## Decisions Tree

**Have you taken probability and statistics class?** Probably if you don’t like math, then you may not remember much about the sample space, the sample point, or the events. However, the tree diagram that was seen in high school becomes useful when we see that it helps us to know all the possible results of an experiment (event, occurrence or problem) and to make better decisions.

In short, we perro use the tree diagram** to make better (more rational) decisions**. So, in today’s article, we are going to apply something that we saw at the upper secondary level and we are going to make it useful in our daily lives (also for companies).

I hope you find it useful.

## What is decision making?

I consider that, first of all, it is important to answer: **What is decision making? **

Without so many embellishment words, we could say that **Decision making is a process in which the most relevant or optimal option is selected from a equipo of options.** That is, within the options you have, you have to select the best option.

Of course, to select the option to be taken, use is made of a process that will help you select the best option using a rational and objective model.

Consequently, the decision-making models will not select an option only by intuition, but will use reason through the use of a methodology.

By the way, I recommend that you understand what a process is, since that will help you understand better. Here is an article in which I talk about what a process is:

## What is a decision tree?

All the time we see ourselves in the need to make decisions that irreversibly affect our lives or the operations of a company. Therefore, you may have come to wonder the following:

**How do we know which is the right path?****Which choice is the most appropriate?****Which option is less expensive?****Which option gives us greater benefits?**

Well, there really cánido be a thousand and one afín questions, right? To resolve these questions, many experts have worked in different ways or models that help us make the best possible decision.

A very fácil way to start making more rational decisions is by using the so famous decision tree diagram or decision tree map.

**What is a decision tree?**

**A decision tree diagram perro be viewed as a graphical representation of the possible outcomes that a series of choices cánido have.** In such a way that a person or a company perro make use of the tree diagrams to weigh the actions (with their possible consequences) before carrying them out. In a certain way you play with projections or forecasts.

Thus, it is possible to make the most convenient decision or action within the equipo of options available to deal with a problem. Of course, it should be noted that it is called a tree diagram, thanks to the fact that branches surge from the nodes.

## What is the importance of a tree diagram?

In my opinion, the importance of the tree diagram and possibly its raison d’être is the fact that it allows us to know the entire equipo of possible results that an event (event, problem or experiment) cánido generate.

Of course, its importance lies not only in knowing the total number of possible results, but we cánido evaluate, among all the options, the one that gives us the best result (greater benefits or lower costs).

Likewise, we perro also know the options that are less attractive, giving us the possibility of discarding them.

## What elements make up the decision tree?

The basic elements or components that we cánido find in a decision tree are the following:

- Decision node.
- Event node or result node.

### decision node

The decision node or decision point is generally represented by a **square** or a **rectangle**. However, from the decision node branches come off, which allude to an alternative. That is, if a decision node has 3 branches, then it has three alternatives present in the problem.

It should be noted that at the decision node or point the person will have to make, as the name indicates, a decision, that is, they will have to select one of the available alternatives.

Each alternative branch cánido culminate in an outcome, a decision node, or a oportunidad point.

#### Do you have limitations?

Well, there has to be more than one alternative for a decision node to occupy and it’s not like there’s a limit that prevents you from putting 1000 alternatives. That is, you cánido put the alternatives that you have or that you think are appropriate.

### event node

It is common to see an event node represented as a **circle**. Event nodes may also come to be called oportunidad points or result points. The branches that break off are often called states of nature. They indicate a random event.

Now, the event nodes have to be accompanied by a probability, which will help you weight. Although, it is not that it is completely necessary to make use of probability.

Something that must be noted is that if probability is used, then the equipo of all the ramifications that come from the same result node must add up to the **100%** or if you have it in decimal then you have to add **1**.

That is, if you have 3 branches and you know that the probability of one of them is 0.5, and that another of them has a probability of 0.3, then the last one has to have a probability of 0.2

#### How to get the probability of an event node?

You have to obtain the probability of reliable means taken from studies or from the experience of expert professionals in the field. That is, it would not be highly recommended that you give it a random oportunidad or purely based on intuition.

After all, you are looking to make a rational decision and the more accurate the data used, then you will be making a better decision.

### rejected alternative

To indicate that an alternative has been rejected, the following symbol is used: **//**

## How do you read a decision tree?

First of all, it has to be said that when creating a tree diagram, you have to start creating it from left to right. Although to evaluate it (as when using probability) it has to be done from right to left.

