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Dynamic Control of a Multiclass Queue with Thin Arrival Streams

Bar Ata

Kellogg School of Management, Northwestern University, Evanston, Illinois 60208
b-ata{at}kellogg.northwestern.edu

As a model of make-to-order production, we consider an admission control problem for a multiclass, single-server queue. The production system serves multiple demand streams, each having a rigid due-date lead time. To meet the due-date constraints, a system manager may reject orders when a backlog of work is judged to be excessive, thereby incurring lost revenues. The system manager strives to minimize long-run average lost revenues by dynamically making admission control and sequencing decisions. Under heavy-traffic conditions the scheduling problem is approximated by a Brownian control problem, which is solved explicitly. Interpreting this solution in the context of the original queueing system, a nested threshold policy is proposed. A simulation experiment is performed to demonstrate the effectiveness of this policy.

Subject classifications: production/scheduling; make-to-order production systems; queues; dynamic scheduling via heavy-traffic approximations; dynamic programming; admission control in queues.
History: Received June 2004; revision received February 2005; accepted October 2005.