Optimal control of processing times in single-stage discrete event dynamic systems with blocking

This note concerns an optimal control problem in single-stage discrete event dynamic systems with finite buffers and blocking. The system is modeled as a deterministic queue, slated to process a finite sequence of jobs. Each job is characterized by its arrival time, service time, and due date, and has associated with it a cost function that penalizes short service times, buffer times, and lateness of completion times with respect to the due date. The sequencing (order) of the jobs at the server is given, and the variable parameter consists of the jobs' service times. Even though the cost function associated with each job is assumed to be convex, the aggregated cost functional is not convex. Therefore, much of the analysis focuses on a decomposition of the problem into a finite sequence of reduced-order convex programming problems which can be solved one at a time. This approach has been investigated in the past, but the present note provides an analysis under the most general and realistic assumptions considered to date.