Dynamic Scheduling of a Multiclass Make-to-Stock Queue

Motivated by make-to-stock production systems, we consider a scheduling problem for a single server queue that can process a variety of different job classes. After jobs are processed, they enter a finished goods inventory that services customer demand. The scheduling problem is to dynamically decide which job class, if any, to serve next in order to minimize the long-run expected average cost incurred per unit of time, which includes linear costs (which may differ by class) for backordering and holding finished goods inventory. Under the heavy traffic condition that the server must be busy the great majority of the time in order to satisfy customer demand, the scheduling problem is approximated by a dynamic control problem involving Brownian motion. The Brownian control problem is solved, and its solution is interpreted in terms of the queueing system to obtain a scheduling policy. A simulation experiment is performed that demonstrates the policy's effectiveness.