Delay announcements informing customers about anticipated service delays are prevalent in service-oriented systems. How delay announcements can influence customers in service systems is a complex problem which depends on both the dynamics of the underlying queueing system and on the customers’ strategic behavior. We examine this problem of information communication by considering a model in which both the firm and the customers act strategically: the firm in choosing its delay announcement while anticipating customer response, and the customers in interpreting these announcements and in making the decision about when to join the system and when to balk. We characterize the equilibrium language that emerges between the service provider and her customers. The analysis of the emerging equilibria provides new and interesting insights into customer-firm information sharing. We show that even though the information provided to customers is non-verifiable, it improves the profits of the firm and the expected utility of the customers. The robustness of the results is illustrated via various extensions of the model. In particular, studying models with incomplete information on the system parameters allows us also to highlight the role of information provision in managing customer expectations regarding the congestion in the system. Further, the information could be as simple as “High Congestion”/“Low Congestion” announcements, or could be as detailed as the true state of the system.We also show that firms may choose to shade some of the truth by using intentional vagueness to lure customers.

Many service providers use delay announcements to inform customers of anticipated delays. However, this information is usually not provided immediately, but rather after a short period of time (spent either waiting or occupied by the system). The focus of this paper is on the impact of this postponement on the ability of the firm to communicate non-verifiable congestion information to its customers as well as on the profits and utilities for the firm and the customers respectively. We show that this postponement can actually help the firm create credibility and augment the equilibrium language. However, in other settings this delay can also detract the equilibrium language. Further, we show that whenever credibility is created it improves not only the profit for the firm, but also the customers’ overall utility.

Provision of real-time information by a firm to its customers has become prevalent in recent years in both the service and retail sectors. In this paper, we study a retail operations model where customers are strategic in both their actions and in the way they interpret information, whereas the retailer is strategic in the way it provides information. This paper focuses on the ability (or the lack thereof) to communicate unverifiable information and influence customers’ actions. We develop a game-theoretic framework to study this type of communication and discuss the equilibrium language emerging between the retailer and its customers. We show that for a single-retailer and homogeneous customer population setting, the equilibrium language that emerges carries no information. In this sense, a single-retailer providing information on its own cannot create any credibility with the customers. We study how the results are impacted due to the heterogeneity of the customers. We provide conditions under which the firm may be able to influence the customer behavior. In particular, we show that the customers’ willingness-to-pay and willingness-to-wait cannot be ranked in an opposite manner. However, even when the firm can influence each customer class separately, the effective demand is not impacted.

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.

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 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.

In this article, we study threshold-based sales-force incentives and their impact on a dealer’s optimal effort. A phenomenon, observed in practice, is that the dealer exerts a large effort toward the end of the incentive period to boost sales and reach the threshold to make additional profits. In the literature, the resulting last-period sales spike is sometimes called the hockey stick phenomenon (HSP). In this article, we show that the manufacturer’s choice of the incentive parameters and the underlying demand uncertainty affect the dealer’s optimal effort choice. This results in the sales HSP over multiple time periods even when there is a cost associated with waiting. We then show that, by linking the threshold to a correlated market signal, the HSP can be regulated. We also characterize the variance of the total sales across all the periods and demonstrate conditions under the sales variance can be reduced.

Having a robustly designed supply chain network is one of the most effective ways to hedge against network disruptions because contingency plans in the event of a disruption are often significantly limited. In this article, we study the facility reliability problem: how to design a reliable supply chain network in the presence of random facility disruptions with the option of hardening selected facilities.We consider a facility location problem incorporating two types of facilities, one that is unreliable and another that is reliable (which is not subject to disruption, but is more expensive).We formulate this as a mixed integer programming model and develop a Lagrangian Relaxation-based solution algorithm. We derive structural properties of the problem and show that for some values of the disruption probability, the problem reduces to the classical uncapacitated fixed charge location problem. In addition, we show that the proposed solution algorithm is not only capable of solving large-scale problems, but is also computationally effective.

We study a rental system where a fixed number of heterogeneous users rent one product at a time from a collection of reusable products. The online DVD rental firm Netflix provides the motivation. We assume that rental durations of each user are i.i.d. with finite mean. We study transient behavior in this system following the introduction of a new product that is desired by all the users. We represent the usage process for this new product in terms of an empirical distribution. This allows us to characterize the asymptotic behavior of the usage process as the number of users increases without bound, via appropriate versions of Glivenko-Cantelli and Donsker’s theorems. Analyzing the usage process, we demonstrate that an increase in the variability of the rental duration distribution can actually help the firm by allowing it to set lower capacity levels to provide a desired quality of service. Further, we show that the firm is better off not imposing any deadlines for the return of the product.

Generalizing earlier work on staffing and routing in telephone call centers, we consider a processing network with multiple server pools, jobs that may require several processing opera- tions, doubly stochastic input flows, differentiated processing modes, and other features as well. Given a finite planning horizon, we address the two-level problem of capacity choice and dynamic system control. A tractable modeling framework is proposed, in which a pointwise stationary fluid model (PSFM) is used to approximate the system’s dynamics. This framework allows one to develop practical policies with a computational burden that is manageable. Earlier work in more restrictive settings suggests that our method is asymptotically optimal in a parameter regime of practical interest, but this paper contains no formal limit theory. Rather, it develops a PSFM calculus that is broadly accessible, with an emphasis on modeling and practical computation.

