It was suggested (e.g. Pollock and Smith, 1985) that the “ art of DP ” can be
resolved by a simple enumeration-aggregation process where the state of the DP
model is identified by inspection using the decision-tree representation of the
underlying problem. This approach is fundamentally flawed. To start with, it requires
the modeller to enumerate all the feasible solutions. Second, the states
identified by this process are not necessarily the conventional DP states because
the proposed method is prone to the whims of specialized circumstances associated
with the particular instance of the problem under consideration. Thus, for instance, the states generated by this method for an instance of the knapsack
problem may not have the “ physical ” meaning of the conventional states associated
with this problem (“ capacity not yet utilized ”). Thirdly, the approach
cannot deal with classes of problems: how do you decide what is a proper state
for the generic knapsack problem? In short, not only that complete enumeration
cannot be accepted as a legitimate tool for determining the states of a DP
model, the mere suggestion of this option is a clear indication of the enormous
difficulties posed by the “ art of DP ”.