An exact optimization approach for personnel scheduling problems in the call center industry

Dissertação de mestrado em Engenharia de SistemasNowadays, the importance of the call center industry is increasing because they are a major mean of communication between organizations and their costumers. So, ensuring good and optimized personnel schedules in call centers is crucial and has several advantages: reduction of total labor costs, reducing overstaffing, employees’ satisfaction, meeting their preferences, and costumers’ satisfaction, presenting acceptable waiting times. The considered problem concerns personnel scheduling in a 24/7 call center where the scheduling process is done manually. So, the main goal is to explore exact solution approaches in order to obtain solutions whose quality is preferable to the manually achieved ones and to reduce the processing time. The proposed optimization model is an Integer Programming model. The purpose of this model is to assign shifts to workers, while minimizing the total penalization that are associated to employees’ time preferences. The model is implemented on ILOG CPLEX Optimization Studio 12.7.0.0, using OPL, and tested with various instances, including randomly generated and real-world data instances. In order to analyze the quality of the model, a computational study of its linear relaxation was carried out, concluding that the model presents null integrality gaps in all the tested instances. So, the proposed model has a strong formulation, that is, a good quality model. Additionally, to evaluate the performance of the model when running large instances, several randomly generated instances were tested using ILOG CPLEX Optimization Studio 12.10.0.0, achieving good computational results.Hoje em dia, a importância da indústria dos call centers tem vindo a aumentar, uma vez que estes são um grande meio de comunicação entre as empresas e os respetivos clientes. Nesse sentido, garantir um bom e otimizado escalonamento de pessoal é crucial e traz consigo bastantes vantagens: redução dos custos totais de trabalho, reduzindo excesso de trabalhadores, aumento da satisfação dos empregados, atendendo às suas preferências, e ainda aumento da satisfação dos clientes, apresentando tempos de espera aceitáveis. O problema considerado envolve escalonamento de pessoal num call center que opera 24 horas por dia, 7 dias por semana. Atualmente, o processo de escalonamento é feito manualmente. Assim, o principal objetivo é explorar abordagens de resolução exata para obter soluções que apresentam qualidade preferível às das soluções obtidas até ao momento e para reduzir o tempo gasto em todo o processo. O modelo de otimização proposto é um modelo de Programação Inteira, cujo objectivo é associar turnos de trabalho aos trabalhadores, minimizando o total das penalizações associadas às preferências horárias dos mesmos. O modelo é implementado no ILOG CPLEX Optimization Studio 12.7.0.0, utilizando linguagem OPL, e testado com várias instâncias, incluindo instâncias geradas aleatoriamente e instâncias com dados reais. A análise da qualidade do modelo passou pelo estudo computacional da sua relaxação linear, podendo concluir-se que o modelo apresenta um intervalo de integralidade nulo em todas as instâncias testadas. Assim, o modelo proposto é um modelo forte, isto é, um modelo de boa qualidade. De forma a avaliar o desempenho do modelo a resolver instâncias grandes, várias instâncias geradas aletoriamente são testadas utilizando o software ILOG CPLEX Optimization Studio 12.10.0.0., apresentando bons resultados computacionais

Workforce scheduling and routing problems: literature survey and computational study

In the context of workforce scheduling, there are many scenarios in which personnel must carry out tasks at different locations hence requiring some form of transportation. Examples of these type of scenarios include nurses visiting patients at home, technicians carrying out repairs at customers’ locations and security guards performing rounds at different premises, etc. We refer to these scenarios as workforce scheduling and routing problems (WSRP) as they usually involve the scheduling of personnel combined with some form of routing in order to ensure that employees arrive on time at the locations where tasks need to be performed. The first part of this paper presents a survey which attempts to identify the common features of WSRP scenarios and the solution methods applied when tackling these problems. The second part of the paper presents a study on the computational difficulty of solving these type of problems. For this, five data sets are gathered from the literature and some adaptations are made in order to incorporate the key features that our survey identifies as commonly arising in WSRP scenarios. The computational study provides an insight into the structure of the adapted test instances, an insight into the effect that problem features have when solving the instances using mathematical programming, and some benchmark computation times using the Gurobi solver running on a standard personal computer

