Using the Decision Tree to Evaluate Three Options

Posted: August 25th, 2021

Using the Decision Tree to Evaluate Three Options

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Using the Decision Tree to Evaluate Three Options

Decisions are a part of every-day life. Each day, one has to make decisions, which are expected to produce the desired outcome. Decision theory represents an approach to making choices that applies to a diverse range of fields. In the business environment, decision theory has multiple applications, including product design, location planning, equipment selection, capacity planning, and other uses. Multiple techniques can be applied when making decisions, each that requires, at least three inputs. They include a set of anticipated conditions (states of nature) that are likely to affect the outcome of a decision (such as changes in demand, weather, or the introduction of competitors), a set of alternatives from which to choose, and a specified payoff for each alternative if the anticipated conditions occur (Stevenson, 2018). The ultimate goal is to minimize the risks and optimize the gains in the business environment.

A frequently used technique involves the construction of decision trees. A decision tree is a tree-like schematic representation of all the possible alternatives in a decision and their associated outcomes (Stevenson, 2018). It comprises nodes and branches. Nodes are the points from which branches emerge and are of three types: decision, chance, or terminal nodes (Khanduja, Mittal, & Tewari, 2017). A decision node (usually represented by a square) indicates the point at which one has to choose from a set of options. The branches emanating from such a node represent the available options. The first decision node is often referred to as the root. Chance nodes (usually symbolized by circles) indicate points at which probable events occur. The branches emanating from these points show the states of nature. Terminal nodes (leaves) (usually represented by triangles) indicate the outcome of a combination of decisions and chances. Each path from the root, through the internal nodes to the leaves, indicates a rule of classification, often referred to as the if-then rules (Lu & Song, 2015). They represent conditional statements and expected outcomes.

Over the years, decision trees have proved to be effective and robust support tools in the business environment. As Drabiková and Škrabul’áková (2017) imply, their accuracy and effectiveness in classifying data have exceeded the expectations of many experts. Cox, Monsalve, Søndergaard, and Strang (2017) also note that the simplicity of these tools consistency and structure are critical in the decision-making process. Decision trees are particularly useful when analyzing scenarios with multiple sequential decisions. Their most significant benefit is in their ability to provide simultaneous suggestions and offer intuitive and straightforward explanations to the decision-making process. They are also simple to construct and easy to interpret.

Decision trees are non-parametric; that is, they do not rely on the normality of a data set (Lu & Song, 2015). They force users to consider all the anticipated outcomes of a decision. These tools provide a basis for comprehensively analyzing the possible consequences along multiple branches and, hence, are suitable for analyzing scenarios with heavily skewed information. Additionally, as stated previously, decision trees are versatile and can be applied in a broad range of business environments. Their algorithms can be integrated into other decision management techniques and tools such as the net present value (NPV) or the project evaluation review technique (PERT). Hence, since specific values are assigned to the branches, decision trees can be useful in reducing management uncertainties.

The process of using a decision tree occurs in at least five stages. First, all the possible states of nature are identified. Second, a list of the possible alternatives is developed. In some cases, one of the options may involve doing nothing. Third, the expected payoff associated with each state of nature is determined. Fourth, probability values are assigned to each state of life. The information on the states of nature, the set of alternatives, anticipated payoffs, and the assigned probabilities are used to construct a decision tree. Finally, the alternatives are evaluated based on a specified criterion. A commonly used criterion is the expected value (EV). The EV of an investment is the anticipated value of the investment at some future point (Durbach & Stewart, 2014). The use of expected benefits allows a manager to choose a scenario with the best possible desired outcome. Scenario analysis using the expected value approach relies on the anticipated probabilities of a set of possible results for a proposed investment. The expected value, EV, is calculated as

Where X_i is the expected return when an outcome occurs, and P(X_i) is the probability of the outcome occurring.

Consider a scenario in which an operation manager of a cereal-producing firm has to choose from a set of at least three alternatives. The first option, A, is a large-scale investment (A) that involves purchasing a new cooker. Although this option can produce a substantial increase in the firm’s revenue net of costs, it requires a capital investment of SR 3,750,000. Extensive market research on this option reveals that it has a 40% probability of creating payoff of SR 9,375,000 and a 60% probability of an SR 3,000,000 payoff. The second option (B) is a small-scale project that involves refurbishing an existing cooker at SR 1,875,000. Although this strategy is less costly, it also has less payoff. Extensive research reveals a 30% probability of gaining SR 3,750,000 and a 70% chance of winning only SR 1,875,000. The third option, C, is to continue with the current operation. If this option is chosen, the company expects no costs and no payoff.

A decision tree can help the manager to choose the most viable option from the three alternatives. In this case, the process involves computing the expected value for each of the options. The computed EV values are then compared against the cost of investment to determine the net gain. The option with the highest net gain should be chosen. The decision tree for the above scenario is in Appendix I. Table 1 shows the payoffs associated with each decision and state of nature.

