Decision Tree free essay sample

Despite this trend surprisingly few good, clear introductions to basic decision tree concepts are available. The present work attempts to meet that need by offering a concise primer for novices. Acknowledgments The author gratefully acknowledges instructor Meryl Natches, CEO of TechProse, for invaluable editing, guidance, and patience. The author also thanks the Technical Communication 1 class participants at UC Berkeley Extension during the spring semester 2007 for review and comments. Rosana Francescato tested the material for clarity and provided helpful feedback in the development of this project. CJ Kalin, Ph. D. , introduced me to the decision tree method in a Project Risk Management class at UC Berkeley Extension. Her real-world examples demonstrated how the decision trees technique helps solve complex project management problems. Despite the aforementioned contributions the author accepts responsibility for any errors or omissions herein. A decision tree is a method you can use to help make good choices, especially decisions that involve high costs and risks. Decision trees use a graphic approach to compare competing alternatives and assign values to those alternatives by combining uncertainties, costs, and payoffs into specific numerical values. If you are a project manager, business analyst, or a project decision-maker, this primer is for you. If you are interested in cognitive science, artificial intelligence, data mining, medical diagnosis, formal problem solving, or game theory, this primer provides an introduction to basic concepts of decision tree analysis. 1. 1 Advantages of using decision trees Decision trees offer advantages over other methods of analyzing alternatives. They are: †¢ Graphic. You can represent decision alternatives, possible outcomes, and chance events schematically. The visual approach is particularly helpful in comprehending sequential decisions and outcome dependencies. †¢ Efficient. You can quickly express complex alternatives clearly. You can easily modify a decision tree as new information becomes available. Set up a decision tree to compare how changing input values affect various decision alternatives. Standard decision tree notation is easy to adopt. Revealing. You can compare competing alternatives—even without complete information—in terms of risk and probable value. The Expected Value (EV) term combines relative investment costs, anticipated payoffs, and uncertainties into a single numerical value. The EV reveals the overall merits of competing alternatives. Complementary. You can use decision trees in conjunction with other project management tools. For example, the decision tree method can help evaluate project schedules. †¢ †¢ 1. 2 About this primer This primer offers an introduction to basic decision tree analysis. After studying this material for an hour, most users will be able to understand and apply decision tree analysis to solve simple and even moderately complex decision problems. You can readily construct and analyze simple decision trees such as those found in this primer with pen, paper, and a calculator. However, a spreadsheet such as Microsoft Excel can dramatically facilitate setting up and modifying decision trees. A number of other software applications are also available. These range from low-cost Microsoft Excel plug-ins to more expensive dedicated applications. For the purposes of this primer, a pen, paper, and calculator are sufficient. 1 Decision Trees A Primer for Decision-making Professionals 1. 3 To use this primer You can use this primer in several ways. If you prefer to get started immediately with drawing and using decision tree notation, then begin with the Decision Scenario, an exercise that puts you in the role of using a decision tree in step-by-step fashion. If you are more comfortable learning by first seeing how a process works, then start with Basic Concepts. Whichever way you begin, make sure to review both of these sections. The Glossary defines underlined terms. After you review the concepts and use the scenario exercise, you can find external references in More to Explore. Icons indicate items of special interest: †¢ †¢ †¢ †¢ Example Exercise Note Tip 2 Decision Trees A Primer for Decision-making Professionals 2. 0 Decision Scenario Consider the following scenario. Really Big Ideas, Inc. a small company that develops inventions for the consumer market, has recruited you as a consultant to make a recommendation on a critical business decision. At 10:00 a. m. , you meet Adam Smith, the Vice President in charge of product development. Smith expresses his wish for an outside opinion on a decision the company must make soon. Your job is to supply such an informed opinion. Smith tells you that a short meeting will pr ovide all the information needed and introduce the project managers for two possible (and competing) products. As Smith ushers you into a conference room he also mentions that he expects your analysis by 11:00 a. m. , scarcely an hour from now! You are given pen, paper, and a calculator. At 10:05 a. m. , you and Smith enter a small meeting room. Smith explains that Really Big Ideas has a three-month window of opportunity to develop a new product using new pattern recognition software the company recently created. Surprisingly, the software adapts easily to different applications. Really Big Ideas only has the resources and time to develop one of two projects, or to develop none. Project Managers Aisha Ali and Ben Bertrand arrive. After brief introductions, Aisha Ali launches her pitch. She says that a smoke and fire detector is the best project to make. The detector goes beyond ordinary smoke detectors. It can detect flames as well as smoke. It will cost $100,000 to develop, and if it succeeds the Business Analysis department says it will generate revenue of $1,000,000. Not to be outdone, Ben Bertrand announces that a motion detector device is the best project to develop. The motion detector, which