Bus driver rostering by hybrid methods based on column generation

Tese de doutoramento, Informática (Engenharia Informática), Universidade de Lisboa, Faculdade de Ciências, 2018Rostering problems arise in a diversity of areas where, according to the business and labor rules, distinct variants of the problem are obtained with different constraints and objectives considered. The diversity of existing rostering problems, allied with their complexity, justifies the activity of the research community addressing them. The current research on rostering problems is mainly devoted to achieving near-optimal solutions since, most of the times, the time needed to obtain optimal solutions is very high. In this thesis, a Bus Driver Rostering Problem is addressed, to which an integer programming model is adapted from the literature, and a new decomposition model with three distinct subproblems representations is proposed. The main objective of this research is to develop and evaluate a new approach to obtain solutions to the problem in study. The new approach follows the concept of search based on column generation, which consists in using the column generation method to solve problems represented by decomposition models and, after, applying metaheuristics to search for the best combination of subproblem solutions that, when combined, result in a feasible integer solution to the complete problem. Besides the new decomposition models proposed for the Bus Driver Rostering Problem, this thesis proposes the extension of the concept of search by column generation to allow using population-based metaheuristics and presents the implementation of the first metaheuristic using populations, based on the extension, which is an evolutionary algorithm. There are two additional contributions of this thesis. The first is an heuristic allowing to obtain solutions for the subproblems in an individual or aggregated way and the second is a repair operator which can be used by the metaheuristics to repair infeasible solutions and, eventually, generate missing subproblem solutions needed. The thesis includes the description and results from an extensive set of computational tests. Multiple configurations of the column generation with three decomposition models are tested to assess the best configuration to use in the generation of the search space for the metaheuristic. Additional tests compare distinct single-solution metaheuristics and our basic evolutionary algorithm in the search for integer solutions in the search space obtained by the column generation. A final set of tests compares the results of our final algorithm (with the best column generation configuration and the evolutionary algorithm using the repair operator) and the solutions obtained by solving the problem represented by the integer programming model with a commercial solver.Programa de Apoio à Formação Avançada de Docentes do Ensino Superior Politécnico (PROTEC), SFRH/PROTEC/67405/201

Optimisation models and algorithms for workforce scheduling and routing

This thesis investigates the problem of scheduling and routing employees that are required to perform activities at clients’ locations. Clients request the activities to be performed during a time period. Employees are required to have the skills and qualifications necessary to perform their designated activities. The working time of employees must be respected. Activities could require more than one employee. Additionally, an activity might have time-dependent constraints with other activities. Time-dependent activities constraints include: synchronisation, when two activities need to start at the same time; overlap, if at any time two activities are being performed simultaneously; and with a time difference between the start of the two activities. Such time difference can be given as a minimum time difference, maximum time difference, or a combination of both (min-max). The applicability of such workforce scheduling and routing problem (WSRP) is found in many industries e.g. home health care provision, midwives visiting future mothers, technicians performing installations and repairs, estate agents showing residences for sale, security guards patrolling different locations, etc. Such diversity makes the WSRP an important combinatorial optimisation problem to study. Five data sets, obtained from the literature, were normalised and used to investigate the problem. A total of 375 instances were derived from these data sets. Two mathematical models, an integer and a mixed integer, are used. The integer model does not consider the case when the number of employees is not enough to perform all activities. The mixed integer model can leave activities unassigned. A mathematical solver is used to obtain feasible solutions for the instances. The solver provides optimal solutions for small instances, but it cannot provide feasible solutions for medium and large instances. This thesis presents the gradual development of a greedy heuristic that is designed to tackle medium and large instances. Five versions of the greedy heuristic are presented, each of them obtains better results than the previous one. All versions are compared to the results obtained by the mathematical solver when using the mixed integer model. The greedy heuristic exploits domain information to speed the search and discard infeasible solutions. It uses tailored functions to deal with each of the time-dependent activity constraints. These constraints make more difficult the solution process. Further improvements are obtained by using tabu search. It provides moves based on the tailored functions of the greedy heuristic. Overall, the greedy heuristic and the tabu search, maintain feasible solutions at all times. The main contributions of this thesis are: the definition of WSRP; the introduction of 375 instances based on five data sets; the adaptation of two mathematical models; the introduction of a greedy heuristic capable of obtaining better results than the solver; and, the implementation of a tabu search to further improve the results

