Abstract
Decision situations can be analyzed using different methods out which decision trees are useful to analyze complex situations. Frequently, decision situation is complicated because the payoffs are not only dependent on the initial decision but also dependent on the additional decisions are taken in the sequential step process. Decision trees can identify the best initial as well as the best subsequent actions. The decision criterion that a decision tree satisfies the Bayesian expected payoff criterion. The present case has multiple alternatives and multiple probabilities; decision tree is the best method for solving this. The resulting decision tree has three alternatives with the first two alternatives having three options with varying probabilities. Once the details are filled on the nodes and branches, the excel add-in used to create the decision tree will calculate the best option using the fold-back process. Using this process, the decision tree shows that the best option for investment for the client is real estate development with a maximum payoff of 2,350,000 USD.
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Introduction
I work for as a consultant for Excellent Consulting Group, which is a consulting company. The client wants my help in deciding about an investment decision. I have to help the client in deciding the most lucrative investment. Research by reviewing all data and outcomes for 10 years about the investment choices has unearthed the following information. There are three options, which are
Real Estate Development that has either a high payoff or no payoff
Retail franchise for Just Hats, which is a boutique style store that sells fashion hats for men and women and is a comparatively a less risky opportunity that has a potentially less risk of failure and less payoff on success
High yield municipal bonds, which is a certainty
Decision Tree
Decision makers use payoff tables to make decisions. Decision situations consist of several elements. One of the elements is alternatives, which are the different options or choices that are available to the decision maker. In the present scenario, the three choices or options are to 1) invest in Real Estate business, 2) take a Franchise in Just Hats business, or 3) to buy Low Yield Municipal bonds out of which one can only choose one. The other component is the state of nature, which is dependent purely on chance and is not in the control of the decision maker. In the present scenario, the first two alternatives have three states of natures High, Medium, and Low, while the third is a certainty. Each of these states of natures has a specific probability of occurrence. A payoff table tabulates the alternatives, the states of natures, and individual probabilities of each of these futures occurring, the net present value (NPV) of each states of nature. We have calculated the value of measure by subtracting the initial investment from the NPV. Table 2 is a payoff table that tabulates these values.
While the decision situation can be analyzed using non-Bayesian techniques such as Maximin, Maximax, and Minimax Regret, they do not, however, consider probabilities. When the decision-making involves multiples alternatives, probabilities, and uncertain outcomes, one can employ decision trees for analysis, which is a Bayesian technique and graphical tool for guiding the analysis.
The Current Problem
In the present scenario, there are three alternatives. The first two alternatives have three states of natures with various probabilities, while the third is a certainty and hence has only one state of nature with a probability of one. Since the decision tree generally deals with situations, which lists all the probabilities, in the case of each of the alternatives, the total of probabilities will be equal to one. A decision tree shows the sequence of events, decision, and outcomes, as well as probabilities and monetary values.
A decision consists of nodes and branches. The nodes represent points in time. A decision node represents a time of the decision. A chance node represents the time when the result reveals an unknown outcome. The decision tree, at the end, completes all the decisions, resolves all the uncertainties, and completes incurring all the payoffs and costs. A decision node branches that are leading out and these represent the possible decisions that a decision-maker can choose. A chance node has branches representing various possible outcomes of uncertain events, which are out of the control of the decision-maker. The chance branches list the probabilities that are conditional on the events that have occurred and the totals of probabilities coming out of a chance node must sum to one. Decision trees also show the value-measures, which are the monetary values, at the end nodes. The decision tree calculates the expected maximum values (EMV) using the folding-back procedure with the maximums of the node written on the respective nodes. Figure 1 shows the decision tree for the current scenario, and the outcome shows that real estate development is the best alternative with a maximum payoff of 2,350,000 USD.
Figure 1: Decision Tree
References
Albright, S. C., Winston, W. L., & Broadie, M. (2015). Business analytics: data analysis and decision making (5th ed.). Stamford, CT: Cengage Learning.
Kazmier, L. J. (2004). Schaum's outline of theory and problems of business statistics (4th ed.). New York, NY: The McGraw-Hill Companies, Inc.
Weiers, R. M., Gray, J. B., & Peters, L. H. (2011). Introduction to business statistics (7th ed.). Mason, OH: South-Western Cengage Learning.