uses conventional household lighting, will only cost $10,000 to develop. He adds that the analysts expect such a device to generate $300,000 in revenue. Smith asks if you have any questions, so you carefully ask about the chances for success. Both project managers agree that Samiksha Singh, the Director of the Business Analysis department, has that information. Smith initiates a conference call with Samiksha Singh. Singh informs the meeting that the smoke and fire detector has a 50% chance of success, and that the motion detector has an 80% chance of success. Smith thanks all the participants and ends the meeting. It is now 10:30 a. . Smith announces that he’ll return within the hour to see if you have decision analysis. Smith leaves you with your notes, paper, pen, and a calculator. Can you help Really Big Ideas to decide which product, if either, to develop? How can you evaluate the alternatives in a measurable way given the various uncertainties involved? You can use a decision tree to describe and then to evaluate the decision alternatives. 3 D ecision Trees A Primer for Decision-making Professionals 2. 1 Describe decision alternatives and outcomes You can now start your decision tree. A decision tree is a diagram of nodes and connecting branches. Nodes indicate decision points, chance events, or branch terminals. Branches correspond to each decision alternative or event outcome emerging from a node. 2. 1. 1 The first decision (root node) Start by drawing a small square on the left side on a piece of paper. This is called the root node, or root. The root node represents the first set of decision alternatives. For each decision alternative draw a line, or branch, extending to the right from the root node. Allow a generous amount of space between the lines to add information. Some branches may split into additional decision alternatives or outcomes. You can also â€Å"bend† branches so that the lines line up horizontally. These techniques make keeping track of alternatives easier. (See figure 2. 1. 1) Label each branch with the decision and its associated investment cost. Write that the smoke and fire detector will cost (-$100,000) to develop. Similarly, write that the motion detector will cost (-$10,000) to develop. Write $0 at the third branch corresponding to the alternative to develop neither product. Tip Show the costs as negative values since they represent a â€Å"preliminary loss. Any future gross revenue will be offset by costs. Showing costs as negative values simplifies the calculation of payoff. Figure 2. 1. 1 The root node is the small square at the left. Branch lines emerge from the root towards the right. Each branch represents one decision alternative. 4 Decision Trees A Primer for Decision-making Professionals 2. 1. 2 Chance outco mes In the Really Big Ideas scenario each product development effort can have one of two outcomes: each project can either succeed or fail. Draw a small circle, or chance node, at the end of the branch for the smoke and fire detector. Draw a chance node at the end of the branch for the motion detector. From each chance node draw two branches towards the right; one branch represents success and the other represents failure. Label the branches accordingly. Figure 2. 1. 2 Chance nodes, shown as small circles, lead to two or more possible outcomes. Draw each outcome as a branch from the chance node. 2. 1. 3 Endpoints and payoffs You can now complete all the branches with endpoints, since there is no further branch information to represent. Draw a small triangle ( ) at the end of each branch to represent the endpoint. Write the payoff value at the endpoint. In business applications the payoff is usually a monetary value equal to the anticipated net profit, or return on investment. Net profit (or net loss) is the difference between the investment cost and the total revenue. A positive value indicates a net profit, while a negative value indicates a net loss. In other words, if revenue exceeds investment, then the effort is profitable. Otherwise the effort is a net loss, or a breakeven result if the payoff is zero. For Really Big Ideas, a successful smoke and fire detector project will earn $1,000,000 in gross revenue. The resulting net profit therefore equals the sum of the gross revenue and the investment cost. Recall that cost can be represented as a negative number. The calculation is therefore $1,000,000 + (-$100,000) = $900,000 net profit, or payoff. Write $900,000 at the end of the branch for success of the smoke and fire detector. 5 Decision Trees A Primer for Decision-making Professionals However, if the smoke and fire detector project is not successful, then no revenue will be earned and all the investment will be lost. The calculation for this event is $0 + (-$100,000) = (-$100,000), a loss or negative payoff. Write (-$100,000) at the end of the branch for failure of the smoke and fire detector. Perform a similar calculation for the success and failure payoffs for the motion detector. Your results should show a $290,000 payoff if successful, and a (-$10,000) payoff (a loss) if it fails. Write these values at the endpoints of their respective branches. The payoff for the decision branch to not develop either project is simply $0. See figure 2. 1. 3. Figure 2. 1. 3 Use endpoints, shown by small triangles with one point connecting to the branch, to indicate that there are no further outcomes or decisions to consider. Write payoff values for each terminated branch to the right of the endpoints. This concludes the basic structure of the decision tree for the Really Big Ideas alternatives. We can now incorporate the likelihood of success and failure and use that to analyze the decision alternatives. 6 Decision Trees A Primer for Decision-making Professionals 2. 2 Incorporate uncertainty (outcome probability) You can now incorporate the relative outcome probability, or uncertainty, associated with each chance event. You can express probabilities as percentages or as decimal fractions.