We consider the decision-making problems that firms face when operating in a changing and uncertain environment. Problems of this type arise in many important decision contexts in various industries and pose challenges for both practitioners and researchers. This paper is a contribution to the development of a general framework for formulating and solving this class of problems through an investigation of current applications and solution methodologies. We consider a general class of problems: multiobjective decision processes under uncertainty, with concentration on its application areas, problem formulations, and solution strategies. A morphology classifies the relevant literature by projecting the problems reported onto a multidimensional problem space. A problem of coordinated capacity planning and inventory control serves as an example of this problem class to illustrate the issues related to formulations and solutions throughout the paper. We develop an approximation architecture that decomposes the planning horizon in time into several subhorizons and constructs a distinct decision model based on the differences in information available for each subhorizon. We link these models through states at boundaries and solve them sequentially backward in time based on the principle of optimality. An iterative solution process, i.e., proposing states forward and propagating Pareto fronts backward, searches for the optimal first stage(s) decisions. We investigate and compare combinations of different approaches in solving the example problem. Numerical results demonstrate the advantages of the proposed approximation scheme and emphasize the importance of tailoring solution strategies to specific problems.