Table 1. Pay-offs associated with each decision and nature state

Item	A	B	C
Large pay-off	0.4 × SR 9,375,000 = SR 3,750,000	0.3 × SR 3,750,000 = SR 1,125,000	0
Small pay-off	0.6 × SR3,000,000 = SR 1,800,000	0.7 × SR 1,875,000 = SR 1,312,500	0
Expected vale	SR 5,550,000	SR 2,437,500	0
Capital	SR 3,750,000	SR 1,875,000	0
Net gain	SR 1,800,000	SR 562,500	0

Each of the first two options, large-scale investment, (A) and small-scale investment (B) is associated with two states of nature, large and small pay-offs. The probable large and small pay-offs for option A are SR 3,750,000 and SR 1,800,000 respectively. The expected value is the sum of the pay-offs for each state of nature, which is SR 5,550,000 (i.e. SR 3,750,000 + SR 1,800,000). The expected net gain over the capital investment if this option is chosen is SR 1,800,000 (i.e. SR 5,550,000 – SR 3,750,000). The probable large and small pay-offs for option B are SR 1,125,000 and SR 1,312,500 respectively. The expected value is the sum of the pay-offs for each state of nature, which is SR 2,437,500 (i.e. SR 1,125,000 + SR 1,312,500). The expected net gain over the capital investment if this option is chosen is SR 562,500 (i.e. SR 2,437,500 – SR 1,875,000). For option C, the expected pay-off is zero.

Based on the above evaluation, the best option for the company is to buy a new cooker. Although the initial investment is costly, the net gain is higher than the ones realizable for the other options. However, even a promising option does not always turn out to be successful (Preuschoff, Mohr & Hsu, 2013). The accuracy of this decision is limited by several factors related to user experience (Cox et al. 2017: Bae, 2014). The assumption used in the above model is that the preliminary investigation identified all the possible outcomes of the decisions. It is also assumed that the probabilities assigned for the states of nature are based on analysis of all the possibilities (Khanduja, Mittal, & Tewari, 2017; Muthusamy, Krishnakumar, Praveenkumar, & Ramachandran, 2015). Therefore, the experience of the manager and their insight into the problem has significant bearings on the accuracy of this decision.

As Bae (2015) cautions, decision trees should be used only as a reference since they do not guarantee success. Additionally, decision trees are not immune to unpredictable events that may influence the returns from an investment. Notably, although decision trees are often cited as being effective management, a review by Cox et al. (2017) suggests that there is no empirical evidence of their effectiveness, especially regarding fairness in the decision-making process. The company should consider all these factors in its evaluation. Such limitations and gaps notwithstanding, decision trees remain preferred tools for analyzing business scenarios.

Decision trees are frequently used in decision support tools. Their effectiveness lies in their ability to function in a diverse range of settings. In the above discussions, an example of the use of this technique is demonstrated using a company that has at least three options: a large-scale investment that involves purchasing a new cooker, a small-scale project that involves refurbishing an existing cooker, and alternative to continue with the current operation. Based on the expected values, the first option appears to be the best out of the three alternatives. However, due to the potential limitations of this technique, such a decision should be made only after thorough exploration.

References

Bae J. M. (2014). The clinical decision analysis using a decision tree. Epidemiology and Health, 36, e2014025. doi:10.4178/epih/e2014025.

Cox, K., Monsalve, C., Søndergaard, S., & Strang, L. (2017). Understanding how organizations ensure that their decision is fair. Santa Monica, CA: RAND Corporation.

Drabiková, E., & Škrabul’áková, E. F. (2017). Decision trees: A powerful tool in mathematical and economic modeling. International Carpathian Control Conference (Sinaia, Romania). Piscataway, NJ: IEEE.

Durbach, I., Stewart, T. (2014). Using expected values to simplify decision making under uncertainty. Omega, 37(2), 312-330.

Khanduja, P., Mittal, K., & Tewari, D. (2017). An insight into “Decision Tree Analysis”. WWJMRD, 3(12), 111-115.

Loh, W. Y. (2014). Fifty years of classification and regression trees. International Statistical Review, 82(3), 329–348. doi: 10.1111/insr.12016.

Lu, Y., & Song, Y. Y. (2015). Decision tree methods: Applications for classification and prediction. Shanghai Archives of Psychiatry, 27(2), 130–135. doi:10.11919/j.issn..

Muthusamy, S., Krishnakumar, P., Praveenkumar, T., & Ramachandran, K. I. (2015).  A study on the classification ability of the decision tree and support vector machine in gearbox fault detection. Applied Mechanics and Materials, 813-814, 1058–1062.

Preuschoff, K., Mohr, P. N., & Hsu, M. (2013). Decision making under uncertainty. Frontiers in Neuroscience, 7, 218. doi:10.3389/fnins.2013.00218

Stevenson, W. (2018). Operations management (13^th ed). New York, NY: McGraw-Hill Education

Appendices

Appendix I: Decision Tree for Evaluating Three Options