The decision tree is an example. Decision making methods

In most cases, decision-making can be carried out at lightning speed, based on our experience, as they say, by eye. But sometimes this option is not considered adequate. And what to do in this case? Especially for this smart people have developed decision-making methods. They allow gradually and with minimal deviations to work out the algorithm of actions.

general information

And the most interesting moment for us is the decision tree method. What is he like? Where is it used? The decision tree method is a graphical depiction of certain actions and states of the environment, in which the corresponding probabilities and gains for certain combinations are indicated. It is used to assess the risks of projects, when you need to invest funds over a significant period of time. The reason for using it is to have two or more consecutive sets of solutions.And they should flow from the previous and / or sets of states of the environment.

On the formal structure

Decision Tree Action Results

What elements are used to create? It:

  1. Solution node. Used to characterize the moment of choice.
  2. Line representing the alternative.
  3. Event node Used to denote a certain randomness, which is the place to be.
  4. A line describing the environment that is the result of an unforeseen event.
  5. Result node. Used to indicate totals. It is associated with a specific state of the environment and decisions.
  6. Node to denote an intermediate result. It is necessary to indicate a situation when another decision should be taken.


How is the decision tree method used in practice? To formulate different development scenarios, it is necessary to have all the necessary and reliable information, which takes into account the probabilities and the time of occurrence of certain events and results. Initially data is collected. To do this, you can use the following algorithm:

  1. The composition and duration of the phases of the life cycle are determined;
  2. Key events are foreseen that will affect (or may change) further development;
  3. The time of their occurrence is determined;
  4. All possible solutions are formulated that are considered as options for key events;
  5. The probability of their adoption is determined;
  6. Estimated cost of the stages in current prices.

On the obtained data, it is quite possible to build a decision tree. It will contain nodes that are considered key events. In essence, these are decision points. They are joined by branches - that is, certain works that are aimed at achieving a certain result. Building a decision tree allows you to calculate the probability for each selected scenario. In addition, attention is paid to other fundamentally important indicators that are necessary for risk analysis and the adoption of effective management actions. It should be noted that this method is usually used for projects that have a foreseeable number of possible options. Indeed, otherwise the scheme becomes too voluminous, which makes it difficult to calculate the optimal solution and select the necessary data. An understanding of how to make a decision tree should already form. Let's take a look at the examples.

Investment projects

making decisions

The best way to clarify a decision tree is an example from life.Therefore, it’s better to start with it and not with abstract mathematics. Suppose we have a choice of three investment projects. We denote them as IP1, IP2 and IP3. Suppose that for their implementation it is necessary to invest respectively 200, 300 and 500 million rubles. Expected profit is 100, 200 and 300 million rubles. There is a risk of losing money. The probability of such a scenario is 10%, 5% and 20% for each of the options. What is better to choose? Finding a purely mathematical answer is quite difficult. But with the use of a decision tree, this task is much easier. Initially, it is necessary to make a decision tree of the investment project. After it is built, we begin to investigate it using reverse analysis. You must go to the figure from right to left. Getting into the circles, we must put in them the mathematical values ​​of the expectation of payments. In our case, the result will look like this:

  1. 100*0,9 – 200*0,1 = 70;
  2. 200*0,95 – 300*0,05 = 175;
  3. 300*0,8 – 500 *0,2 = 140.

Based on the calculations, it is easy to see that IP2 is most beneficial for us. And now let's dive into mathematics and consider some abstract problems on the decision tree.

Simplest example

In this case, we will have only two options - “no” or “yes.”Or, in the language of Boolean logic, we will have 0 or 1. Understanding such an example of a decision tree can be difficult, so we will use “no” or “yes”. Suppose we are offered to work for 160 rubles per hour. We can say no, and then nothing will change. Or we say “yes”, and then, having worked a little, we can feel how in our pocket it became heavier for 160 rubles. You can slightly complicate the model, and in case of agreement add a continuation. For example - work hard? If “yes”, then the payment is 300 rubles, if “no”, then we remain at the same level of 160.

Elaboration of life behavior strategies

investment project decision tree

It may seem to many that the example of a decision tree is only used for large investments and abstract mathematical research. But it is not. You can, of course, memorize theory. And you can adopt it and win. And now we are going to look at the formula that Jean-Paul Getty suggested, entitled “How to become rich.” She expresses briefly: “Get up early”, “Work hard”, “You will find oil”. Let's look at modeling the sequence of decisions made:

  1. We need to choose between "Get up early" and "Sleep late." This is the simplest choice.
  2. We need to choose between “Work hard” and “After sleeves”. This is also the simplest choice.
  3. At the same time the event "Found oil" can occur with a certain probability. Its value depends on the sequence of our decisions.

If we found oil, we became rich. There are no deposits found - it means that there are only losses, spending on search. And if you sleep up late and work carelessly, then you can not even look for oil. The most preferred option is “Get up early” and “Work hard”.

