A Decision Tree Model and Its Analysis • The following concepts are introduced through the use of a simple decision tree example (the Bill Sampras' summer job decision): Decision tree Decision node Event node Mutually exclusive and collectively exhaustive set of events Branches and final values Expected Monetary Value (EMV) Optimal decision strategy • Introduction of the folding back or backward induction procedure for solving a decision tree. • Discussion on sensitivity analysis in a decision tree. Summary of the General Method of Decision Analysis. Another Decision Tree Model and Its Analysis • Detailed formulation, discussion, and solution of the Bio-Imagining example, which is a problem with more alternatives and event nodes than the Bill Sampras example. • Discussion on sensitivity analysis and analysis of other alternatives faced by Bio-Imaging and Medtech (a related company). The Need for a Systematic Theory of Probability • Discussion on the "Suds-Away" dishwashing detergent example, which introduces the need for probability theory to properly assign probabilities to branches at event nodes (conditional probabilities). • The solution to this example is postponed to Chapter 2. Further Issues and Concluding Remarks On Decision Analysis • Discussion on the following subjects: • Risk analysis when using the EMV procedure. • Non-quantifiable consequences not necessarily considered by a decision tree analysis. • Benefits of using decision analysis: Clarity of decision problem Insight into decision process Importance of key data Suggestion of other ways to look at the problem
Manual to accompany Data, Models & Decisions: The Fundamentals of Management Science by Bertsimas and Freund. Copyright 2000, South-Western College Publishing. Prepared by Manuel Nunez, Chapman University.
Generally, students find more difficult the formulation of a problem as a decision tree than following the procedure for solving it. Finding the right logical sequence of events and identifying decision and event nodes is hard to do for many students. It is recommendable to present a few decision tree examples emphasizing the design and structure of the trees without necessarily solving them in class. A detailed presentation of the Bio-Imagining decision tree example from the textbook may take a long time. This example is very good for the students to read on their own. If the goal is to reinforce in class the concepts introduced in the Bill Sampras example, it is a good idea to ask the students to prepare the BioImagining example in advance or, alternatively, to present a less detailed example, perhaps from the exercise list. The discussion on the EMV criterion and risk can be enhanced by showing a simple payoff matrix decision example where different decisions are optimal depending on other criteria such as a greedy strategy (highly risky) or a mini-max strategy (highly conservative). A matrix decision example can be also used to introduce the general subject of decision analysis. In presenting a decision tree case in class, it is recommendable to ask the students (cold-calls) the following: (a) What are the decisions in the case? (b) What are the uncertainties involved in the case? (c) What are the branch-probability values and the endpoint evaluation of the tree? (d) Ask for volunteers to play the role of the main characters in the case. (e) If you were the person making the decision, what would you do?
Answers to Chapter Exercises
(a) Mary’s optimal strategy is to continue with the show. The EMV of this strategy is $5,550.
Manual to accompany Data, Models & Decisions: The Fundamentals of Management Science by Bertsimas and Freund. Copyright 2000, South-Western College Publishing. Prepared by Manuel Nunez, Chapman University....