Research focuses on developing Brownian approximations of mathematically intractable dynamic scheduling (or resource allocation) problems in order to develop effective scheduling policies for a variety of production systems. These systems include multiclass, multistation closed queueing networks (which are perhaps the most prominent mathematical models of manufacturing, computer, and communication systems), make-to-stock queueing systems (that is, production/inventory systems, where the production system is modeled as a queueing system) with random yields and substitutable demands (motivated by semiconductor manufacturing), and multiechelon repairable inventory systems.//