A simple and effective algorithm for the maximum happy vertices problem

In a recent paper, a solution approach to the Maximum Happy Vertices Problem has been proposed. The approach is based on a constructive heuristic improved by a matheuristic local search phase. We propose a new procedure able to outperform the previous solution algorithm both in terms of solution quality and computational time. Our approach is based on simple ingredients implying as starting solution gen- erator an approximation algorithm and as an improving phase a new matheuristic local search. The procedure is then extended to a multi-start configuration, able to further improve the solution quality at the cost of an acceptable increase in compu- tational time

Total Tardiness Minimization in a Single-Machine with Periodical Resource Constraints

In this paper we introduce a variant of the single machine considering resource restriction per period. The objective function to be minimized is the total tardiness.  We proposed an integer linear programming modeling based on a bin packing formulation. In view of the NP-hardness of the introduced variant, heuristic algorithms are required to find high-quality solutions within an admissible computation times. In this sense, we present a new hybrid matheuristic called Relax-and-Fix with Variable Fixing Search (RFVFS).  This innovative solution approach combines the relax-and-fix algorithm and a strategy for the fixation of decision variables based on the concept of the variable neighborhood search metaheuristic. As statistical indicators to evaluate the solution procedures under comparison, we employ the Average Relative Deviation Index (ARDI) and the Success Rate (SR). We performed extensive computational experimentation with a testbed composed by 450 proposed test problems. Considering the results for the number of jobs, the RFVFS returned ARDI and SR values of 35.6% and 41.3%, respectively. Our proposal outperformed the best solution approach available for a closely-related problem with statistical significance

Metaheuristics For Solving Real World Employee Rostering and Shift Scheduling Problems

Optimising resources and making considerate decisions are central concerns in any responsible organisation aiming to succeed in efficiently achieving their goals. Careful use of resources can have positive outcomes in the form of fiscal savings, improved service levels, better quality products, improved awareness of diminishing returns and general output efficiency, regardless of field. Operational research techniques are advanced analytical tools used to improve managerial decision-making. There have been a variety of case studies where operational research techniques have been successfully applied to save millions of pounds. Operational research techniques have been successfully applied to a multitude of fields, including agriculture, policing, defence, conservation, air traffic control, and many more. In particular, management of resources in the form of employees is a challenging problem --- but one with the potential for huge improvements in efficiency. The problem this thesis tackles can be divided into two sub-problems; the personalised shift scheduling & employee rostering problem, and the roster pattern problem. The personalised shift scheduling & employee rostering problem involves the direct scheduling of employees to hours and days of week. This allows the creation of schedules which are tailored to individuals and allows a fine level over control over the results, but with at the cost of a large and challenging search space. The roster pattern problem instead takes existing patterns employees currently work, and uses these as a pool of potential schedules to be used. This reduces the search space but minimises the number of changes to existing employee schedules, which is preferable for personnel satisfaction. Existing research has shown that a variety of algorithms suit different problems and hybrid methods are found to typically outperform standalone ones in real-world contexts. Several algorithmic approaches for solving variations of the employee scheduling problem are considered in this thesis. Initially a VNS approach was used with a Metropolis-Hastings acceptance criterion. The second approach utilises ER&SR controlled by the EMCAC, which has only been used in the field of exam timetabling, and has not before been used within the domain of employee scheduling and rostering. ER&SR was then hybridised with our initial approach, producing ER&SR with VNS. Finally, ER&SR was hybridised into a matheuristic with Integer Programming and compared to the hybrid's individual components. A contribution of this thesis is evidence that the algorithm ER&SR has merit outside of the original sub-field of exam scheduling, and can be applied to shift scheduling and employee rostering. Further, ER&SR was hybridised and schedules produced by the hybridisations were found to be of higher quality than the standalone algorithm. In the literature review it was found that hybrid algorithms have become more popular in real-world problems in recent years, and this body of work has explored and continued this trend. Problem formulations in this thesis provide insight into creating constraints which satisfy the need for minimising employee dissatisfaction, particularly in regards to abrupt change. The research presented in this thesis has positively impacted a multinational and multibillion dollar field service operations company. This has been achieved by implementing a variety of techniques, including metaheuristics and a matheuristic, to schedule shifts and roster employees over a period of several months. This thesis showcases the research outputs by this project, and highlights the real-world impact of this research

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

Multi-agent deep Q-network-based metaheuristic algorithm for Nurse Rostering Problem

The Nurse Rostering Problem (NRP) aims to create an efficient and fair work schedule that balances both the needs of employees and the requirements of hospital operations. Traditional local search-based metaheuristic algorithms, such as adaptive neighborhood search (ANS) and variable neighborhood descent (VND), mainly focus on optimizing the current solution without considering potential long-term consequences, which may easily get stuck in local optima and limit the overall performance. Thus, we propose a multi-agent deep Q-network-based metaheuristic algorithm (MDQN-MA) for NRP to harness the strengths of various metaheuristics. Each agent encapsulates a metaheuristic algorithm, where its available actions represent different perspectives of the problem environment. By combining their strengths and various perspectives, these agents can work collaboratively to navigate and search for a broader range of potential solutions effectively. Furthermore, to improve the performance of an individual agent, we model its neighborhood search as a Markov Decision Process model and integrate a deep Q-network to consider long-term impacts for its neighborhood sequential decision-making. The experimental results clearly show that an individual agent in MDQN-MA can outperform ANS and VND, and multiple agents in MDQN-MA even perform better, achieving the best results among metaheuristic algorithms on the Second International Nurse Rostering Competition dataset

