
解：计算各点的收益期望值：
点⑧：(80×0.8+10×0.2)×6=396
点⑨：(40×0.8+5×0.2)×6=198
点⑧和⑨期望值相比，前者较大，所以应选择扩建，对不扩建进行删枝。把点⑧期望值减投资后所得246万元移到点⑥上来，这是第一次决策。
点④：(80×0.8+10×0.2)×6=396
点⑤：(80×0.2+10×0.2)×6=144
点⑥：396-150=246
点⑦：(40×0.2+5×0.8)×6=72
点②：(80×0.6+10×0.4)×4+396×0.6+144×0.4=503.2
点③：(40×0.6+5×0.4)×4+246×0.6+72×0.4=280.4
各方案实际收益期望值：
建大厂：503.2-350=153.2(万元)
建小厂：280.4-170=110.4(万元)
结论：应采用直接建大厂的方案，净收益期望值为 153.2 万元。
References:
Author: scholar Wan Yau
link: https: //www.jianshu.com/p/e9ba945e7906