16 research outputs found
Fluid Approximation of a Call Center Model with Redials and Reconnects
In many call centers, callers may call multiple times. Some of the calls are
re-attempts after abandonments (redials), and some are re-attempts after
connected calls (reconnects). The combination of redials and reconnects has not
been considered when making staffing decisions, while ignoring them will
inevitably lead to under- or overestimation of call volumes, which results in
improper and hence costly staffing decisions. Motivated by this, in this paper
we study call centers where customers can abandon, and abandoned customers may
redial, and when a customer finishes his conversation with an agent, he may
reconnect. We use a fluid model to derive first order approximations for the
number of customers in the redial and reconnect orbits in the heavy traffic. We
show that the fluid limit of such a model is the unique solution to a system of
three differential equations. Furthermore, we use the fluid limit to calculate
the expected total arrival rate, which is then given as an input to the Erlang
A model for the purpose of calculating service levels and abandonment rates.
The performance of such a procedure is validated in the case of single
intervals as well as multiple intervals with changing parameters
A Note on an M/M/s Queueing System with two Reconnect and two Redial Orbits
A queueing system with two reconnect orbits, two redial (retrial) orbits, s servers and two independent Poisson streams of customers is considered. An arriving customer of type i, i = 1, 2 is handled by an available server, if there is any; otherwise, he waits in an infinite buffer queue. A waiting customer of type i who did not get connected to a server will lose his patience and abandon after an exponentially distributed amount of time, the abandoned one may leave the system (lost customer) or move into one of the redial orbits, from which he makes a new attempt to reach the primary queue, and when a customer finishes his conversation with a server, he may comeback to the system, to one of the reconnect orbits where he will wait for another service. In this paper, a fluid model is used to derive a first order approximation for the number of customers in the redial and reconnect orbits in the heavy traffic. The fluid limit of such a model is a unique solution to a system of three differential equations
Call Center Experience Optimization: A Case for a Virtual Predictive Queue
The evolution of the call center into contact centers and the growth of their use in providing customer-facing service by many companies has brought considerable capabilities in maintaining customer relationships but it also has brought challenges in providing quality service when call volumes are high. Limited in their ability to provide service at all times to all customers, companies are forced to balance the costs associated with hiring more customer service representatives and the quality of service provided by a fewer number. A primary challenge when there are not enough customer service representatives to engage the volume of callers in a timely manner is the significant wait times that can be experienced by many customers. Normally, callers are handled in accordance with a first-come, first-served policy with exceptions being skill-based routing to those customer service representatives with specialized skills. A proposed call center infrastructure framework called a Virtual Predictive Queue (VPQ) can allow some customers to benefit from a shorter call queue wait time. This proposed system can be implemented within a call center’s Automatic Call Distribution (ACD) device associated with computer telephony integration (CTI) and theoretically will not violate a first-come, first served policy
Qualitative Strategy for Inbound Call Center Outsourcing
An analysis of the various challenges of the call center industry, together with the challenges of outsourcing, revealed a need for developing a strategy that acts as a guide for organizations that are willing to outsource their call center operations. This research therefore develops a strategy for this purpose. The research first provides mitigation strategies for the challenges of outsourcing and the challenges of the call center industry, followed by a strategy for the outsourcing of call center services.
Telephone call centers are an integral part of today‘s business world, serving as a primary channel for customer contact for organizations in many industries. Globalization, the advancements in the telecommunication and technology industries, and the availability of cost effective work forces around the world are compelling organizations to outsource their functions (call center services) to reap the benefits that come with outsourcing.
Organizations outsource functions, especially a function that is not their core competence, for a multitude of reasons. These reasons may include cost savings, quality enhancement/improvement, reduced time to market, tax benefits, and risk management.
