Using different response-time requirements to smooth time-varying demand for service

Whitt, Ward

doi:10.1016/s0167-6377(99)00006-1

Cited by 12 publications

(5 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Leadtime differentiation may be even more valuable in a setting with time-dependent arrival rates. Whitt (1999) estimates the capacity savings that can be obtained by postponing the service of "patient" customers to an off-peak period.…”

Section: Literature Reviewmentioning

confidence: 99%

Optimal Leadtime Differentiation via Diffusion Approximations

Plambeck

2004

Operations Research

View full text Add to dashboard Cite

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 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 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.Subject classifications: pricing; capacity; dynamic leadtime quotation and sequencing in production/scheduling; diffusion approximations for priority queues.

show abstract

Section: Literature Reviewmentioning

confidence: 99%

Optimal Leadtime Differentiation via Diffusion Approximations

Plambeck

2004

Operations Research

View full text Add to dashboard Cite

show abstract

“…By choosing a balking probability of 0 if L S o K and 1 otherwise, their model can also approximate systems with a finite waiting room. Whitt [228] develops the fluid approximation for an MðtÞ=G=c=PPrio system by reducing the service rate of a given class by the demand of all higher classes. Ridley et al [192] derive the fluid approximation for a two-class MðtÞ=M=c=PPrio system that is supported by a limit theorem.…”

Section: (T)/g/c(t) M(t)/g/c(t)/k Wall and Worthington [225] M(t)/g/cmentioning

confidence: 99%

Performance Analysis of Time-Dependent Queueing Systems: Survey and Classification

2015

View full text Add to dashboard Cite

“…In the following, before describing the mathematical model, we first derive a formula for calculating the total penalty costs over the planning horizon, which obviously depends on L and C. In order to do so, we need to calculate the queue length and the number of delayed jobs in the system at any period. Our approach for computing the queue length is inspired by the work of (Whitt, 1999), who applied a deterministic fluid model to estimate the time-dependent queue length under deterministic, continuous demand.…”

Section: Assumptionsmentioning

confidence: 99%