Progressive processing allows a system to satisfy a set of requests under time pressure by limiting the amount of processing allocated to each task based on a predefined hierarchical task structure. It is a useful model for a variety of real-time AI tasks such as diagnosis and planning in which it is necessary to trade-off computational resources for quality of results. This paper addresses progressive processing of information retrieval requests that are characterized by high duration uncertainty associated with each computational unit and dynamic operation allowing new requests to be added at run-time. We introduce a new approach to scheduling the processing units by constructing and solving a particular Markov decision problem. The resulting policy is an optimal schedule for the progressive processing problem. Finally, we evaluate the technique and show that it offers a significant improvement over existing heuristic scheduling techniques.