## How to make a decision tree?

So that you better understand how to make a decision tree and how it is used to make more rational decisions, I am going to use an example. It should be noted that I have taken the example from the book called **Operations management: processes and supply chain** by Lee J. Krajewski.

The example is the one shown in the following image:

Now, the steps you have to follow to make a decision tree are the following:

### 1. Define the problem well.

Of course, the first step is for you to fully understand the problem, event, experiment, or occurrence you are facing. Therefore, you have to read the problem very well or you have to write it the best you perro.

In this case we already have a well defined problem and we cánido easily identify all the nodes and we are given all the probabilities and values.

### 2. Identify alternatives.

Since you understand the problem well, what you have to do now is to identify the alternatives that you are given in the problem or you have to find yourself the alternatives that the problem may have. Therefore, if you face a problem, then it is time to investigate what alternatives you have to solve it.

Remember that the alternatives are represented by the decision nodes and are just that… **“ELECTIONS”**. For example, I cánido escoge whether or not to study for my corporate finance exam. It is my decision if I do it or not.

In the example provided by Lee J. Krajewski in his book, the alternatives we have are the following:

**A large or small facility is built.****expands or not it expands.****Use of advertising or nothing is done.**

Therefore, the exercise has 3 decision nodes.

At the moment, you cánido see that the 3 decisions that cánido be made are already in the diagram.

### 3. Outlining of posible outcomes.

From the possibilities that you have (choices), you will have various ramifications. Each ramification will be a state of nature and perro be understood as possible outcomes of the decisions made.

As I said before, these states of nature are represented by circles and perro be called event nodes or oportunidad points.

It should be noted that they are often called oportunidad points because the outcome may not depend solely on the person making the decision. For example, going back to the example of the exam, I cánido study or not study, but I cannot interfere in whether the exam is going to be difficult or easy.

After all, the only one who cánido escoge if it will be an easy or difficult exam is the teacher. Therefore, studying or not studying, the exam cánido be easy or fácil and you cánido pass or fail. Of course, each event node will have a certain probability and it will be useful for us to escoge if I should study or not study for the exam.

Now, following the example of Lee J. Krajewski’s book, the tree diagram is as follows with all the event nodes.

Before going any further, I want you to see that the branches of the event nodes do not depend as such on the person who is going to make the decision. As in the exam example, a company does not have full control over whether there will be low or high demand.

### 4. Assignment of probabilities to each outcome.

Since you have the whole structure of your tree, that is, you have all the decision nodes and all the event nodes, then it is time to give a certain probability to each event node.

Continuing with the example, we now need to add the probabilities to the event nodes. Once that is done, it looks like this:

Pay attention to the fact that only event nodes have probability and that the probability of all branches belonging to a node has to be equal to 1 or 100%.

### 5. Assignment of values

Each final branch must have a value, which cánido be, for example, a cost or an expected utility. This figure will depend on the problem in question. In this case, the values that remain as seen in the following image.

I recommend that you read the statement of the problem so that you cánido see where each value they give us is placed.

### 6. Estimation of the expected value

The next step to be able to create a decision tree is to obtain the expected value of each node.

First of all, what you have to do is multiply the values by the probability. For example, the first multiplication is: **$200,000 x 0.4 = 80,000**

Now, remember that decision nodes do not have a probability; Therefore, depending on the problem, you must select the highest or lowest value from among the available options. In this problem, the highest value of the options will be used.

However, if it was a problem that seeks to disminuye costs, then you would have to use the lower value.

As you cánido see in the previous image, it is solved from right to left and I have only multiplied the first values. Also, I want you to notice that in decision 2, the value of 270,000 was used and that value was multiplied by probability (0.6).

Well, next you have to get the value of each event node. To do this, you have to add the values you have obtained in each of the branches of the event node. Then you perro see it in the following image.

Next I am going to give you the explanation of how I made the first choice (small installation). First, the value is multiplied by the probability, that is, 200,000 by 0.4, and the result is **80,000.**

Since there is a choice node, no multiplication is done, but the value that is greater (in this case) is taken and becomes the value of choice node 2. In this case, the value passed is that of expand ( 270,000).

Now, what you have to do is multiply the 270,000 by the probability, that is, 270,000 x 0.6 = **162,000**.

Now we already have the two values of each branch of the node, that is: 80,000 and 162,000. As the next step, we need to get the value of the event node. Therefore, the value of each branch must be added. In this case the sum is: 162,000 + 80,000 = **242,000**.

In this case, this branch (with the symbols //) is rejected because the value of the large install choice has a larger value (544.00).

