This paper considers stochastic linear programming models for production planning where cost coefficient and RHS term uncertainties are represented by finite discrete probability distribution functions. The solution of the two-stage fixed recourse problem is considered, for which a sensitivity-based successive disaggregation algorithm is proposed. The bounding properties of the aggregate sub-problems are examined in the context of the disaggregation algorithm. The partitioning algorithm converges to the exact solution in a finite number of iterations, and has a highly parallel decomposition and computer implementation. Example problems for the two-stage case are presented to demonstrate the solution technique. Results are compared with the alternative solution methods, variants of Benders decomposition schemes tailored to the dynamic staircase LP structure. Theoretical properties of the algorithm are examined, and several example problems are solved where the certainty equivalent problem involves millions of variables and constraints.