We are looking for our oil

decision tree example

And now for the calculations. The considered example of a decision tree is better explained using tables. Suppose we work optimally. Then our option:

We get up early and work hard

Event possible

Oil found


Profit (loss) in rubles

10 000 000

- 200 000

Probability of occurrence



Risk (= Profit (loss) * Probability)

1 000 000

- 180 000

Expected Result

1 000 000 – 180 000 = 820 000

As you can see, the most profitable option offers pretty good prospects. Is it possible to use this table in full to see this example? Yes, and it is not as difficult as it may seem at first glance:


Get up early (long day)

Stay up late

Work hard

The probability of finding oil (H) = 10%

Failure = (1-H) = 90%

Expected result: (0.1 * 10 000 000) + 0.9 * (- 200 000) = 820 000

(Н) = 5% Failure = (Н-Н) = 95% Potential winnings: (0.05 * 10 000 000) + 1,95 * (- 200 000) = 310 000

Work with coolness

(N) = 1% Failure = (1-H) = 99% Expected result: (0.01 * 10 000 000) + 0.99 * (- 200 000) = - 98 000

(N) = 0% Failure = (1-H) = 100% Potential gain: (0 * 10 000 000) + 1 * (- 200 000) = - 200 000

This example of a decision tree shows us clearly that the key to success is in hard work. The size of the working day may bring us closer to the goal of becoming rich and increasing the size of the state Although, of course, the data here are fairly generalized, but we hope that the general train of thought is understandable.

Improving example

decision tree options

Some may argue - well, a decision tree is useful. But the options considered are too exaggerated, and using them in a real situation is quite problematic. This opinion has the right to exist, but only for those who did not understand. The decision tree can be quite complex and more flexible. Therefore, we will refine the oil example a little. And this time we need to take into account the payback. Suppose that funds for the search for oil are spent instantly. If we find a mineral, then all investments that were made in exploration, will instantly pay off. Revenues will come in two years.As you can see, we have receipts and payments scattered throughout the time period. And we need to bring all the amounts to the available money. Suppose that the discount rate is 20%, then our formula for a person working hard and getting up early will look like this: (0.1 * 10 000 000) / 1.22 + 0.9 (-200 000) = 514 444. For other variants of activity, the values ​​will be: 157,222, - 128,555, and - 200,000 rubles. Agree, this is more like a rationale for the project! Despite the fact that income levels have fallen, the option to work hard and get up early is still the most effective. Then how to sleep late does not attract. And what decision making is beneficial for us, both in life and in calculations?

Warm up example

decision tree life example

We offer readers to consolidate their knowledge. Suppose we have a doc. He produces P1 products in the amount of 1 thousand units. The head of the DOK considers that the market for goods P2 is expanding. Studies were conducted that allowed to establish the proposed development options: P1mak = 1000; P1min = 5000; P2mak = 8000; P2min = 4000. Here min and poppy is the probability of demand for a certain amount of goods. That is, a thousand P1 is not a problem to implement. But 5000 may not be able to do.The likelihood of demand is: S1mak = 0.7; C1min = 1-C1mak = 0.3; S2mak = 0.6; C2min = 1 - C2mak = 0.4. Per unit of goods P1, we make a profit in the amount of 1 monetary unit. For A2, this figure is 0.9. But there is a problem - the minimum demand for both products exceeds the existing and available capacities of the MLC. What will be the costs (now equal to K) to double them for parallel production in equivalent, if:

  1. costs are K = 0.4 * 103 monetary units;
  2. equivalent amount of P1 = 1000, and P2 = 900;
  3. the maximum and current demand for P1 and P2 is respectively: (K1mak = 2 * 103; K1min = 1.4 * 103) and (K2mak = 1.2 * 103; K2min = 0.8 * 103).

And having such data, it is necessary to determine whether it is advisable to replace the manufactured products and develop capacity.

The solution of the problem

decision tree building

Is it difficult to figure it out on your own? Well, a small hint - you can use the algorithm that was used in the example with oil. For those who could not master it, a solution will be written. Initially, we establish the consequences of our decisions for the production of one type (P1 or P2). Then explore the option with both. To do this, we discard the irrational actions for the development of capacities and highlight the data on possible gains separately in the column.We take into account the probability of demand and estimate the average efficiency at branch points. If we calculate, we will see that with prolonged production of P1 products, it is more beneficial for us in the development of capacities and simultaneous production than the transition to one P2. Although, this is if the minimum expectations. And what about the maximum demand? In this case, we need to draw another branch that will consider this solution. To calculate its effectiveness, we summarize the first and second options and subtract the cost of doubling the capacity. And it turns out that this is the most profitable solution. As a result, we come to the conclusion that it is necessary to develop capacities and ensure the simultaneous release of P1 and P2.

Set goals

This is what a decision tree is. Examples of solving problems of risks allow us to understand this method and adopt it. Of course, there may be certain difficulties at first, but they are successfully solved by practice. In this, the books on mathematics, econometrics, cybernetics and a number of other disciplines can help.

Ability to automate

Decision making methods have a clear structure.Therefore, computer technologies can work with them quite easily. As another example, the process of issuing a loan in a bank. At the same time, for a computer, a decision tree is presented in the form of a logical construct “if ... then ...”. Although, by the way, it is based on this principle for people, but when interacting with technology, it is necessary to concentrate on this. Suppose the first step is the question of age. If a person is less than forty years old, then they ask about his education and wages. More - is there a house. The answer is yes - we issue a loan. Negative - ask about the level of income. Less than 20 thousand rubles a month - we refuse. This is done quickly and efficiently.


decision tree tasks

If there are several behaviors and scenarios, then you should use a decision tree to find the best situation. It will allow putting all available information and calculations on paper and improve the efficiency of decision making.

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