### Decision Tree

A decision tree is a management tool that is used to determine the best choice or course of action out of several possible alternatives (deVille 3; Rokach and Maimon 5). In this case, the tree depicts how the different decisions will affect the available choices, that is, it shows the projected outcomes for each course of action. In other words, it presents a balanced visual depiction of the rewards and risks associated with each possible choice or course of action (Aggarwal 46). Thus, it is a means of forecasting (Goetz 4). In this respect, it can be used to determine the feasibility of setting up a waste management plant.

**Case Summary**

The local community faces a pollution challenge and thus I must decide whether to take action to reduce the impact of the issue or not. In this case, I can either build a waste management facility or not. In reference to that, in a favorable market, a large facility would produce monthly returns of 100,000 AED, while a small facility would produce monthly returns of 60,000 AED. Conversely, if the market is unfavorable, then the large facility may cause a monthly loss of 40,000 AED, while the small facility may cause a monthly loss of 10,000 AED. In addition, a pilot study can be conducted to establish the feasibility of the project at a cost of 10,000 AED. In this case, the probability that the study will be favorable is 0.65. If the study is favorable, then the likelihood that the project will be feasible is 0.8. Otherwise, the chance that the project will fail is 0.9. Also, it is worth noting that without conducting a pilot study, the probability that the project will be feasible is 0.6. Figure 1 below depicts all the variables.

Figure 1: Decision Tree for the Waste management Plant Case

**Evaluation of the Decision Tree**

The main decision to be made is whether to build the waste management facility or not. By building the facility, the community will have a chance to address its pollution problem, while failure to do so will allow toxic waste to continue piling up. In this case, the chosen option will be determined by the feasibility of the project, that is, the possibility that the facility will generate sufficient revenues for its maintenance.

The feasibility of the project can be determined by conducting a pilot study. In this case, the study will cost 10,000 AED and has a 0.65 chance of turning out to be favorable, which means that there is a 35 % chance that the study will show that the project should not be undertaken. Additionally, if the study is conducted and it shows that the project should be implemented, then there is an 80 percent chance that the project will actually succeed, which means that the probability that the project will fail under such circumstances is 20%. Conversely, if the pilot study indicates that the project should be abandoned, then the likelihood that the project will actually fail is 90%, which means that there is only a 10% chance of success if one disregards the warning from the study. I can also opt to bypass the pilot study and hence implement the project straightaway. In this case, there is a 60% likelihood that the project will turn out to be successful, which means that in such circumstances, the chance that the project will fail is 40%. Thus, the pilot study significantly impacts the decision whether to implement the project.

The feasibility of the project is also determined by the expected returns. In this case, there are two options to consider in relation to the returns: setting up a large facility or a small one. In a favorable market, a large facility can generate about 100,000 AED every month, while a small one can yield about 40,000 AED on a monthly basis. In contrast, in an unfavorable market, the large facility will create losses of 40,000 AED every month, while the small one can cause losses of about 10,000 AED on a monthly basis.

**Determination of the Tree Values**

The values of the decision trees are obtained by combining the probabilities of their branches. For the first tree, multiplying the probability of having a favorable market after achieving a favorable pilot study – 0.8 – with the probability that the outcome of the study will show that the project should be implemented – 0.65 – yields 52%. For the second decision tree, multiplying the probability of having an unfavorable market after achieving a favorable pilot study – 0.2 – with the probability that the outcome of the study will show that the project should be implemented – 0.65 – yields 13%. For the third tree, multiplying the probability of having a favorable market after achieving an unfavorable pilot study – 0.1 – with the probability that the outcome of the study will show that the project should not be implemented – 0.35 – yields 3.5%. For the fourth tree, multiplying the probability of having an unfavorable market after achieving an unfavorable pilot study – 0.9 – with the probability that the outcome of the study will show that the project should not be implemented – 0.35 – yields 31.5%. Finally, for the last trees, the probability of having a favorable market after failing to conduct a pilot study is 60 percent, thus there is a 40% chance of having an unfavorable market.

**Determination of the Returns**

*Pilot Study Conducted*

The cost of the pilot study has been established to be 10,000 AED, which means that if it is conducted, then the monthly returns for the large facility will be:

[(0.52 x 100,000) – (0.13 x 40,000) + (0.035 x 100,000) – (0.315 x 40,000)] AED

= 52,000 – 5,200 + 3,500 – 12,600 AED = __37,700 AED__.

For the same situation, the monthly returns for the small facility will be:

[(0.52 x 60,000) – (0.13 x 10,000) + (0.035 x 60,000) – (0.315 x 10,000)] AED

= 31,200 – 1,300 + 2,100 – 3,150 AED = __28,850 AED__

*No Pilot Study Conducted*

If no pilot study is conducted, then the monthly returns for the large facility will be:

[(0.6 x 100,000) – (0.4 x 40,000)] AED = 60,000 – 16,000 AED = __44,000 AED__.

For the same situation, the monthly returns for the small facility will be:

[(0.6 x 60,000) – (0.4 x 10,000)] AED = 36,000 – 4,000 AED = __32,000 AED__.

*Non-construction of the Waste Management Facility*

The cost of failing to set up the waste management facility is the determined by calculating the opportunity cost of each of the other four outcomes. In this case, the cost will be a monthly value of 37,700 AED for the large facility and 28,850 AED for the small facility if the pilot study is conducted at a cost of 10,000 AED. If the pilot study is not conducted, then the monthly opportunity cost will be 44,000 AED for the large facility and 32,000 AED for the small facility.

**Conclusion**

Based on the values of the different outcomes, one must agree that the best decision is to construct the waste management facility without carrying out the pilot study. The reason for that is that the decision yields the highest monthly returns – 44, 000 AED. In this respect, one has no option but to accept that a decision tree can be used to determine the feasibility of establishing a waste management facility.

Works Cited

Aggarwal, Charu. *Data Streams: Models and Algorithms*. Berlin, Heidelberg: Springer Science and Business Media, 2007. Print.

deVille, Barry. *Decision Trees for Business Intelligence and Data Mining: Using SAS Enterprise Miner.* Cary, North Carolina: SAS Publishing, 2006. Print.

Goetz, Thomas. *The Decision Tree: How to Make Better Choices and Take Control of Your Health*. New York: Rodale, 2011. Print.

Rokach, Lior, and Oded Maimon. *Data Mining with Decision Trees: Theory and Applications*. Singapore: World Scientific, 2008. Print.