We study a capacity sizing problem in a service system that is modeled as a single-class queue with multiple servers and where customers may renege while waiting for service. A salient feature of the model is that the mean arrival rate of work is random (in practice this is a typical consequence of forecasting errors). The paper elucidates the impact of uncertainty on the nature of capacity prescriptions, and relates these to well established rules-of-thumb such as the square-root safety staffing principle. We establish a simple and intuitive relationship between the incoming load (measured in Erlangs) and the extent of uncertainty in arrival rates (measured via the coefficient of variation) that characterizes the extent to which uncertainty dominates stochastic variability or vice versa. In the former case it is shown that traditional square-root safety staffing logic is no longer valid, yet simple capacity prescriptions derived via a suitable newsvendor problem are surprisingly accurate.service systems, capacity sizing, parameter uncertainty

We analytically study optimal capacity and flexible technology selection in parallel queuing systems. We consider N stochastic arrival streams that may wait in N queues before being processed by one of many resources (technologies) that differ in their flexibility. A resource's ability to process k different arrival types or classes is referred to as level-k flexibility. We determine the capacity portfolio (consisting of all resources at all levels of flexibility) that minimizes linear capacity and linear holding costs in high-volume systems where the arrival rate → . We prove that "a little flexibility is all you need": the optimal portfolio invests O in specialized resources and only O √ in flexible resources and these optimal capacity choices bring the system into heavy traffic. Further, considering symmetric systems (with type-independent parameters), a novel "folding" methodology allows the specification of the asymptotic queue count process for any capacity portfolio under longest-queue scheduling in closed form that is amenable to optimization. This allows us to sharpen "a little flexibility is all you need": the asymptotically optimal flexibility configuration for symmetric systems with mild economies of scope invests a lot in specialized resources but only a little in flexible resources and only in level-2 flexibility, but effectively nothing (o √ ) in level-k > 2 flexibility. We characterize "tailored pairing" as the theoretical benchmark configuration that maximizes the value of flexibility when demand and service uncertainty are the main concerns.

We study the classical problem of capacity and flexible technology selection with a newsvendor network model of resource portfolio investment. The resources differ by their level of flexibility, where "level-k flexibility" refers to the ability to process k different product types. We present an exact set-theoretic methodology to analyze newsvendor networks with multiple products and parallel resources. This simple approach is sufficiently powerful to prove that (i) flexibility exhibits decreasing returns and (ii) the optimal portfolio will invest in at most two, adjacent levels of flexibility in symmetric systems, and to characterize (iii) the optimal flexibility configuration for asymmetric systems as well. The optimal flexibility configuration can serve as a theoretical performance benchmark for other configurations suggested in the literature. For example, although chaining is not optimal in our setting, the gap is small and the inclusion of scale economies quickly favors chaining over pairing. We also demonstrate how this methodology can be applied to other settings such as product substitution and queuing systems with parameter uncertainty.inventory production, stochastic models, programming, linear, applications, queues, networks, flexibility, newsvendor networks

We consider queueing systems in which customers arrive according to a Poisson process and have exponentially distributed service requirements. The customers are impatient and may abandon the system while waiting for service after a generally distributed amount of time. The system incurs customer-related costs that consist of waiting and abandonment penalty costs. We study capacity sizing in such systems to minimize the sum of the long-term average customer-related costs and capacity costs. We use fluid models to derive prescriptions that are asymptotically optimal for large customer arrival rates. Although these prescriptions are easy to characterize, they depend intricately upon the distribution of the customers' time to abandon and may prescribe operating in a regime with offered load (the ratio of the arrival rate to the capacity) greater than 1. In such cases, we demonstrate that the fluid prescription is optimal up to O 1. That is, as the customer arrival rate increases, the optimality gap of the prescription remains bounded.

We consider a setting in which consumers experience distinct instances of need for a durable product at random intervals. Each instance of need is associated with a random utility and the consumers are dierentiated according to the frequency with which they experience such instances of need. We use our model of consumer utility to characterize the rm's optimal strategy of whether to sell, rent, or do a combination of both in terms of the transaction costs and consumers' usage characteristics. We nd that the two modes of operation serve dierent roles in allowing the rm to price discriminate. While sales allow the rm to discriminate among consumers of dierent usage frequencies, rentals allow it to discriminate according to consumers' realized valuations. Consequently, even when transaction costs are negligible, it is often optimal for the rm to simultaneously rent and sell its product. In addition, we nd that although sales and rentals are substitutes and that the oering of sales weakly increases rental prices, it is possible that the introduction of rentals to a pure selling operation can either increase or decrease the optimal sales prices.

We study a profit-maximizing firm providing a service to price and delay sensitive customers. We are interested in analyzing the scale economies inherent in such a system. In particular, we study how the firm's pricing and capacity decisions change as the scale, measured by the potential market for the service, increases. These decisions turn out to depend intricately on the form of the delay costs seen by the customers; we characterize these decisions up to the dominant order in the scale for both convex and concave delay costs. We show that when serving customers on a first-come, first-served basis, if the customers' delay costs are strictly convex, the firm can increase its utilization and extract profits beyond what it can do when customers' delay costs are linear. However, with concave delay costs, the firm is forced to decrease its utilization and makes less profit than in the linear case. While studying concave delay costs, we demonstrate that these decisions depend on the scheduling policy employed as well. We show that employing the last-come, first-served rule in the concave case results in utilization and profit similar to the linear case, regardless of the actual form of the delay costs.service systems, pricing, capacity planning, large market size, nonlinear delay costs, convex delay costs

We study the value of dynamic pricing to maximize revenues in queueing systems with price- and delay-sensitive customers. The system queue length is visible so that upon arrival, customers decide to join the system based on the congestion and the price at that time. We analyze this problem in the asymptotic regime of large customer market size and capacity. We find that dynamic pricing performs significantly better than static pricing at mitigating the effect of uncertainty. Asymptotically, the revenue in such systems consists of a positive deterministic component and a negative stochastic component, the latter representing the impact of variability. Static pricing leads to the n1/2-scale effect of variability, i.e., the expected steady-state queue length is Kn1/2 for some K > 0, where n represents the system size. However, dynamic pricing can lower this effect of variability to the n1/3-scale. We further show that a simple policy of using only two prices can achieve most of the benefits of dynamic pricing. We also discuss how our results can apply to other dynamic control problems in queueing systems. The e-companion is available at https://doi.org/10.1287/opre.2017.1668 .

This paper studies a rental firm that offers reusable products to price- and quality-of-service-sensitive customers--Netflix or Blockbuster can be thought of as the canonical example. Customers' perception of quality is determined by their likelihood of obtaining the product or service immediately upon request. We study the alternatives of offering either a subscription option that limits the number of concurrent rentals in return for a flat fee per-unit time, or a pay-per-use option with no such restriction. Customers are assumed to desire a nominal usage rate of the product, which they meet by adjusting their request rate in either option. Thus, they have a higher request rate in the subscription option. We propose a Markov chain model for customer behavior under the subscription option equivalent to the standard Poisson model under the pay-per-use option. In a large market setting, assuming exponential demand, we show that using the subscription option is more profitable for the firm. Further, via a numerical study, we show that this assumption is not essential for the result to hold. However, we show that the subscription option does not necessarily dominate the pay-per-use option in quality of service. The firm manages the trade-off between price and quality of service better in the subscription option. Moreover, we show that social welfare and the consumer surplus can also be higher in the subscription option, indicating that both the firm and the consumers can benefit from the subscription option.subscription services, pay-per-use services, operational benefits, pricing, capacity sizing, finite customer population, loss system, on-off model, diffusion approximation