  Dynamic resource allocation (DRA) problems are an important class of dynamic
stochastic optimization problems that arise in a variety of important
real-world applications. DRA problems are notoriously difficult to solve to
optimality since they frequently combine stochastic elements with intractably
large state and action spaces. Although the artificial intelligence and
operations research communities have independently proposed two successful
frameworks for solving dynamic stochastic optimization problems---Monte Carlo
tree search (MCTS) and mathematical optimization (MO), respectively---the
relative merits of these two approaches are not well understood. In this paper,
we adapt both MCTS and MO to a problem inspired by tactical wildfire and
management and undertake an extensive computational study comparing the two
methods on large scale instances in terms of both the state and the action
spaces. We show that both methods are able to greatly improve on a baseline,
problem-specific heuristic. On smaller instances, the MCTS and MO approaches
perform comparably, but the MO approach outperforms MCTS as the size of the
problem increases for a fixed computational budget.
