Decision Tree Essay Example

promotion of decision analysis training and application by the Electric Power Research Institute (EPRI). Decision analysis has been utilized in areas such as capacity planning, environmental compliance, fuel procurement, and plant operations [Farghal, El-Dewniey, and Abdel Aziz 1987; Mobasheri and Williams 1990; Norris, Sweet, and Borison 1991; Oatman and Figure 1: Florida is a net power buyer, while Alabama, South Carolina, and Georgia are net power sellers. umer-owned distribution cooperatives in Georgia.

In 1990, the peak demand reached 3,700 MW, while energy production totaled 14,000,000 MWb. This amount accounts for more than 20% of the power in the state. Georgia Power Company (GPC), a subsidiary of the Southern Company system, dominates the rest of the market. Both OPC and GPC operate their own generation facilities and have joint ownership of some plants. Through intricate legal agreements, OPC and GPC jointly own and manage most of Georgia's transmission grid.

Several connections, amounting to thousands of megawatts, connect the transmission grids. Additionally, significant advancements have been made by commercial vendors in the development of rapid, adaptable, and potent software [Call and Miller 1990]. ADA has contributed DPL in this field. These tools have assisted in increasing the willingness of electric utility analysts and managers to employ decision analysis. The OPC study encompassed three main groups: the senior management team accountable for reviewing recommendations and making decisions, and the analytic team responsible for conducting analysis and formulating recommendations.

This team consisted of staff from both OPC and ADA and included OPC experts who provided input on specific topics that arose during the analysis. The represented groups included contract negotiations, federal regulations, generation planning, rates and pricing, substation maintenance, system operations,

and transmission planning. The senior management and analytic teams selected experts as the study progressed and it became clear which topics required in-depth analysis. The project compressed a multistep decision analysis process into less than two weeks, thanks in part to the use of DPL software and the prior experience of the analytic team.

The problem formulation stage involved precisely specifying the decision problem. This entailed providing a clear problem statement and organizing the problem based on principles of decision analysis. Initially, we identified a problem statement that emerged from an initial evaluation of the transmission line matter: Should OPC proceed with the proposal to construct a 500 kV transmission line for Florida Power Corporation? Additionally, we needed to determine the framework for the business deal if the proposal moved forward. At OPC, we structured the problem by identifying the key decisions, uncertainties, and values at stake. This information served as the basis for creating an influence diagram and schematic decision tree (Figures 2 and 3).

We iteratively improved these visual elements over multiple meetings with the analytical team and important experts. As we constructed the influence diagram and schematic decision tree, it became evident that OPC had three distinct decisions rather than just a single one. These decisions encompassed the determination of constructing the transmission line (Line), upgrading related transmission facilities (Upgrade), and defining the control over the new facilities (Control). Each decision consisted of different alternatives resulting in a total of 18 decision policies (3 X 2 X 3).

OPC's main issue was deciding between three alternatives: March-April 1995 27 BORISON Cost Upgrade Line Savings Control Revenue Line Availability Spot Amount Operating Savings Power Avaiiabiiity Figure

2; The influence diagram illustrates the components of the transmission line problem and their connections with the Line decision. Integrated Transmission System (ITS) and No ITS represent two potential financing options. No ITS involves an independent approach, while ITS entails a joint venture with GPC. No Line implies that OPC would not invest in the line at all. OPC encountered five significant uncertainties: the cost of constructing new facilities (construction Control Upgrade Construction Cost cost), power demand in Florida, and market conditions (competitive situation, OPC share, and spot price).

Figure 4 illustrates the 405 scenarios of uncertain variables: 5 X 3. The optimal expected savings policy, as depicted by the bold lines, is Line ^ No ITS, Control = OPC, and Upgrade = NoUpgrade. In Figure 2's influence diagram, the multiple arrows leading to the final value node show how savings are calculated from other variables.

The text describes various variables related to revenues from contract power sales, spot market power sales, and wheeling of power in Florida. It also mentions the direct operating savings and the completion of an influence diagram and schematic decision tree as key products of the problem formulation stage. Using these products, OPC managers were confident that the key issues were addressed and the problem was structured appropriately for quantitative analysis.

Deterministic Analysis

To perform quantitative analysis, a model and data were developed to calculate the final value measure based on the settings of decision and chance variables. Electric utilities often use extensive models with substantial data requirements for such analysis.

Although more complex models are sometimes used, simpler models with smaller data requirements, such as spreadsheets, are sometimes preferred. In this particular

study conducted in March-April 1995, a relatively straightforward approach was taken to develop the value model. The final value and savings were calculated using basic spreadsheet equations that took into account decision variables, chance variables, and other parameters. For instance, in this model, the savings were determined by calculating the difference between revenue and cost.

