What is OR

Decision Analysis – Decision Trees

We all make decisions in our jobs, our communities and in our personal lives that involve significant uncertainty.
  • How much should a company bid on an oil lease and how much should it invest in developing an oil field? On a personal level, how much should I invest in a particular stock or mutual fund?
  • How much capacity should be added to the manufacturing plant?
  • Should millions be invested in new drug that has proven effective in animal tests?
  • Which type of eye surgery should I have?
  • Should the next baseball player at bat bunt?
There is uncertainty as to the oil reserves of the oil field and the market demand for a new product. The link between animal drug trials and human effectiveness is far from perfect. What are the risks with the various types of surgery? Decision analysis is an operations research modeling tool used to select the best decision in the presence of uncertainty.

The oil industry was one of the earliest users of the tool and continues to lead in its application. Pharmaceutical companies apply decision trees, which are an application of probability trees to make R&D decisions. Industrial giants such as DuPont, Kodak and GM use it to plan new products and capacity. The Decision Analysis Affinity Group (www.daag.org) is an organization that runs conferences at which corporate practitioners of decision analysis share experiences. There is also the Decision Analysis Society which is an organization affiliated with INFORMS. They maintain a homepage at http://faculty.fuqua.duke.edu/daweb/.

The methodology involves creating a probabilistic tree for every alternative. The nodes of a tree represent either decisions or random events. The branches emanating from a node correspond to alternative decisions or alternative outcomes. The best alternative either maximizes the expected profit or minimizes the expected cost. Modern software such as Precision Tree, an Excel add-on, facilitates the analysis and offers graphical representations of the results. These enable a decision maker to explore the strengths and weaknesses of the alternatives.

As decision analysis developed, the leaders in the field recognized two critical psychological and practical issues that needed to be addressed in order to make the tool of greater practical value. The models required estimates of probabilities that were often not readily obtainable through detailed analysis of data. Subject matter experts, therefore, were interviewed in order to estimate the probabilities. Decision analysts, along with mathematical psychologists, became leaders in the effort to understand biases and misconceptions that individuals display when asked to make a forecast. They developed interview protocols to elicit expert opinion in a manner that reduced the likely bias. For example, project managers are often overly optimistic when they forecast how quickly a project will be completed. The interviewer encourages the manager to recall his experiences when projects did not go as planned and to use that relevant experience to make a more realistic forecast for the current project.

The expected value, however, does not capture the fact that people are often fearful of taking risks, especially large ones. This risk aversion is the foundation for all of the insurance industry and the huge market in extended warranties. Decision analysts became leaders in researching attitudes towards risk and designing a methodology called utility theory, that captures this behavior. Utility theory is used to capture the decision maker's risk attitude and incorporate his value system into the decision tree structure.


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