Decision tree analysis

Abstract

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In every persons personal and professional life, they are faced with decisions. Decision-making is a part of every single project, and project managers have numerous tools available to help them with those decisions. A method that is often used is decision tree analysis, which revolves around mapping out the outcomes of possible decisions and how they could determine other outcomes to help project managers and others to make the best possible decision. The purpose of this article is to show the main concepts of decision tree analysis and teach people how to use it. Making the right decision, or the best decision given the information at hand is a vital part in a project’s managers role. This article will shed light on the steps involved in using the decision tree analysis and how it can be used to guide project managers as well as others into making the best decision possible. The different concepts are discussed, and a step-by-step guidance is introduced. Furthermore, this article will discuss the limitations and shortcomings of decision tree analysis that need to be kept an eye on when applying the method.

Big Idea

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Decision tree analysis is a method that uses graphical representation to show the decision-making process given certain conditions. It’s most often used to determine the optimal decision based on data and to estimate the potential consequences of a decision when faced different circumstances. The history of decision tree analysis is complex, with several mathematicians and others developing it over time. However, in the industrial environment, decision making usually involves analysing the data to reach a conclusion. Decision tree analysis has, over the years, become increasingly more used in real life, and numerous case studies show its usefulness in improving efficiency in organizations and customer satisfaction. A common use of decision tree analysis is to help with project-selection, which is a necessary part of decision-making process. A number of different instances call for the use of decision tree analysis, and the procedure has bee shown to provide important benefits in a lot of different instances.

Decision tree analysis can be used in project, program, and portfolio management to help with the decision-making process in relation to project selection, prioritization as well as risk management. Decision tree analysis can assist managers and other people responsible for making decisions in determining the best course of action and effectively allocate resources by examining many scenarios and potential outcomes.

Overview of decision tree analysis

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Decision trees are structures, similar to flowcharts, and are often used in decision analysis for both visual and analytical support tool. When competing options, based on their projected values, decision trees are particularly helpful. In decision tree analysis there are a few concepts that are used in connection to it. These concepts are:

• Nodes: Decision trees consist of three types of nodes. The first type is the root node, which is also known as the decision node. This node represents a choice that divides all records into two or more mutually exclusive subsets. The second type is internal nodes, also referred to as chance nodes. These nodes represent one of the available choices at that point in the tree structure. The top edge of the node connects it to the parent node, while the bottom edge connects it to its child nodes or leaf nodes. The third type is leaf nodes, which are also known as end nodes. These nodes represent the final result of a combination of decisions or events.

• Branches: The branches in a decision tree model represent chance outcomes or occurrences that arise from root nodes and internal nodes. Decision trees are constructed by organizing branches into a hierarchy. Each path from the root node through internal nodes to a leaf node represents a classification decision rule, which can also be expressed as an "if-then" statement. For instance, "if condition 1 and condition 2 and condition...and condition k occur, then outcome j occurs."

• Splitting: This involves using only input variables related to the target variable to divide parent nodes into more child nodes of the same kind. This can be done using both discrete and continuous input variables, which are collapsed into two or more categories. To begin this process, the most important input variables must first be identified. Then, the records at the root node and subsequent internal nodes are split into two or more categories or "bins" based on the status of these variables. This splitting process continues until predetermined homogeneity or stopping criteria are met. It's worth noting that not all potential input variables may be used in building the decision tree model, and sometimes a specific input variable may be used multiple times at different levels of the decision tree.

• Stopping: Complexity and robustness are two key factors to consider when building a statistical model, especially when developing a decision tree. The complexity of the model can negatively impact its reliability when predicting future records. For instance, a highly complex decision tree model that produces leaf nodes with 100% pure records may be overfitted to the existing observations, making it unreliable in predicting future cases. To avoid this, stopping rules should be applied when building the decision tree to prevent it from becoming too complex. Common parameters used in stopping rules include the minimum number of records in a leaf, the minimum number of records in a node before splitting, and the depth of any leaf from the root node. It's important to select stopping parameters based on the analysis goal and the dataset's characteristics.

• Pruning: Stopping rules may not always be effective in preventing decision trees from becoming overly complex. Instead, one alternative is to grow a larger tree and then prune it to its optimal size by removing nodes that add less value. One way to select the best sub-tree from several candidates is to consider the proportion of records with prediction errors. Another option is a validation dataset that can be used by dividing the sample into two sets and testing the model developed on the training dataset on the validation dataset. For smaller samples, cross-validation can be used by dividing the sample into 10 groups, developing the model from nine groups, and testing it on the 10th group, repeating the process for all ten combinations, and averaging the error rates. There are different types of pruning, which have different attributes, the best choice differs from tree to tree.

