Optimization of a Call Centre Performance Using the Stochastic Queueing Models

Background: A call centre usually represents the first contact of a customer with a given company. Therefore, the quality of its service is of key importance. An essential factor of the call centre optimization is the determination of the proper number of operators considering the selected performance measure. Results of previous research show that this can be done using the queueing theory approach. Objectives: The paper presents the practical application of the stochastic queueing models aimed at optimizing a Slovenian telecommunication provider’s call centre. Methods/Approach: The arrival and the service patterns were analysed, and it was concluded that the call centre under consideration can be described using the M/M/r {infinity/infinity/FIFO} queueing model. Results: An appropriate number of operators were determined for different peak periods of the working day, taking into consideration the following four performance measures: the expected waiting time, the expected number of waiting customers, the probability that a calling customer will have to wait, and the call centre service level. Conclusions: The obtained results prove the usefulness and applicability of the queueing models as a tool for a call centre performance optimization. In practice, all the data needed for such a mathematical analysis are usually provided. This paper is aimed at illustrating how such data can be efficiently exploited

Arbeitsbericht Nr. 2020-02, März 2020

Determining size and structure of a company’s workforce is one of the most challenging tasks in human resource planning, especially when considering a long-term planning horizon with varying demand. In this paper an approach for integrated staffing and scheduling in a strategic long-term context is presented by applying evolutionary bilevel optimization. For demonstration, the example of determining the number of employees in different categories over the period of one year in a midsized call center of a utility is used. In doing so, two contrary objectives were optimized simultaneously: reduce the overall workforce costs and retain a high scheduling quality. The results show that the proposed approach could be used to support corporate decision making related to strategic workforce planning, not only for call centers but for any other kind of workforce planning involving personnel scheduling

Modelización, Simulación y Optimización del personal operativo en la administración de Call/Contact Center

El presente trabajo expone una descripción del proceso de la estimación óptima de los requerimientos de agentes, y se analiza a través de la simulación el problema de la programación de turnos de trabajos, desde la perspectiva de la programación matemática no lineal, para la administración efectiva y eficiente del recurso humano en los Centros de Llamadas o Contactos Telefónicos (Telephone Call/Contact Centers). La simulación que se implementa lleva a cabo dos procesos de optimización: 1) La determinación óptima de los recursos humanos necesarios para la atención de los clientes, que se materializa con la resolución de un modelo de programación lineal. 2) La determinación de la política más adecuada para la asignación de turnos, bajo la restricción de mantener un cierto nivel de servicio. Para éste último, se utiliza el método de las Combinaciones Lineales basadas en función objetivo no lineal y restricciones lineales convexas. El software de simulación que se implementó, está basado en la técnica de simulación de eventos discretos permitiendo un diseño visual de los modelos de análisis. El aporte significativo y novedoso del trabajo, se orienta hacia la utilización de técnicas sencillas de la Programación Matemática No Lineal en la programación de turnos, y el uso de la herramienta de simulación para hacer una predicción precisa de los requerimientos de personal y la asignación de turnos.Sociedad Argentina de Informática e Investigación Operativ

Modelling for the proposed roll-out of the ‘111’ service in Wales: a case study

NHS Direct Wales provides a single point of access where members of the public can telephone and seek medical support and/or advice. The service is provided for all the Health Boards in Wales by a single virtual call centre run from a main location in Swansea with 2 satellite locations. Patients in Wales can also access a local General Practitioner service during the evenings and at weekends, by phoning their Out of Hours service. The introduction of a ‘111’ service is intended to combine these two operations on a pan-Wales basis using the existing NHS Direct Wales call centre and staff, with the existing Health Board Out of Hours ‘hubs’. The merger of the two services is intended to improve the overall performance of both services. This paper focuses on the planned introduction of ‘111’ in Cwm Taf and Hywel Dda University Health Boards. The purpose of the case study was to support the merger of the two telephony systems from both an organisational and service delivery perspective, by developing a Discrete Event Simulation to model the impact on service levels and staffing. In particular, to examine the percentage increase / decrease in the staffing requirements needed under partial or full integration of the two services. The results from the scenario analysis highlight that extra staffing resources would be required in certain groups (nurses and call handlers) whilst savings could be achieved in others, provided that there wasn’t an increase in call volume after implementation of the new service

Forecasting call center arrivals: Fixed-effects, mixed-effects, and bivariate models

Abstract We consider different statistical models for the call arrival process in telephone call centers. We evaluate the forecasting accuracy of those models by describing results from an empirical study analyzing real-life call center data. We test forecasting accuracy using different lead times, ranging from weeks to hours in advance, to mimic real-life challenges faced by call center managers. The models considered are: (i) a benchmark fixed-effects model which does not exploit any dependence structures in the data; (i) a mixed-effects model which takes into account both interday (day-to-day) and intraday (within day) correlations; (ii) two new bivariate mixed-effects models, for the joint distribution of the arrival counts to two separate queues, which exploit correlations between different call types. Our study shows the importance of accounting for different correlation structures in the data

Forecasting call center arrivals: Fixed-effects, mixed-effects, and bivariate models

Abstract We consider different statistical models for the call arrival process in telephone call centers. We evaluate the forecasting accuracy of those models by describing results from an empirical study analyzing real-life call center data. We test forecasting accuracy using different lead times, ranging from weeks to hours in advance, to mimic real-life challenges faced by call center managers. The models considered are: (i) a benchmark fixed-effects model which does not exploit any dependence structures in the data; (ii) a mixed-effects model which takes into account both interday (day-to-day) and intraday (within day) correlations; (iii) two new bivariate mixed-effects models, for the joint distribution of the arrival counts to two separate queues, which exploit correlations between different call types. Our study shows the importance of accounting for different correlation structures in the data