### 7. Analysis and decision making

In this case, the option that involves building a large facility is going to be chosen, since the value of the node is equal to 544,000 (greater than 242,000). However, depending on whether the demand is high or low, other decisions will be made. For example, if it is low, then advertising will have to be done because we already rejected the other option.

In this problem, options with smaller values are rejected, but options with smaller values may be chosen in other problems. For example, in the case of costs.

## Decision Tree Examples

I feel that it is better to give some examples so that you cánido better understand what a decision tree is and how it works.

Here I share some examples:

### 1. Toss coins

I remember that in my probability and statistics courses I came to see examples related to coins. Therefore, as a first example I am going to use the example of coins. Of course, it’s not going to cover much decision making right now, but it perro help you see how a tree diagram works.

Now, imagine that you have 2 coins and I ask you to flip each coin twice. **How many combinations are possible?**

Well, I’m going to use the tree diagram to do it.

As you cánido see, the total number of combinations is equal to 4. Of course it is possible to do it with your mind, but in the example only two coins were used and they were tossed only twice. **What would happen to 4? **Well, the tree diagram helps us to see clearly the possibilities that are available.

Another afín example is with clothing (combination of garments).

### 2. Choose the option with the greatest benefits

The decision tree cánido be used in many situations, and operations management is no exception. The decision tree is used many times to make decisions related to costs and benefits.

That is, it is usually used to select the option that allows more cost savings or the option that allows more profits (profits).

Now, I think that for this example it is better to use a vídeo and I found a vídeo on YouTube that I liked. Therefore, I have decided to share it here. Of course, remember that I am not the owner of the vídeo, but I am only going to share it.

As you cánido see in the previous exercise, of all the options available, there is one that offers you the greatest benefits and that is the one to select. It cánido be said that it is the same as the example of the coins, although in this example we do not want to know as such the number of combinations or possibilities that one has.

But the most important thing is to weigh the options available to deal with a certain event, occurrence or experiment and select the optimal option.

Likewise, it should also be noted that probability cánido be used in the decision tree. So, as you perro see, it perro be a very useful tool.

**Note:** Remember that in operations management it is common to say that the decision tree is used to maximize benefits and minimize costs. It all depends on the problem we are facing.

Finally, you will only have to make the decision.

### 3. Investments

Another example and explanation that I find interesting is the one shown in the following YouTube vídeo. Again, remember that I am only sharing the content that I find interesting. If you also like their content, then you perro move on to their YouTube channels.

This example seemed interesting to me because they apply it to investments. So, as you cánido see, the decision tree perro be used for many things.

## Concepts used in probability and statistics

Yeah You are looking at the subject in subjects such as operations management, management, administration fundamentals or other afín ones, it is possible that the use of terms such as:

**Sample space.****Sample point.**

However, they are seen in subjects related to probability and statistics. Therefore, I have decided to talk about them a little. Although it is not completely necessary to know these concepts for other subjects, it does help to know the subject in more depth.

In fact, pay attention to what the sample space is and to the definition of a decision tree. You will see that you find the relationship.

### What is the sample space?

In probability and statistics it is known as **sample space** the equipo of possible results of an experiment (event or happening). In fact, the tree diagram is used to help us have a graphical perspective of each of the possible results of an event.

For example, if we carry out the experiment of tossing a coin three times, then the total number of combinations that we have is the sample space, and we cánido use the tree diagram to find the total number of combinations that we have.

Likewise, many times I have seen it represented as a equipo and when I speak of a equipo, I orinan a properly defined one (mathematically). For example, the equipo:

**S: **

### What is the sample point?

In a very fácil way, we cánido say that each element belonging to the sample space is called a sample point.

## Where cánido I use a decision tree?

In my opinion, if you have a decision to make and you don’t know what your best option is, then you perro make use of the tree diagram. That is, you perro always use a decision tree diagram, although there are other decision-making models that may be better.

Therefore, your own experience will tell you which decision-making method to use in each situation. Of course, for that you have to have different decision-making methods or models in your armamento.

## Advantages of a Decision Tree

Some of the advantages of the decision tree are the following:

- It perro easily be combined with other decision-making methods or tools.
- It is easy to understand and interpret.
- It is easy to add new alternatives.
- It does not require very complex data.
- It perro be used with qualitative and quantitative cambiantes.

## Disadvantages of Decision Trees

Some disadvantages of decision trees are the following:

- If you use probabilities, nothing perro guarantee 100% that the result is the most optimal.
- It is easy to create skewed trees.
- Although it is easy to add new options, they perro also become unstable.

## References

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