Outsourcing also comes with its share of issues. A few examples of the challenges involved in outsourcing include cultural differences, knowledge transfer to suppliers while protecting intellectual property (IP), knowledge retention, language barriers, ethics, norms of behavior, distance and time zones, infrastructure, privacy and security, skill set/quality, objectivity, geopolitical climate, labor backlash, communication, end-user resistance, and governance. There are also many challenges associated with the call center industry, such as, but not limited to, deploying the right number of staff members with the right skills to the right schedules in order to meet an uncertain and time-varying demand of service, forecasting traffic, acquiring capacity, deploying resources, and managing service delivery. Therefore, despite the advancements in telecommunications and information technology, the challenges faced by client organizations that outsource their inbound call center services abound.
While choosing outsourcing/offshoring as their strategy, an organization can avoid many of the disadvantages that arise due these risks/issues by adapting a proactive and careful approach such as the strategy developed in this research
Stochastic optimization of staffing for multiskill call centers
Dans cette thèse, nous étudions le problème d’optimisation des effectifs dans les centres d’appels, dans lequel nous visons à minimiser les coûts d’exploitation tout en offrant aux clients une qualité de service (QoS) élevée. Nous introduisons également l'utilisation de contraintes probabilistes qui exigent que la qualité de service soit satisfaite avec une probabilité donnée. Ces contraintes sont adéquates dans le cas où la performance est mesurée sur un court intervalle de temps, car les mesures de QoS sont des variables aléatoires sur une période donnée. Les problèmes de personnel proposés sont difficiles en raison de l'absence de forme analytique pour les contraintes probabilistes et doivent être approximées par simulation. En outre, les fonctions QoS sont généralement non linéaires et non convexes. Nous considérons les problèmes d’affectation personnel dans différents contextes et étudions les modèles proposés tant du point de vue théorique que pratique. Les méthodologies développées sont générales, en ce sens qu'elles peuvent être adaptées et appliquées à d'autres problèmes de décision dans les systèmes de files d'attente.
La thèse comprend trois articles traitant de différents défis en matière de modélisation et de résolution de problèmes d'optimisation d’affectation personnel dans les centres d'appels à compétences multiples. Les premier et deuxième article concernent un problème d'optimisation d'affectation de personnel en deux étapes sous l'incertitude. Alors que dans le second, nous étudions un modèle général de programmation stochastique discrète en deux étapes pour fournir une garantie théorique de la consistance de l'approximation par moyenne échantillonnale (SAA) lorsque la taille des échantillons tend vers l'infini, le troisième applique l'approche du SAA pour résoudre le problème d’optimisation d'affectation de personnel en deux étapes avec les taux d’arrivée incertain. Les deux articles indiquent la viabilité de l'approche SAA dans notre contexte, tant du point de vue théorique que pratique.
Pour être plus précis, dans le premier article, nous considérons un problème stochastique discret général en deux étapes avec des contraintes en espérance. Nous formulons un problème SAA avec échantillonnage imbriqué et nous montrons que, sous certaines hypothèses satisfaites dans les exemples de centres d'appels, il est possible d'obtenir les solutions optimales du problème initial en résolvant son SAA avec des échantillons suffisamment grands. De plus, nous montrons que la probabilité que la solution optimale du problème de l’échantillon soit une solution optimale du problème initial tend vers un de manière exponentielle au fur et à mesure que nous augmentons la taille des échantillons. Ces résultats théoriques sont importants, non seulement pour les applications de centre d'appels, mais également pour d'autres problèmes de prise de décision avec des variables de décision discrètes.
Le deuxième article concerne les méthodes de résolution d'un problème d'affectation en personnel en deux étapes sous incertitude du taux d'arrivée. Le problème SAA étant coûteux à résoudre lorsque le nombre de scénarios est important. En effet, pour chaque scénario, il est nécessaire d'effectuer une simulation pour estimer les contraintes de QoS. Nous développons un algorithme combinant simulation, génération de coupes, renforcement de coupes et décomposition de Benders pour résoudre le problème SAA. Nous montrons l'efficacité de l'approche, en particulier lorsque le nombre de scénarios est grand.
