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Dynamic Control of a Make-to-Order, Parallel-Server System with Cancellations

Melanie Rubino, Bar Ata

Wolverine Trading LLC, Chicago, Illinois 60604
Kellogg School of Management, Northwestern University, Evanston, Illinois 60208
mrubino{at}wolve.com
b-ata{at}kellogg.northwestern.edu

Motivated by make-to-order production systems, we consider a dynamic control problem for a multiclass, parallel-server queueing system. The production system serves multiple classes of customers who require rigid due-date lead times and may cancel their order subject to a cancellation penalty. To meet the due-date constraints, a system manager may outsource orders when the backlog of work is judged excessive, thereby incurring outsourcing costs. The system manager strives to minimize long-run average costs by dynamically making outsourcing and resource allocation decisions. Under heavy-traffic conditions, the scheduling problem is approximated by a Brownian control problem. Interpreting the solution of the Brownian control problem in the context of the original queueing system, a nongreedy outsourcing and resource allocation policy is proposed. A simulation experiment is performed to demonstrate the effectiveness of this policy.

Subject classifications: make-to-order production; parallel-server queues; heavy-traffic approximations; diffusion models.
History: Received October 2006; revision received September 2007; accepted November 2007.