Achal Bassamboo

Design and Control of a Large Call Center: Asymptotic Analysis of an LP-Based Method

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 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 managers 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.

Dynamic Routing and Admission Control in High-Volume Service Systems: Asymptotic Analysis via Multi-Scale Fluid Limits

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 models optimal control policy in our original service system context, and prove that the proposed implementation is asymptotically optimal in the first-order sense.

Portfolio Credit Risk with Extremal Dependence: Asymptotic Analysis and Efficient Simulation

We consider the risk of a portfolio comprising loans, bonds, and financial instruments that are subject to possible default. In particular, we are interested in performance measures such as the probability that the portfolio incurs large losses over a fixed time horizon, and the expected excess loss given that large losses are incurred during this 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 is semiparametric, does not hinge solely on correlation, and supports extremal dependence among obligors. A particular instance within the proposed class of models 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 heterogeneous mix of obligors, and the fact that default events are rare and mutually dependent make 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 importance-sampling algorithms that are shown to be asymptotically optimal and can be used to efficiently compute portfolio credit risk via Monte Carlo simulation.

Facility Location Decisions with Random Disruptions and Imperfect Estimation

Supply chain disruptions come with catastrophic consequences in spite of their low probability of occurrence. In this paper, we consider a facility location problem in the presence of random facility disruptions where facilities can be protected with additional investments. Whereas most existing models in the literature implicitly assume that the disruption probability estimate is perfectly accurate, we investigate the impact of misestimating the disruption probability. Using a stylized continuous location model, we show that underestimation in disruption probability results in greater increase in the expected total cost than overestimation. In addition, we show that, when planned properly, the cost of mitigating the misestimation risk is not too high. Under a more generalized setting incorporating correlated disruptions and finite capacity, we numerically show that underestimation in both disruption probability and correlation degree result in greater increase in the expected total cost compared to overestimation. We, however, find that the impact of misestimating the correlation degree is much less significant relative to that of misestimating the disruption probability. Thus, managers should focus more on accurately estimating the disruption probability than the correlation.

Optimal Flexibility Configurations in Newsvendor Networks: Going Beyond Chaining and Pairing

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.

Capacity Sizing Under Parameter Uncertainty: Safety Staffing Principles Revisited

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.

On a Data-Driven Method for Staffing Large Call Centers

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 pool. We propose a simple and computationally tractable method for solving this problem that requires as input only 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.

Bounded Rationality in Service Systems

The traditional operations management and queueing literature typically assumes 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 model in which customers are incapable of accurately estimating their expected waiting time. We investigate the impact of bounded rationality from both a profit-maximizing firms perspective and a social planners perspective. For visible queues with the optimal price, bounded rationality results in revenue and welfare loss; with a fixed price, bounded rationality can lead to strict social welfare improvement. For invisible queues, bounded rationality benefits the firm when its level is sufficiently high. Ignoring bounded rationality, when present yet small, can result in significant revenue and welfare loss.

A Little Flexibility Is All You Need: On the Asymptotic Value of Flexible Capacity in Parallel Queuing Systems

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 resources 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 λ → ∞. We prove that “a little flexibility is all you need”: the optimal portfolio invests Oλ in specialized resources and only O√λ 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√λ 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.

How Do Delay Announcements Shape Customer Behavior? An Empirical Study

In this paper, we explore the impact of delay announcements using an empirical approach by analyzing the data from a medium-sized call center. We first explore the question of whether delay announcements impact customers’ behavior using a nonparametric approach. The answer to this question appears to be ambiguous. We thus turn to investigate the fundamental mechanism by which delay announcements impact customer behavior, by constructing a dynamic structural model. In contrast to the implicit assumption made in the literature that announcements do not directly impact customers’ waiting costs, our key insights show that delay announcements not only impact customers’ beliefs about the system but also directly impact customers’ waiting costs. In particular, customers’ per-unit waiting cost decreases with the offered waiting times associated with the announcements. The results of our counterfactual analysis show that it may not be necessary to provide announcements with very fine granularity. This paper was accepted by Yossi Aviv, operations management .