Comparing Dynamic Programming / Decision Trees and Simulation Techniques BDAuU, Prof. Eckstein

Decision Trees / Dynamic Programming Outcomes / Paths Decision Trees / Dynamic Programming Simulation Looks exhaustively at all outcomes / paths of random events DP does this in a “smart” way Looks at a sample of possible event sequences

Decision Trees / Dynamic Programming Model Building Decision Trees / Dynamic Programming Simulation For decision trees, some tools such as TreePlan are available For DP, relatively difficult to build “model”, which includes solution algorithm No computer modeling environments / software tools for DP (yet) Straightforward modeling along a single sample path Separation of model and calculation enabling software tools: @Risk, Crystal Ball, YASAI etc. for Monte Carlo simulation in Excel Numerous discrete-event simulation tools (like Arena)

Decision Trees / Dynamic Programming Accuracy Decision Trees / Dynamic Programming Simulation Finds exact optimal EMV of model Only modeling errors Has sampling error as well as modeling errors

Multiple Kinds of Random Events Decision Trees / Dynamic Programming Simulation Multiple kinds of random events mean nested loops and extra programming complexity Multiple kinds of random events easy to model

Decision Trees / Dynamic Programming Policy Complexity Decision Trees / Dynamic Programming Simulation Can assemble very detailed strategies from locally optimal “chunks” What to do in stage t, state i Does not care about total number of different policy combinations Typically needs a full simulation of each possible policy Policies need to be described by a relatively small number of parameter value combinations (There are limited ways to avoid this restriction, but the techniques are quite advanced)

Distributions and Risk Decision Trees / Dynamic Programming Simulation The basic forms we have learned give no information on outcome distributions or risk (There are partial ways around this if you use more advanced techniques) Automatically yields sample distribution information

Decision Trees / Dynamic Programming Number of States Decision Trees / Dynamic Programming Simulation Needs every sequence of events to be reducible to a sequence of states, where the number of possible states is not too large Does not care about the number of states

Decision Trees / Dynamic Programming Variance Decision Trees / Dynamic Programming Simulation Variance of outcomes has little or no effect on accuracy of the optimal policy and EMV calculations Large variance requires a large sample

Decision Trees / Dynamic Programming “Lumping” Decision Trees / Dynamic Programming Simulation To hold down the tree size or number of states, it helps to “lump” various random outcomes For example, high, medium, or low sales of a product Lumping can increase modeling inaccuracy Doesn’t care about number of states, so no need for “lumping” But sampling error remains, of course