Application

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How to create a decision tree

Creating a decision tree is fairly simple, it can be good to split the process into 5 main steps:

1. What decision has to be made

Begin the decision tree analysis with one idea, or decision that has to be made. That will be the decision node and from that add branches for the different options that have to be chosen. For example, if a project manager is considering three different options for a new software development project. The three different options are:

• Develop a custom software solution in-house
• Outsource the software development to a third-party vendor
• Buy and customize an off-the-shelf software solution

2. Add chance and decision nodes

After adding your main idea to the tree, continue adding chance or decision nodes after each decision to expand your tree further. A chance node may need an alternative branch after it because there could be more than one potential outcome for choosing that decision. After the initial idea, the next step is to add chance and decision nodes after every decision to expand the tree. Chance nodes might need more branches after them since there can be more than one outcome. In the example mentioned, the chance nodes could be: "Success of the project". and have two branches, one for low success and the other for high success. These nodes then can have expected revenue branches for the corresponding decisions.

3. Expand the tree until completion

To create a comprehensive decision tree, continue adding chance and decision nodes until the tree can no longer be expanded. When the tree is fully developed, add end nodes to show that the decision tree creation process is finished. With the completed decision tree, you can start analysing each of the decisions, evaluating their potential outcomes and associated risks.

4. Calculate tree values

In an ideal scenario, decision trees should have quantifiable data associated with them. The most common data used in decision trees is monetary value, where costs and expected returns are taken into consideration to make the final decision. For instance, outsourcing the software development project has different costs and profits than developing it in house. Quantifying these values under each decision can help in the decision-making process.

Moreover, it is also possible to estimate the expected value of each decision, which can be helpful in selecting the best possible outcome. Expected value is calculated based on the likelihood of each possible outcome and its associated cost. This calculation can be performed using the following formula: Expected value (EV) = (First possible outcome x Likelihood of outcome) + (Second possible outcome x Likelihood of outcome) - Cost

In order to calculate the expected value, multiply both possible outcomes by the likelihood that each outcome will occur, and then add those values. Finally, subtract any initial costs from the total value to get the expected value of each outcome. This can help to identify the most cost-effective and beneficial option among the various available choices in a decision-making process.

5. Evaluate outcomes

After calculating the expected values for each decision in the decision tree, the next step is to evaluate the level of risk option has. It is necessary to understand that the decision with the highest expected value may not necessarily be the best option. The level of risk associated with the decision should also be taken into account.

Risk is an inherent aspect in project management, and each decision has its own level of risk. Therefore, it is crucial to evaluate the risk level associated with each decision to determine if it aligns with the project's goals and objectives. If a decision has a high expected value but also comes with high project risk, it may not be the best choice for the project.

Figure 1: Example of a decision tree (source: own figure)

Decision trees in project management

Using decision tree analysis can be a powerful tool that project managers can use to help them make informed decisions in relation to project management. This method can add value to projects, with thorough analysis of all available options and their possible risks.

There are many ways that decision tree analysis can be used in project management, for example project selection, risk management, resource allocation and project execution. Using it for project selection can involve comparing potential value for each of the options with regards to profits, costs and risks. This allows project managers to make informed decisions and select the project with the most potential to add value to their companies and organizations. An example of this is a business can use decision tree analysis to decide which project to invest in by comparing the expected profit for the different projects.

In risk management, decision tree analysis is useful to identify and assess threats at the same time, make actions to mitigate those threats. By conducting analysis of all the various risk scenarios with the use of decision trees, project managers are able to prioritize the biggest and most critical risks and develop strategies to mitigate them and increase the likelihood of a successful project. This method helps to reduce the negative impacts of risks that can affect the outcome of projects and increase the likelihood of meeting the project objectives.

Another category where decision trees can be applied in project management is resource allocation. Using decision trees allows project managers to evaluate various scenarios with different resource allocation while analysing the expected value of each option as well as the risks involved. This helps project managers in allocating resources to the right places to maximize the value of projects and minimizing the risks.

Lastly, it’s possible to use decision tree analysis to compare various options of project execution. There are often different ways of executing projects, some strategies are more aggressive while others are more conservative. Decision tree analysis can be used to compare the costs involved with these strategies and the potential profits to determine which strategy is the best choice to add the most value to the project.

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Application in other sectors

Numerous industries use decision tree analysis to help people make decisions from a variety of options. These applications include social, business, banking, libraries, hospitals and more. Any project or product's success depends on a number of choices made during the production process, including the selection of raw material and component vendors, equipment, workforce, sales, and marketing strategies. Decision tree analysis can offer quantitative terms to help the decision maker in instances when a choice must be made from a variety of options.