Integration of operations research and artificial intelligence approaches to solve the nurse rostering problem

Please note, incorrect date on spine and title page (2016). Degree was awarded in 2019.Nurse Rostering can be defined as assigning a series of shift sequences (schedules)to several nurses over a planning horizon according to some limitations and preferences. The inherent benefits of generating higher-quality rosters are a reduction in outsourcing costs and an increase in job satisfaction of employees.This problem is often very dicult to solve in practice, particularly by applying a sole approach. This dissertation discusses two hybrid solution methods to solve the Nurse Rostering Problem which are designed based on Integer Programming,Constraint Programming, and Meta-heuristics. The current research contributes to the scientific and practical aspects of the state of the art of nurse rostering. The present dissertation tries to address two research questions. First, we study the extension of the reach of exact method through hybridisation. That said, we hybridise Integer and Constraint Programming to exploit their complementary strengths in finding optimal and feasible solutions, respectively. Second,we introduce a new solution evaluation mechanism designed based on the problem structure. That said, we hybridise Integer Programming and Variable Neighbourhood Search reinforced with the new solution evaluation method to efficiently deal with the problem. To benchmark the hybrid algorithms, three different datasets with different characteristics are used. Computational experiments illustrate the effectiveness and versatility of the proposed approaches on a large variety of benchmark instancesNurse Rostering can be defined as assigning a series of shift sequences (schedules)to several nurses over a planning horizon according to some limitations and preferences. The inherent benefits of generating higher-quality rosters are a reduction in outsourcing costs and an increase in job satisfaction of employees.This problem is often very dicult to solve in practice, particularly by applying a sole approach. This dissertation discusses two hybrid solution methods to solve the Nurse Rostering Problem which are designed based on Integer Programming,Constraint Programming, and Meta-heuristics. The current research contributes to the scientific and practical aspects of the state of the art of nurse rostering. The present dissertation tries to address two research questions. First, we study the extension of the reach of exact method through hybridisation. That said, we hybridise Integer and Constraint Programming to exploit their complementary strengths in finding optimal and feasible solutions, respectively. Second,we introduce a new solution evaluation mechanism designed based on the problem structure. That said, we hybridise Integer Programming and Variable Neighbourhood Search reinforced with the new solution evaluation method to efficiently deal with the problem. To benchmark the hybrid algorithms, three different datasets with different characteristics are used. Computational experiments illustrate the effectiveness and versatility of the proposed approaches on a large variety of benchmark instance

Shift Scheduling of Short Time Workers in Large-Scale Home Improvement Center by using Cooperative Evolution

There are a lot of large-scale Home Improvement Center (HIC) in Japan. In the large-scale HIC,about hundred short time workers are registered. And about forty workers are working every day. A managercreates a monthly shift schedule. The manager selects the workers required for each working day, assigns theworking time and break time for each worker and also work placement. Because there are many requirementsfor the scheduling, the scheduling consumes time costs and efforts. Therefore, we propose the technique to createand optimize the schedule of the short time workers in order to reduce the burden of the manager. A cooperativeevolution is applied for generating and optimizing the shift schedule of short time worker. Several problems hasbeen found in carrying out this research. This paper proposes techniques to automatically create and optimize theshift schedule of workers in large-scale HIC by using a Cooperative Evolution (CE), to solve the situation thatmany workers concentrate in a speci c time zone, and to solve the situation where many breaks are concentratedin a speci c break time zone, and an effective mutation operators

A hybrid integer programming and variable neighborhood search algorithm to solve Nurse Rostering Problems

The Nurse Rostering Problem (NRP) is defined as assigning a number of nurses to different shifts during a specified planning period, considering some regulations and preferences. This is often very difficult to solve in practice particularly by applying a sole approach. In this paper, we propose a novel hybrid algorithm combining the strengths of Integer Programming (IP) and Variable Neighbourhood Search (VNS) algorithms to design a hybrid method for solving the NRP. After generating the initial solution using a greedy heuristic, the solution is further improved by employing a Variable Neighbourhood Descent algorithm. Then IP, deeply embedded in the VNS algorithm, is employed within a ruin-and-recreate framework to assist the search process. Finally, IP is called again to further refine the solution during the remaining time. We utilize the strength of IP not only to diversify the search process, but also to intensify the search efforts. To identify the quality of the current solution, we use a new generic scoring scheme to mark the low-penalty parts of the solution. Based on the computational tests with 24 instances recently introduced in the literature, we obtain better results with our proposed algorithm, where the hybrid algorithm outperforms two state-of-the-art algorithms and Gurobi in most of the instances. Furthermore, we introduce 11 randomly generated instances to further evaluate the efficiency of the hybrid algorithm, and we make these computationally challenging instances publicly available to other researchers for benchmarking purposes