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

Intelligent Procedures for Intra-Day Updating of Call Center Agent Schedules

For nearly all call centers, agent schedules are typically created several days or weeks prior to the time that agents report to work. After schedules are created, call center resource managers receive additional information that can affect forecasted workload and resource availability. In particular, there is significant evidence, both among practitioners and in the research literature, suggesting that actual call arrival volumes early in a scheduling period (typically an individual day or week) can provide valuable information about the call arrival pattern later in the same scheduling period. In this paper, we develop a flexible and powerful heuristic framework for managers to make intra-day resource adjustment decisions that take into account updated call forecasts, updated agent requirements, existing agent schedules, agents’ schedule flexibility, and associated incremental labor costs. We demonstrate the value of this methodology in managing the trade-off between labor costs and service levels to best meet variable rates of demand for service, using data from an actual call center

Data-driven Service Operations Management

This dissertation concerns data driven service operations management and includes three projects. An important aim of this work is to integrate the use of rigorous and robust statistical methods into the development and analysis of service operations management problems. We develop methods that take into account demand arrival rate uncertainty and workforce operational heterogeneity. We consider the particular application of call centers, which have become a major communication channel between modern commerce and its customers. The developed tools and lessons learned have general appeal to other labor-intensive services such as healthcare. The first project concerns forecasting and scheduling with a single uncertain arrival customer stream, which can be handled by parametric stochastic programming models. Theoretical properties of parametric stochastic programming models with and without recourse actions are proved, that optimal solutions to the relaxed programs are stable under perturbations of the stochastic model parameters. We prove that the parametric stochastic programming approach meets the quality of service constraints and minimizes staffing costs in the long-run. The second project considers forecasting and staffing call centers with multiple interdependent uncertain arrival streams. We first develop general statistical models that can simultaneously forecast multiple-stream arrival rates that exhibit inter-stream dependence. The models take into account several types of inter-stream dependence. With distributional forecasts, we then implement a chance-constraint staffing algorithm to generate staffing vectors and further assess the operational effects of incorporating such inter-stream dependence, considering several system designs. Experiments using real call center data demonstrate practical applicability of our proposed approach under different staffing designs. An extensive set of simulations is performed to further investigate how the forecasting and operational benefits of the multiple-stream approach vary by the type, direction, and strength of inter-stream dependence, as well as system design. Managerial insights are discussed regarding how and when to take operational advantage of the inter-stream dependence. The third project of this dissertation studies operational heterogeneity of call center agents with regard to service efficiency and service quality. The proxies considered for agent service efficiency and service quality are agents' service times and issue resolution probabilities, respectively. Detailed analysis of agents' learning curves of service times are provided. We develop a new method to rank agents' first call resolution probabilities based on customer call-back rates. The ranking accuracy is studied and the comparison with traditional survey-driven methods is discussed.Doctor of Philosoph

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

Operations and Maintenance Optimization of Stochastic Systems: Three Essays

This dissertation presents three essays on topics related to optimally operating and maintaining systems that evolve randomly over time. Two primary areas are considered: (i) joint staffing and pricing strategies for call centers that use co-sourcing to improve service operations and reduce costs; and (ii) optimally maintaining stochastically degrading systems when either multiple systems are associated via a common environment, or when a single-unit system is maintained using a population of heterogeneous spare parts. First we present a queueing and stochastic programming framework for optimally staffing a call center utilizing co-sourced service capacity. The interplay between the call center and external service provider is modeled as a leader-follower game in which the call center, acting as the follower, solves a two-stage stochastic integer program. The problem is reformulated as a quadratically-constrained linear program to obtain the optimal contract prices and the optimal staffing problem yields a closed-form solution. Numerically we demonstrate that significant cost reductions can be achieved, even in the presence of imperfect and asymmetric information. Second the problem of optimally replacing multiple stochastically degrading systems using condition-based maintenance is considered. Properties of the optimal value function and policy motivate a tractable, approximate model with state- and action-space transformations and a basis-function approximation of the action-value function. It is demonstrated that near optimal policies are attainable and significantly outperform heuristics. Finally, we consider the problem of optimally maintaining a stochastically degrading system using spares of varying quality. Conditions are provided under which the optimal value function exhibits monotonicity and the optimal policy is characterized. Numerically we demonstrate the utility of our proposed framework, and provide insights into the optimal policy as an exploration-exploitation type policy

Enabling flexibility through strategic management of complex engineering systems

”Flexibility is a highly desired attribute of many systems operating in changing or uncertain conditions. It is a common theme in complex systems to identify where flexibility is generated within a system and how to model the processes needed to maintain and sustain flexibility. The key research question that is addressed is: how do we create a new definition of workforce flexibility within a human-technology-artificial intelligence environment? Workforce flexibility is the management of organizational labor capacities and capabilities in operational environments using a broad and diffuse set of tools and approaches to mitigate system imbalances caused by uncertainties or changes. We establish a baseline reference for managers to use in choosing flexibility methods for specific applications and we determine the scope and effectiveness of these traditional flexibility methods. The unique contributions of this research are: a) a new definition of workforce flexibility for a human-technology work environment versus traditional definitions; b) using a system of systems (SoS) approach to create and sustain that flexibility; and c) applying a coordinating strategy for optimal workforce flexibility within the human- technology framework. This dissertation research fills the gap of how we can model flexibility using SoS engineering to show where flexibility emerges and what strategies a manager can use to manage flexibility within this technology construct”--Abstract, page iii

An Integrated Approach for Shift Scheduling and Rostering Problems with Break Times for Inbound Call Centers

It may be very difficult to achieve the optimal shift schedule in call centers which have highly uncertain and peaked demand during short time periods. Overlapping shift systems are usually designed for such cases. This paper studies shift scheduling and rostering problems for in bound call centers where overlapping shift systems are used. An integer programming model that determines which shifts to be opened and how many operators to be assigned to these shifts is proposed for the shift scheduling problem. For the rostering problem both integer programming and constraint programming models are developed to determine assignments of operators to all shifts, weekly days-off, and meal and relief break times of the operators. The proposed models are tested on real data supplied by an outsource call center and optimal results are found in an acceptable computation time. An improvement of 15% in the objective function compared to the current situation is observed with the proposed model for the shift scheduling problem. The computational performances of the proposed integer and constraint programming models for the rostering problem are compared using real data observed at a call center and simulated test instances. In addition, benchmark instances are used to compare our Constraint Programming (CP) approach with the existing models. The results of the comprehensive computational study indicate that the constraint programming model runs more efficiently than the integer programming model for the rostering problem. The originality of this research can be attributed to two contributions: (a) a model for shift scheduling problem and two models for rostering problem are presented in detail and compared using real data and (b) the rostering problem is considered as a task-resource allocation and considerably shorter computation times are obtained by modeling this new problem via CP