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Near-Optimal Dynamic Lead-Time Quotation and Scheduling Under Convex-Concave Customer Delay Costs

Bar Ata, Tava Lennon Olsen

Kellogg School of Management, Northwestern University, Evanston, Illinois 60208
Washington University in St. Louis, St. Louis, Missouri 63130
b-ata{at}kellogg.northwestern.edu
olsen{at}olin.wustl.edu

We consider a make-to-order system where customers are dynamically quoted lead times (and prices). Customers are homogenous but have general (nonlinear) disutility for delay. Because the firm is a monopolist, the pricing problem is trivial and the dynamic problem reduces to one of lead-time quotation and order sequencing. We also consider the (static) problem of up-front capacity installation. We use a large-capacity asymptotic regime to make the problem tractable. We provide recommended policies for convex, concave, and convex-concave lead-time cost functions and prove that these policies are asymptotically optimal. The policies are both highly intuitive and readily implementable. Moreover, they provide delay guarantees for all served customers. They are tested numerically; we find that significant benefits can accrue by using the prescribed dynamic policies instead of first-come-first-served type policies.

Subject classifications: production/scheduling; dynamic lead-time quotation; queues; limit theorems.
History: Received January 2007; revision received January 2008; accepted March 2008.