Optimizing daily agent scheduling in a multiskill call center

We examine and compare simulation-based algorithms for solving the agent scheduling problem in a multiskill call center. This problem consists in minimizing the total costs of agents under constraints on the expected service level per call type, per period, and aggregated. We propose a solution approach that combines simulation with integer or linear programming, with cut generation. In our numerical experiments with realistic problem instances, this approach performs better than all other methods proposed previously for this problem. We also show that the two-step approach, which is the standard method for solving this problem, sometimes yield solutions that are highly suboptimal and inferior to those obtained by our proposed method.<br/

Programación de agentes de un call center con prestación del servicio de asignación de citas

Se desarrolla una metodología que permita programar los agentes necesarios para cubrir los requerimientos de la demanda de llamadas que ingresan a un Call Center encargado de la prestación del servicio de asignación de citas de una EPS con presencia en Colombia.MaestríaMAGISTER EN INGENIERÍA ÉNFASIS INGENIERÍA INDUSTRIA

Modelo matemático para a gestão de escalas de serviço para controladores de tráfego aéreo

Orientador: Prof. Dr. José Eduardo Pécora JuniorCoorientador: Prof. Dr. Cassius Tadeu ScarpinDissertação (mestrado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Engenharia de Produção. Defesa : Curitiba, 28/02/2020Inclui referências: p.62-64Resumo: O espaço aéreo sob responsabilidade brasileira passa dos 20.000.000 km² (vinte milhões de km²) e para garantir a segurança de todas as aeronaves no espaço aéreo durantes as diversas fases do voo, os Serviços de Tráfego Aéreo funcionam ininterruptamente, sendo necessário que os profissionais desta área trabalhem em regime de escalas. Estudos indicam que profissionais sujeitos a esse regime de trabalho sofrem efeitos em decorrência de fatores relacionados aos horários irregulares, incluindo trabalhos noturnos. Este trabalho apresenta um modelo matemático de programação linear inteira misto desenvolvido para a designação de escalas de serviço para operadores de um Centro de Controle de Área, onde se realiza o controle de tráfego aéreo. A proposição deste modelo objetiva a maximização das preferências declaradas pelos Controladores e a redução dos custos, considerando restrições opcionais ou de qualidade (restrições soft) e restrições obrigatórias (restrições hard). As declarações de preferências dos operadores pelas designações foram alvo de um estudo buscando identificar qual a melhor composição das declarações para uma boa gestão das escalas em questões de satisfação com o trabalho e qualidade de vida dos profissionais. Foram definidos os cenários para análise e as instâncias para testes em tamanho real, com 120 trabalhadores e considerando um horizonte de planejamento de um mês. O modelo demonstrou capacidade de utilização e encontrou soluções ótimas em grande parte das instâncias em tempos computacionais considerados baixos em média. Dois cenários foram escolhidos como os melhores para a gestão das escalas de serviço, a partir da análise das soluções encontradas, identificou-se que o modelo é capaz de atender 83% das preferências indicadas pelos profissionais, proporcionando aumento na satisfação com o trabalho. O modelo também possibilita que os profissionais tenham mais liberdade na gestão dos horários de trabalho, uma vez que é possível indicar combinações de suas preferências para folgas, tendo em vista que essas indicações foram atendidas em mais de 99% dos casos. Estes resultados demonstram que o modelo é uma ferramenta adequada para a gestão das escalas de serviço para Controladores de Tráfego Aéreo minimizando os efeitos negativos relacionados ao regime de trabalho por escalas, como a redução dos níveis de fadiga, melhora na qualidade do sono e no bem-estar no trabalho, melhores condições para participar de atividades de lazer, entre outros. Palavras-chave: Escala de Serviço. Controle de Tráfego Aéreo. Programação Linear Inteira Mista. Qualidade de Vida no Trabalho.Abstract: The airspace under Brazilian responsibility goes from 20,000,000 km² (twenty million km²) and to guarantee the safety of all aircraft in the airspace during the various phases of the flight, the Air Traffic Services operate around the clock, being necessary that the professionals work in scales. Studies indicate that professionals subject to this work regime suffer effects due to factors related to irregular hours, including night work. This work presents a mathematical model of mixed integer linear programming developed for the designation of shifts work for Air Traffic Controllers in a center control, which aims to maximize the preferences declared by workers and reduce costs, considering optional or quality restrictions (soft constraints) and mandatory restrictions (hard constraints). The operators' declarations of preference for the designations were the subject of a study seeking to identify the best composition of the declarations for a good management of the shifts in matters of satisfaction with the work and quality of life of the professionals. Scenarios for analysis and instances for life-size tests were defined, with 120 workers and considering a planning horizon of one month. The model demonstrated usability and found optimal solutions in most instances in computational times considered low on average. Two scenarios were chosen as the best ones for the management of shifts schedules, from the analysis of the results found. It was identified that the model is capable of meeting 83% of the preferences indicated by the professionals, providing an increase in job satisfaction. The model also allows professionals to have more freedom in the management of working hours, since it is possible to indicate combinations of their preferences for time off, given that these indications were met in more than 99% of cases. These results demonstrate that the model is an adequate tool for the management of shift scheduling for Air Traffic Controllers, minimizing the negative effects related to the work regime by scales, such as the reduction of fatigue levels, improvement in the quality of sleep and well-being at work, better conditions to participate in leisure activities, among others. Keywords: Shift Scheduling. Air Traffic Control. Mixed Integer Linear Programming. Quality of Life at Work