# Decision Tree Quantitative Analysis

## Decision Tree Quantitative Analysis

Decision Tree Quantitative Analysis

Problem Statement

The primary problem is that the researcher, who is a property owner, is required to select a course of action among three alternative possibilities, which include a large-scale investment (1) a smaller scale project (2), and maintaining the current operation without change (3). Moreover, the researcher acknowledges that every choice made has an implication, which may or may not prompt action. The first choice which involves making a large-scale investment focuses on improving his present apartments. Taking this option could potentially yield a substantial pay-off in increased bottom lines but will require him to invest \$ 1,400,000, which is a significant amount of money. Following comprehensive market research, which is the primary source of data collection, the researcher believes that there is a 40 percent chance of receiving a pay-off of \$2,500,000. However, market research also suggests that there is a 60 percent chance that the pay-off will only be \$800,000.

The second choice involves investing in a smaller scale project by re-decorating the current units. The researcher projects that it will cost \$500,000, which is cheaper than the first choice but also yields a lower pay-off. The market research conducted shows that there is a 30 percent chance of the researcher gaining \$1,000,000 and a 70 percent probability of the investment yielding only \$500,000. Finally, the researcher can decide to maintain the status quo and continue with the current operations. This choice will not incur any costs, but it will also not yield any pay-offs. Moreover, clients are likely to be unhappy, making it more difficult to rent the flats. The researcher will leverage the decision tree, which is a quantitative analysis approach to decision-making, to help in selecting the most suitable business choice. This problem is significant for the study because it helps in developing the insights necessary to highlight a comprehensive overview of the potential decision using a decision tree, which can be used by business owners and managers to graph the alternative decision paths.

Solution Procedure and Rationale

The decision tree will help the researcher in taking the most suitable decision by following four main steps. Firstly, the decision tree will highlight the different options open to the researcher. The tree will starts with a decision point also referred to as a node, which is depicted by the grey square (Figure 1). The three lines emerging from the decision node have been labeled appropriately to represent the three possible options.

Figure 1. Decision Tree Start Point

Secondly, the probabilities, chance nodes, as well as the outcomes are added. Figure 2 shows that each of the possible options ends with their likely outcome; therefore, this is marked using a circle. In the researcher’s case, there is only one outcome for the ‘as is’ option and two possible outcomes for the investment options. The appropriate data has been added to the diagram.

Figure 2. Shows each of the possible options ending with their likely outcomes

The third step involves calculating the expected values starting from the right. The outcomes are multiplied by their respective probabilities and the answers are added together for each option. Figure 3 shows how each respective answer is placed above its appropriate circle.

Figure 3. Shows the decision tree with the outcomes and their respective returns

The final step involves adjusting for the costs of each possible decision. The cost of each option was subtracted from the expected value and the respective amount marked on the diagram (Figure 4). The decision-making process involves rejecting the options with the lowest net expected value which was the large-scale project and stay ‘as is’ options. Therefore, the decision selected involves taking the small-scale development option.

Figure 4. Shows the complete decision tree diagram

Results and Discussion

Although the large-scale project has an expected value of \$800,000, the results generated from the quantitative analysis conducted indicate that the smaller project is the best option despite its expected value only being \$250,000. The researcher should choose the small-scale development project because in both cases, the low return likelihood has a high probability and the large scale project can always be done later after the likelihood of a good return improves. Moreover, the researcher should focus on the project with the least risks of loss and highest return which is the small scale project. The primary theory that guides in selecting the most suitable decision is the utility theory which provides a framework for helping decision maker’s to account for the inherent risks. The utility theory holds that the preferred option is the one that maximizes the overall utility (Wallenius et al. 1336). As such, the different outcomes in the decision tree should be defined in terms of utility. Generally, the decision tree is employed by business owners seeking to evaluate different decisions under conditions of risk.

One of the limitations of using the decision tree is that most people tend to confuse it with the Analytic Hierarchy Process (AHP). However, unlike decision trees which are graphical representations of decision options, the AHP is a general theory of measurement often used to derive ratio scales from evaluations that are either discreetly or and continuously paired (Yu 1 and Saaty 161-176). Finally, the decision tree does not make the decision for the researcher, but instead, it takes all the underlying factors and options into consideration which is essential in making an informed decision. As such, it is the process of designing and drawing the diagram as well as deliberating about the different options and returns that makes the decision tree a valuable tool for quantitative analysis. Another possible expansion for the decision tree involves helping the manager to be explicit in quantitatively analyzing the underlying conditions associated with future decisions as well as determining the outcome of different alternatives. Therefore, the decision tree is a flexible analysis tool that can be employed in different situations, especially those that emphasis on sequential decision making.

Works Cited

Saaty, Roseanna W. “The analytic hierarchy process—what it is and how it is used.” Mathematical modelling 9.3-5 (1987): 161-176. (Attached)

Wallenius, Jyrki, et al. “Multiple criteria decision making, multiattribute utility theory: Recent accomplishments and what lies ahead.” Management science 54.7 (2008): 1336-1349. http://people.terry.uga.edu/rsteuer/PDF_Links/TenYear.pdf

Yu, Oliver. “Assessing and Improving Consistency of a Pairwise Comparison Matrix in the Analytic Hierarchy Process.” 2017 Portland International Conference on Management of Engineering and Technology (PICMET). IEEE, 2017. (attached)

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