This article presents an algebraic approach to formulating and solving large models for sequential decisions under uncertainty. With this approach, decision analysis optimization methods can be applied to complex decision problems which are generally analyzed in management science practice using heuristics. Using the approach, a decision problem is formulated in terms of decision variables, random variables, and functions relating these variables. This leads to a compact representation, and a simple algorithm can be used to quickly solve algebraic models that would have decision trees with several hundred thousand endpoints. An application to research and development planning illustrates the usefulness of such large sequential decision models.