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 In the former case it is shown that traditional square-root safety staffing logic is no longer valid, yet simple capacity prescriptions derived via a suitable newsvendor problem are surprisingly accurate.service systems, capacity sizing, parameter uncertainty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.