We consider a call center model with multiple customer classes and multiple server pools. Calls arrive randomly over time, and the instantaneous arrival rates are allowed to vary both temporally and stochastically in an arbitrary manner. The objective is to minimize the sum of personnel costs and expected abandonment penalties by selecting an appropriate staffing level for each server pools. We propose a simple and computationally tractable method for solving this problem that only requires as input a few system parameters, and historical call arrival data for each customer class; in this sense the method is said to be data-driven. The efficacy of the proposed method is illustrated via numerical examples. An asymptotic analysis establishes that the prescribed staffing levels achieve near-optimal performance and characterizes the magnitude of the optimality gap.

We consider the risk of a portfolio comprised of loans, bonds, and financial instruments that are subject to possible default. In particular, we are interested in the probability that the portfolio will incur large losses over a fixed time horizon. Contrary to the normal copula that is commonly used in practice (e.g., in the CreditMetrics system), we assume a portfolio dependence structure that supports {\it extremal dependence} among obligors and does not hinge solely on correlation. A particular instance within this model class is the so-called $t$-copula model that is derived from the multivariate Student $t$ distribution and hence generalizes the normal copula model. The size of the portfolio, the heterogenous mix of obligors, and the fact that default events are rare and mutually dependent makes it quite complicated to calculate portfolio credit risk either by means of exact analysis or naive Monte Carlo simulation. The main contributions of this paper are twofold. We first derive sharp asymptotics for portfolio credit risk that illustrate the implications of extremal dependence among obligors. Using this as a stepping stone, we develop multi-stage importance sampling algorithms that are shown to be asymptotically optimal and can be used to efficiently compute portfolio credit risk via Monte Carlo simulation.

We consider importance sampling simulation for estimating rare event probabilities in the presence of heavy-tailed distributions that have polynomial-like tails. In particular, we prove the following negative result: there does not exist an asymptotically optimal state-independent change-of-measure for estimating the probability that a random walk (respectively, queue length for a single server queue) exceeds a "high" threshold before going below zero (respectively, becoming empty). Furthermore, we derive explicit bounds on the best asymptotic variance reduction achieved by importance sampling relative to naive simulation. We illustrate through a simple numerical example that a good" state-dependent change-of-measure may be developed based on an approximation of the zero-variance measure

This paper analyzes a call center model with m customer classes and r agent pools. The model is one with doubly stochastic arrivals, which means that the m-vector λ of instantaneous arrival rates is allowed to vary both temporally and stochastically. Two levels of call center management are considered: staffing the r pools of agents, and dynamically routing calls to agents. The system manager’s objective is to minimize the sum of personnel costs and abandonment penalties. We consider a limiting parameter regime that is natural for call centers and relatively easy to analyze, but apparently novel in the literature of applied probability. For that parameter regime, we prove an asymptotic lower bound on expected total cost, which uses a strikingly simple distillation of the original system data. We then propose a method for staffing and routing based on linear programming (LP), and show that it achieves the asymptotic lower bound on expected total cost; in that sense the proposed method is asymptotically optimal.

This paper analyzes a call center model with m customer classes and r agent pools. The model is one with doubly stochastic arrivals, which means that the m-vector λ of instantaneous arrival rates is allowed to vary both temporally and stochastically. Two levels of call center management are considered: staffing the r pools of agents, and dynamically routing calls to agents. The system manager’s objective is to minimize the sum of personnel costs and abandonment penalties. We consider a limiting parameter regime that is natural for call centers and relatively easy to analyze, but apparently novel in the literature of applied probability. For that parameter regime we prove an asymptotic lower bound on expected total cost, which uses a strikingly simple distillation of the original system data. We then propose a method for staffing and routing based on linear programming (LP), and show that it achieves the asymptotic lower bound on expected total cost; in that sense the proposed method is asymptotically optimal.

Motivated by applications in telephone call centers, we consider a service system model with m customer classes and r server pools. The model is one with doubly stochastic arrivals, which means that the m-vector λ of instantaneous arrival rates is allowed to vary both temporally and stochastically. Two levels of dynamic control are considered: customers may be either blocked or accepted at the time of their arrival, and then accepted customers of each class must be routed, either immediately upon acceptance or after some period of waiting, to a server pool that is qualified to handle that class. Customers who are made to wait before commencement of their service are liable to defect. The objective is to minimize the expected sum of blocking costs, waiting costs and defection costs over a fixed and finite planning horizon. We consider an asymptotic parameter regime in which (i) the arrival rates, service rates and defection rates are uniformly accelerated by a large factor κ, then (ii) arrival rates are increased by an additional factor g(κ), and the number of servers in each pool is increased by g(κ) as well. This produces a separation of time scales, justifying a pointwise stationary stochastic fluid approximation for our original system model. In the stochastic fluid approximation, optimal admission control and routing decisions are determined by a simple linear program that uses the current arrival rate vector λ as data. We explain how to implement the fluid model’s optimal control policy in our original service system context, and prove that the proposed implementation is asymptotically optimal in the first-order sense.