Dans le dernier article, nous examinons les problèmes de contraintes en probabilité sur les mesures de niveau de service. Notre méthodologie proposée dans cet article est motivée par le fait que les fonctions de QoS affichent généralement des courbes en S et peuvent être bien approximées par des fonctions sigmoïdes appropriées. Sur la base de cette idée, nous avons développé une nouvelle approche combinant la régression non linéaire, la simulation et la recherche locale par région de confiance pour résoudre efficacement les problèmes de personnel à grande échelle de manière viable. L’avantage principal de cette approche est que la procédure d’optimisation peut être formulée comme une séquence de simulations et de résolutions de problèmes de programmation linéaire. Les résultats numériques basés sur des exemples réels de centres d'appels montrent l'efficacité pratique de notre approche.
Les méthodologies développées dans cette thèse peuvent être appliquées dans de nombreux autres contextes, par exemple les problèmes de personnel et de planification dans d'autres systèmes basés sur des files d'attente avec d'autres types de contraintes de QoS. Celles-ci soulèvent également plusieurs axes de recherche qu'il pourrait être intéressant d'étudier. Par exemple, une approche de regroupement de scénarios pour atténuer le coût des modèles d'affectation en deux étapes, ou une version d'optimisation robuste en distribution pour mieux gérer l'incertitude des données.In this thesis, we study the staffing optimization problem in multiskill call centers, in which we aim at minimizing the operating cost while delivering a high quality of service (QoS) to customers. We also introduce the use of chance constraints which require that the QoSs are met with a given probability. These constraints are adequate in the case when the performance is measured over a short time interval as QoS measures are random variables in a given time period. The proposed staffing problems are challenging in the sense that the stochastic constraints have no-closed forms and need to be approximated by simulation. In addition, the QoS functions are typically non-linear and non-convex. We consider
staffing optimization problems in different settings and study the proposed models in both theoretical and practical aspects. The methodologies developed are general, in the sense that they can be adapted and applied to other staffing/scheduling problems in queuing-based systems.
The thesis consists of three articles dealing with different challenges in modeling and solving staffing optimization problems in multiskill call centers.
The first and second articles concern a two-stage staffing optimization problem under uncertainty. While in the first one, we study a general two-stage discrete stochastic programming model to provide a theoretical guarantee for the consistency of the sample average approximation (SAA) when the sample sizes go to infinity, the second one applies the SAA approach to solve the two-stage staffing optimization problem under arrival rate uncertainty. Both papers indicate the viability of the SAA approach in our context, in both theoretical and practical aspects.
To be more precise, in the first article, we consider a general two-stage discrete stochastic problem with expected value constraints. We formulate
its SAA with nested sampling. We show that under some assumptions that hold in call center examples, one can obtain the optimal solutions of the original problem by solving its SAA with large enough sample sizes. Moreover, we show that the probability that the optimal solution of the sample problem is an optimal solution of the original problem, approaches one exponentially fast as we increase the sample sizes. These theoretical findings are important, not only for call center applications, but also for other decision-making problems with discrete decision variables.
The second article concerns solution methods to solve a two-stage staffing problem under arrival rate uncertainty. It is motivated by the fact that the SAA version of the two-stage staffing problem becomes expensive to solve with a large number of scenarios, as for each scenario, one needs to use simulation to approximate the QoS constraints. We develop an algorithm that combines simulation, cut generation, cut strengthening and Benders decomposition to solve the SAA problem. We show the efficiency of the approach, especially when the number of scenarios is large.
In the last article, we consider problems with chance constraints on the service level measures. Our methodology proposed in this article is motivated by the fact that the QoS functions generally display ``S-shape'' curves and might be well approximated by appropriate sigmoid functions. Based on this idea, we develop a novel approach that combines non-linear regression, simulation and trust region local search to efficiently solve large-scale staffing problems in a viable way. The main advantage of the approach is that the optimization procedure can be formulated as a sequence of steps of performing simulation and solving linear programming models. Numerical results based on real-life call center examples show the practical viability of our approach.
