  Dynamic programming algorithms have been successfully applied to
propositional stochastic planning problems by using compact representations, in
particular algebraic decision diagrams, to capture domain dynamics and value
functions. Work on symbolic dynamic programming lifted these ideas to first
order logic using several representation schemes. Recent work introduced a
first order variant of decision diagrams (FODD) and developed a value iteration
algorithm for this representation. This paper develops several improvements to
the FODD algorithm that make the approach practical. These include, new
reduction operators that decrease the size of the representation, several
speedup techniques, and techniques for value approximation. Incorporating
these, the paper presents a planning system, FODD-Planner, for solving
relational stochastic planning problems. The system is evaluated on several
domains, including problems from the recent international planning competition,
and shows competitive performance with top ranking systems. This is the first
demonstration of feasibility of this approach and it shows that abstraction
through compact representation is a promising approach to stochastic planning.