We study the problem of optimal flexibility capacity portfolio selection by introducing a new notion of submodularity in correspondences, which extends the classical notion of submodular functions. In particular, we prove that the correspondence that maps flexible resources to the set of demands that they can process is submodular, and use the properties of submodular correspondences to compare different flexibility configurations and derive insights into the optimal capacity portfolio.

Motivated by airline baggage fees, we consider a service provider offering a main service (e.g., transporting a person) and an ancillary service (e.g., transporting a checked bag) that an individual customer may or may not need. We ask whether the firm should bundle the two services and post a single price or unbundle them and price the ancillary service separately. We consider two motivations for unbundling the services. The first focuses on altering consumer behavior to lower the firm’s costs. We assume that providing the ancillary service is costly but consumers can exert effort in order to reduce the rate at which the ancillary service is needed. We show that the firm unbundles and sets the fee for the ancillary service at the same level the social planner would. Profit maximization thus results in social efficiency. The second rationale for unbundling is segmentation. We assume that there are two segments that differ in the rate at which they use the ancillary service. The optimal contracts impose higher ancillary service fees on those less likely to use the service. In the airline setting, this would imply that business travelers would face higher baggage fees than leisure travelers. We conclude that the way in which airlines have implemented baggage fees is more consistent with attempts to control consumer behavior than segment customers.

The traditional economics and queueing literature typically assume that customers are fully rational. In contrast, in this paper, we study canonical service models with boundedly rational customers. We capture bounded rationality using a framework in which better decisions are made more often, while the best decision needs not always be made. We investigate the impact of bounded rationality on social welfare and revenue of a profit maximizing firm when the queue is visible and not visible to the customers. For invisible queues, from the firm’s perspective, higher bounded rationality always leads to higher optimal prices and higher revenue when customers are sufficiently boundedly rational. From the social planner’s perspective, there may be strictly positive social welfare losses when customers are sufficiently boundedly rational. For visible queues with a fixed price, we prove that a little bit of bounded rationality can lead to strict social welfare improvement, and we provide a simple inequality under which this improvement happens. With the optimal prices, however, bounded rationality always decreases social welfare, and a little bit of bounded rationality always results in revenue losses. We demonstrate that ignoring bounded rationality may result in significant revenue and social welfare loss.

Recent times have witnessed the emergence of large-scale, web-based service marketplaces where many small service providers compete among themselves on catering to customers with diverse needs. Customers who frequent these marketplaces seek quick resolutions and thus usually trade-off prices with waiting times. The main goal of the paper is to discuss the role of the moderating firm in facilitating information gathering, operational efficiency, and communication among agents. Surprisingly, operational efficiency may be detrimental to the overall efficiency of the marketplace. Further, we show that to reap the "expected" gains of operational efficiency, the moderating firm may need to complement the operational efficiency by enabling communication among its agents. The study emphasizes the large-scale of such marketplaces and the impact it has on the outcomes.

In this paper, we extend the concept of chaining introduced by Jordan and Graves (1995) for designing a robust supply chain network in which the link and nodes are susceptible to disruptions. We introduce the concept of fragility to quantify the change in system performance resulting from a disruption. Although one may anticipate that networks with longer chains will be more robust (smaller fragility) than shorter ones, our study reveals that this is not always true. We show that the fragility with respect to a single link failure decreases as the size of the chain decreases; however, the fragility with respect to a single node failure increases as the size of the chain increases. We also show that multiple failures in a network can be decomposed into a set of multiple subnetworks with a single failure; hence we can analyze the impact of large-scale disruptions by studying each single failure networks. Simulation experiments are used to extend insights from single link or node failures to multiple failure cases.

We analyze the problem of product allocation to customers following the introduction of a new product in a closed rental system, such as Netflix. We consider two types of customers who differ in their rental time distributions. All customers desire the newly introduced product, and if a customer’s request for this product is denied, she receives a substitute product and requests for the new product upon return. We study the control problem of minimizing the mean delay encountered by customers before obtaining the new product in a large market setting. We show that asymptotically this problem is equivalent to solving a linear program that depends on the entire rental duration distribution as opposed to mean alone. The optimal policy turns out to be a mixed priority rule that prioritizes the slower customer class while maintaining a base allocation to the faster customer class to ensure quick return.

In recent times due to the commoditization of goods, many traditional firms often offer services as well. In this paper, we study the role of services apart from being another revenue source and understand how to manage services. We first understand their role in pricing of the underlying good. Next we study the impact of services on good variety offered by the firm. Lastly, we study the impact of services on markets of durable goods with its specific characteristics. We characterize the optimal behavior of the firm and relate that to concepts of bundling and market segmentation. We show that existence of services help firms offer a wider variety of underlying goods. Further, we show that in the market of durable goods, offering service resolve some of key problems such as time inconsistency.