In this paper the problem of planning under uncertainty is addressed. Short term production planning with a time horizon of a few weeks or months and long-range planning including capacity expansion options are considered. Based on the postulation of general probability distribution functions describing process uncertainty, a two-stage stochastic programming formulation is developed where the objective is to determine an optimal plan (i.e., process utilization levels, purchases and sales of materials) and/or an optimal capacity expansion policy that maximize an expected profit. A decomposition-based optimization approach is proposed, where planning decisions are taken by coupling economic optimality and plan feasibility without requiring an "a priori" discretization of the uncertainty. The proposed algorithmic procedure features a highly parallel solution structure which can be exploited for computational efficiency. Three example problems are presented to illustrate the steps of the novel planning under uncertainty optimization algorithm.