Optimal Lead Time Differentiation via Diffusion Approximations

This study illustrates how a manufacturer can use lead time differentiation–selling the same product to different customers at different prices based on delivery lead time–to simultaneously increase revenue and reduce capacity requirements. The manufacturer’s production facility is modeled as an exponential single-server queue with two classes of customers that differ in price sensitivity and delay sensitivity. The manufacturer chooses the service rate and a static price for each class of customer, and then dynamically quotes lead times to potential customers and decides the order in which customers are processed. The arrival rate for each class decreases linearly with price and lead time. The manufacturer’s objective is to maximize profit, subject to the constraint that each customer must be processed within the promised lead time. Assuming that some customers will tolerate a long delivery lead time, 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 lead time proportional to the current queue length. Queue length and lead time 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 lead time for the class 2 (patient) customers that is longer than the actual queueing delay.