Optimal Leadtime Differentiation Via Diffusion Approximations

Stanford GSB Research Paper No. 1743

40 Pages Posted: 30 Dec 2003

See all articles by Erica L. Plambeck

Erica L. Plambeck

Stanford Graduate School of Business

Date Written: May 2002


This study illustrates how a manufacturer can use leadtime differentiation- selling the same product to different customers at different prices based on delivery leadtime- to simultaneously increase revenue and reduce capacity requirements. The manufacturer's production facility is modeled by exponential single-server queue with two classes of customers that differ in price- and delay-sensitivity. The manufacturer chooses the service rate and a static price for each class of customer, and then dynamically quotes leadtimes to potential customers and decides the order in which customers are processed. The arrival rate for each class decreases linearly with price and leadtime. The manufacturer's objective is to maximize profit, subject to the constraint that each customer must be processed within the promised leadtime. Assuming that some customers will tolerate a long delivery leadtime, we show that this problem has a simple near-optimal solution. Under our proposed policy, capacity utilization is near 100%. Impatient customers pay a premium for immediate delivery and receive priority in scheduling, whereas patient customers are quoted a leadtime proportional to the current queue length. Queue length and leadtime can be closely approximated by a reflected Ornstein Uhlenbeck diffusion process. Hence, we have a closed form expression for profit, and choose prices and capacity to optimize this. In case customers may choose either the class 1 deal or the class 2 deal, the proposed policy is made incentive compatible by quoting a leadtime for the class 2 (patient) customers that is longer than the actual queueing delay.

Keywords: pricing, capacity, dynamic leadtime quotation and sequencing in production/scheduling, diffusion approximations for priority queues

Suggested Citation

Plambeck, Erica L., Optimal Leadtime Differentiation Via Diffusion Approximations (May 2002). Stanford GSB Research Paper No. 1743, Available at SSRN: https://ssrn.com/abstract=323921 or http://dx.doi.org/10.2139/ssrn.323921

Erica L. Plambeck (Contact Author)

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

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