Revenue is the combined total of contract revenue, spot revenue, wheeling revenue, and operating savings. Spot revenue is obtained by multiplying spot amount with spot price, which is directly assessed. The equations for this value model are directly specified in DPL code. After constructing a value model, sensitivity analysis is usually conducted to identify the most significant uncertainties.

A variable is considered sensitive if its uncertainty impacts the decision being made. Such variables are treated probabilistically in subsequent stages of the decision analysis process. Conversely, insensitive variables are assigned nominal or expected values. This approach ensures that limited resources are focused on the most critical matters, and reduces computation time by constraining the size of the final decision tree. Nonetheless, in this particular study, a sensitivity analysis was unnecessary to reduce the problem's scope.

All five variables that were uncertain in the original influence diagram were treated as sensitive and analyzed probabilistically. Using the value model developed in the deterministic analysis, we were able to calculate the final value - savings - associated with any set of chance outcomes based on a specified decision policy. Next, we assigned probabilities to each individual outcome for the five chance events: construction cost, OPC share, competitive situation, Florida demand, and spot price.

We evaluated the probability distribution for each of these events, whether they were discrete

or continuous. When one chance event depended on the outcome of another decision or chance event, we took that into consideration during the assessment. For instance, in this specific problem, the assessment of OPC share and Florida demand was contingent on the line decision. Probability assessment is a complex procedure typically conducted by trained encoders, who spend an hour or more on each event. (Refer to Stael von Holstein and Matheson [1979] or Merkhofer [1987] for further details on the encoding process).

In the OPC study, our in-depth assessments were limited due to time constraints. Instead, we conducted quick probability assessments with the understanding that further probabilistic sensitivity analysis would uncover areas for improvement. To ensure accuracy, we engaged the relevant experts to contribute their insights and inputs during the formulation stage of each chance event. Upon completing these probability assessments, we had a comprehensive decision tree consisting of almost 8,000 paths. The evaluation process began by determining the "optimal" decision policy, which focused on maximizing expected savings.

The optimal policy proposed here is suitable for a decision maker who is not concerned about risks. It serves as a good starting point for evaluating other possible policies. Figure 4 depicts the best policy in terms of expected savings, outlining choices for line, control, and upgrade decisions. Next, we assess the risks associated with this policy. If it offers not only the highest expected savings but also low risk, it would be an compelling option and further examination of alternative policies may not be required. Figure 6 illustrates the varying levels of risk among the three main alternatives when compared to the baseline transmission policy.

Percentages are omitted for

proprietary reasons. The ITS policy has a lower expected savings compared to the No ITS policy. The ITS policy is considered the least attractive option as it poses more risk and lower expected savings compared to the No Line policy. At this stage, OPC managers have to choose between a high-risk, high-savings strategy (No ITS) and a low-risk, low-savings strategy (No Line). The final decision on these policies will largely depend on the corporate risk-taking attitude. However, instead of being restricted to this choice, we made an effort to find or create a policy that maintains the potential for high savings while reducing risk.

OPC managers preferred an informal judgmental approach to risk and believed that a dominant policy would be ideal, surpassing both the No ITS and No Line options. The focus was on finding a low-risk, high-savings policy by identifying factors that could raise costs with the No ITS policy. Additionally, they considered gathering more information on the competitive landscape and potentially improving their position among other utilities in the Southeast.

A policy that includes actions along this line could be both feasible and desirable. We conducted an analysis to confirm and measure the benefits of information and control in relation to the competitive situation. In the value-of-information analysis, uncertainty about the competitive situation is revealed prior to making a policy decision. In the value-of-control analysis, the competitive situation is assumed to be at its most favorable state. Figure 8 shows that additional information about the competitive situation has value, and control over the competitive situation has even greater value. This validates the need for OPC to acquire more knowledge or enhance the competitive situation

before committing to the transmission line.

During our most recent evaluation activity, we focused on examining how sensitive our results were to changes in input assumptions. As part of this analysis, we conducted a sensitivity analysis on the discount rate, represented in Figure 9 using a rainbow diagram. Based on our findings, we have two recommendations for OPC management:

• If an immediate commitment regarding the transmission line is necessary, OPC management should choose between two options: a high-risk, high-savings policy (No ITS) or a low-risk, low-savings policy (No Line).
• If an immediate commitment is not necessary, OPC management should prioritize learning about and improving its competitive situation before making any decisions.

The evaluation step yielded a variety of answers and insights, ultimately leading to this recommendation for management.

During the communication phase, we presented the results to management in order to inspire action. In the OPC study, we utilized traditional handouts, overhead transparencies, and real-time displayed DPL software graphics to deliver our presentation to management. We started by providing a condensed version of the influence diagram illustrated in Figure 2 to demonstrate the extent of the study. Next, we utilized a risk profile, similar to the one presented in Figure 6, to justify our answers, insights, and recommendations by incorporating all three primary alternatives.

We utilized this figure for illustrating the different policies and comparing the No ITS and No Line alternatives, as well as clarifying the importance of the competitive situation.