The methodologies developed in this thesis can be applied in many other settings, e.g., staffing and scheduling problems in other queuing-based systems with other types of QoS constraints. These also raise several research directions that might be interesting to investigate. For examples, a clustering approach to mitigate the expensiveness of the two-stage staffing models, or a distributionally robust optimization version to better deal with data uncertainty
Queueing Variables and Leave-Without-Treatment Rates in the Emergency Room
Hospitals stand to lose millions of dollars in revenue due to patients who leave without treatment (LWT). Grounded in queueing theory, the purpose of this correlational study was to examine the relationship between daily arrivals, daily staffing, triage time, emergency severity index (ESI), rooming time, door-to-provider time (DTPT), and LWT rates. The target population comprised patients who visited a Connecticut emergency room between October 1, 2017, and May 31, 2018. Archival records (N = 154) were analyzed using multiple linear regression analysis. The results of the multiple linear regression were statistically significant, with F(9,144) = 2902.49, p \u3c .001, and R2 = 0.99, indicating 99% of the variation in LWT was accounted for by the predictor variables. ESI levels were the only variables making a significant contribution to the regression model. The implications for positive social change include the potential for patients to experience increased satisfaction due to the high quality of care and overall improvement in public health outcomes. Hospital leaders might use the information from this study to mitigate LWT rates and modify or manage staffing levels, time that patients must wait for triage, room placement, and DTPT to decrease the rate of LWT in the emergency room
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Asymptotic Analysis of Service Systems with Congestion-Sensitive Customers
Many systems in services, manufacturing, and technology, feature users or customers sharing a limited number of resources, and which suffer some form of congestion when the number of users exceeds the number of resources. In such settings, queueing models are a common tool for describing the dynamics of the system and quantifying the congestion that results from the aggregated effects of individuals joining and leaving the system. Additionally, the customers themselves may be sensitive to congestion and react to the performance of the system, creating feedback and interaction between individual customer behavior and aggregate system dynamics.This dissertation focuses on the modeling and performance of service systems with congestion-sensitive customers using large-scale asymptotic analyses of queueing models. This work extends the theoretical literature on congestion-sensitive customers in queues in the settings of service differentiation and observational learning and abandonment. Chapter 2 considers the problem of a service provider facing a heterogeneous market of customers who differ based on their value for service and delay sensitivity. The service provider seeks to find the revenue maximizing level of service differentiation (offering different price-delay combinations). We show that the optimal policy places the system in heavy traffic, but at substantially different levels of congestion depending on the degree of service differentiation. Moreover, in a differentiated offering, the level of congestion will vary substantially between service classes. Chapter 3 presents a new model of customer abandonment in which congestion-sensitive customers observe the queue length, but do not know the service rate. Instead, they join the queue and observe their progress in order to estimate their wait times and make abandonment decisions. We show that an overloaded queue with observational learning and abandonment stabilizes at a queue length whose scale depends on the tail of the service time distribution. Methodologically, our asymptotic approach leverages stochastic limit theory to provide simple and intuitive results for optimizing or characterizing system performance. In particular, we use the analysis of deterministic fluid-type queues to provide a first-order characterization of the stochastic system dynamics, which is demonstrated by the convergence of the stochastic system to the fluid model. This also allows us to crisply illustrate and quantify the relative contributions of system or customer characteristics to overall system performance
The Overproduction of Death
In this Article, Professor Liebman concludes that trial actors have strong incentives to – and do – overproduce death sentences, condemning to death men and women who, under state substantive law, do not deserve that penalty. Because trial-level procedural rights do not weaken these incentives or constrain the overproduction that results, it falls to post-trial procedural review – which is ill-suited to the task and fails to feed back needed information to the trial level – to identify the many substantive mistakes made at capital trials. This system is difficult to reform because it benefits both pro-death penalty trial actors (who generate more death sentences than otherwise) and anti-death penalty lawyers (who concentrate their resources on post-trial review proceedings where, given high rates of trial error, they prevail abnormally often). Reforms that focus only on trials or appeals cannot solve the problem. Professor Liebman offers a comprehensive 10-part plan to adjust the skewed incentives and curb the overproduction of death