Optimisation models and algorithms for workforce scheduling and routing

This thesis investigates the problem of scheduling and routing employees that are required to perform activities at clients’ locations. Clients request the activities to be performed during a time period. Employees are required to have the skills and qualifications necessary to perform their designated activities. The working time of employees must be respected. Activities could require more than one employee. Additionally, an activity might have time-dependent constraints with other activities. Time-dependent activities constraints include: synchronisation, when two activities need to start at the same time; overlap, if at any time two activities are being performed simultaneously; and with a time difference between the start of the two activities. Such time difference can be given as a minimum time difference, maximum time difference, or a combination of both (min-max). The applicability of such workforce scheduling and routing problem (WSRP) is found in many industries e.g. home health care provision, midwives visiting future mothers, technicians performing installations and repairs, estate agents showing residences for sale, security guards patrolling different locations, etc. Such diversity makes the WSRP an important combinatorial optimisation problem to study. Five data sets, obtained from the literature, were normalised and used to investigate the problem. A total of 375 instances were derived from these data sets. Two mathematical models, an integer and a mixed integer, are used. The integer model does not consider the case when the number of employees is not enough to perform all activities. The mixed integer model can leave activities unassigned. A mathematical solver is used to obtain feasible solutions for the instances. The solver provides optimal solutions for small instances, but it cannot provide feasible solutions for medium and large instances. This thesis presents the gradual development of a greedy heuristic that is designed to tackle medium and large instances. Five versions of the greedy heuristic are presented, each of them obtains better results than the previous one. All versions are compared to the results obtained by the mathematical solver when using the mixed integer model. The greedy heuristic exploits domain information to speed the search and discard infeasible solutions. It uses tailored functions to deal with each of the time-dependent activity constraints. These constraints make more difficult the solution process. Further improvements are obtained by using tabu search. It provides moves based on the tailored functions of the greedy heuristic. Overall, the greedy heuristic and the tabu search, maintain feasible solutions at all times. The main contributions of this thesis are: the definition of WSRP; the introduction of 375 instances based on five data sets; the adaptation of two mathematical models; the introduction of a greedy heuristic capable of obtaining better results than the solver; and, the implementation of a tabu search to further improve the results

An Integrated Framework for Staffing and Shift Scheduling in Hospitals

Over the years, one of the main concerns confronting hospital management is optimising the staffing and scheduling decisions. Consequences of inappropriate staffing can adversely impact on hospital performance, patient experience and staff satisfaction alike. A comprehensive review of literature (more than 1300 journal articles) is presented in a new taxonomy of three dimensions; problem contextualisation, solution approach, evaluation perspective and uncertainty. Utilising Operations Research methods, solutions can provide a positive contribution in underpinning staffing and scheduling decisions. However, there are still opportunities to integrate decision levels; incorporate practitioners view in solution architectures; consider staff behaviour impact, and offer comprehensive applied frameworks. Practitioners’ perspectives have been collated using an extensive exploratory study in Irish hospitals. A preliminary questionnaire has indicated the need of effective staffing and scheduling decisions before semi-structured interviews have taken place with twenty-five managers (fourteen Directors and eleven head nurses) across eleven major acute Irish hospitals (about 50% of healthcare service deliverers). Thematic analysis has produced five key themes; demand for care, staffing and scheduling issues, organisational aspects, management concern, and technology-enabled. In addition to other factors that can contribute to the problem such as coordination, environment complexity, understaffing, variability and lack of decision support. A multi-method approach including data analytics, modelling and simulation, machine learning, and optimisation has been employed in order to deliver adequate staffing and shift scheduling framework. A comprehensive portfolio of critical factors regarding patients, staff and hospitals are included in the decision. The framework was piloted in the Emergency Department of one of the leading and busiest university hospitals in Dublin (Tallaght Hospital). Solutions resulted from the framework (i.e. new shifts, staff workload balance, increased demands) have showed significant improvement in all key performance measures (e.g. patient waiting time, staff utilisation). Management team of the hospital endorsed the solution framework and are currently discussing enablers to implement the recommendation

Developing Optimal Peer-to-Peer Ridesharing Strategies

69A43551747123Thanks to recent developments in ride-hailing transit services, the Peer-to-Peer (P2P) ridematching problem has been actively considered in academia in recent years. P2P ridematching not only reduces travel costs for riders but also benefits drivers by saving them money in exchange for their additional travel time and costs. However, assigning riders to drivers in an efficient way is a complex problem that requires a focus on maximizing the benefits for both riders and drivers. This study first aims to formulate a multi-driver multirider (MDMR) P2P ride-matching problem based on rational preferences and cost allocation for both driver and rider. This model also enables riders to transfer between multiple drivers to complete their journeys if needed. To solve the ride-matching problem, a Tabu Search (TS) for system optimum ride-matchings and Greedy Matching (GM) algorithm for the stable ridematchings were created to produce stable ride-matchings