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

2. 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

3. 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)

4. 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

5. 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

6. 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)

7. 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

8. 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

9. 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

10. 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