One of the most important analytical tools often used by management executives for decision making is decision tree analysis. The most well-known approach to solve decision tree problems is the roll-back method (based on dynamic programming). With respect to the shortcomings and limitations of this solution approach, I would like to know whether there exists any decision tree problems that cannot be solved using the roll-back method.
I know roll-back method as backtracking.
- Decision tree problems with intricate constraints between variables.
- The roll-back method may struggle to navigate a large search space efficiently due to exponential time complexity.
- Irregular tree structures may not fit well with the roll-back approach. Handling arbitrary branching factors or varying depths can complicate the implementation of the roll-back method.
- In applications where decisions must be made in real-time or incrementally as new information becomes available.
Those are, for me, the main limitations.
Paulo Bolinhas Thanks for your answer. I agree with you that the roll-back method struggles when problem size grows. With respect to the third bullet point, I wonder you know any irregular decision tree problems that cannot be solved using the roll-back method. Any particular problem is appreciated.
Maybe a decision tree scenario where the outcomes of certain decisions depend on external factors that evolve over time or are uncertain.
Imagine you're planning a weekend trip to the beach, and your decision tree involves choosing between driving and taking public transportation. However, the weather forecast is uncertain, and it might rain unpredictably during the weekend.
Paulo Bolinhas Thanks! In this example, if the decision tree is well defined with respect to all possible outcomes (including the uncertain ones), I cannot see why the DP could struggle.
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