For example, decision tree analysis can be useful when there are multiple objectives that have to be considered at the same time, making it difficult for a decision maker to weigh the potential negative consequences on one element vs another. Decision tree analysis, often along with additional tools or methods, can be helpful in certain situations. In addition to direct benefits, decision makers can also acquire indirect ones by selecting the best choice, which can be done with the use of decision tree analysis. A well-informed choice can also assist organizations in attaining their long-term objectives, emphasizing the value of decision-making not just as a situational activity but also as a strategy for long-term success

Limitations

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Decision trees have few disadvantages that can affect their usefulness in certain contexts. One major issue is their tendency to become overly complex, which can make them difficult for experts to interpret and can hinder decision-making processes, especially in high-stakes situations where incorrect decisions can have serious consequences. Another limitation is their limited performance with complex interactions between attributes. While decision trees can effectively represent simple relationships between attributes, they may struggle to capture complex interactions, in those cases, other methods might be more applicable.

Decision trees can also be overly sensitive to noise and irrelevant attributes, which can lead to suboptimal performance, particularly if the decision tree is overfitted to the training data. Another potential drawback is the impact of the decision maker's inexperience on the accuracy of the decision tree. Inexperienced decision makers may not fully understand the decision space or may not be able to accurately interpret the results of the decision tree, which can make the decision-making process more complicated.

Overfitting and underfitting are also potential problems with decision trees, especially when working with small datasets, which can limit the usability and robustness of the models. Strong correlations between the input variables can result in the selection of variables that improve the model statistics but are not related to the outcome, which can lead to inaccurate or misleading results. As such, it is important to be careful and critical in thinking when interpreting decision tree models and to consider the limitations of the approach when using it to make decisions.

Conclusion

In today's environment, decision-making has become a necessary skill for individuals as well as organizations. The ability to make effective and good decisions, especially in high-stress situations, can be the difference between successful individuals and organizations and those who struggle. Decision tree analysis is a useful tool that can be used to make more informed decisions by visually representing the decision-making process.

Decision tree analysis has been around for many years, with numerous mathematicians and other experts developing and refining the technique and making it better. Decision tree analysis is usually used to determine the optimal decision to make based on data and to estimate the potential consequences of a decision under different circumstances. This method has proven useful in a lot of different circumstances, including project, program, and portfolio management.

In decision tree analysis, the tree structure consists of nodes and branches. Nodes are decision points or chance events, while branches represent possible outcomes or paths the decision could take. Splitting involves using input variables related to the target variable to divide parent nodes into more child nodes of the same kind. Stopping rules should be applied when building the decision tree to prevent it from becoming too complex, and pruning can be used to optimize the decision tree.

Decision tree analysis can be useful in a wide range of applications, including project selection, prioritization, and risk management. By examining many scenarios and potential outcomes, decision tree analysis can assist managers and other decision-makers in determining the best course of action and effectively allocating resources.

To create a decision tree, start with one decision or idea and add branches for different options or possible outcomes. Use data to determine the likelihood of each outcome and evaluate the potential consequences of each decision. By visually representing the decision-making process, decision tree analysis can help to identify the most effective decision while also highlighting potential risks and uncertainties.

In conclusion, decision tree analysis is a valuable tool that can help individuals and organizations make more informed decisions. By visually representing the decision-making process and analysing data to estimate the potential outcomes of different decisions, decision tree analysis can assist in project, program, and portfolio management, as well as risk management. Decision tree analysis can help decision-makers identify the best course of action, allocate resources effectively, and mitigate potential risks, making it an invaluable tool in today's complex business environment.

Annotated bibliography

Kapil Mittal, Dinesh Khanduja and Puran Chandra Tewari. An Insight into “Decision Tree Analysis”. 2017.
This article discusses the concept of decision tree analysis as a technique to help with decision-making, both in personal and professional contexts. The authors provide an overview of the history and evolution of decision tree analysis and its application in various industries. They also describe the advantages and disadvantages of using this methodology and provide examples to demonstrate the positive effects decision tree analysis has on productivity in an industrial environment.

Yan-yan Song and Ying Lu. Decision tree methods: applications for classification and prediction. 2015.
This article provides an overview of the decision tree methodology. The authors discuss the algorithm's non-parametric nature and its ability to handle large, complex datasets. They also describe how the methodology can be used to divide datasets into training and validation sets, and introduce frequently used algorithms for developing decision trees. Finally, they describe the SPSS and SAS programs that can be used to visualize the tree structure.

Prasanta Kumar Dey. Project risk management using multiple criteria decision-making technique and decision tree analysis: a case study of Indian oil refinery. 2012.
This study proposes an integrated framework for managing project risks using a combination of various criteria decision-making techniques and decision tree analysis. The author develops a model for risk management, which he then applies through action research on a petroleum oil refinery construction project in India. The author uses cause and effect diagrams to identify risks, the analytic hierarchy process to analyze risks, and a risk map to develop responses. Decision tree analysis is then used to model different options for risk response development and to optimize the selection of a risk mitigating strategy. The proposed framework is designed to be easily adoptable and integrated with other project management knowledge areas.

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