The objective of this project is to study sequencing decisions in state-of-the-art semiconductor manufacturing lines. The specific problem being addressed is the "what next" scheduling decision, the decision as to what should be done next when an operator has completed a task on a machine tool, and both the tool and operator are ready to perform another task. The project involves extensive industrial interaction and focuses on a production line that manufactures logic and memory chips. The research approach consists of periodically comparing the current status of the manufacturing line with current and projected demands for chips of different part numbers. The set of constraints under which the manufacturing line is operating is also considered. A constrained optimization problem will be formulated and solved to determine which operations should be performed during the period in order to place the line in a better position of meeting the demand. Priorities for the operations to be performed during the next period are also computed using both dual and primal information from the optimization.