89 research outputs found
The Use Of Heuristic Ordering And Particle Swarm Optimization For Nurse Scheduling Problem
The scheduling of nurse has been the important management functions and directly affected the hospital services and the patient care as well. The challenge of nurse scheduling is the substantial amount of time for assigning shifts to a set of nurses that involves a large set of constraints. To satisfy all the constraints cannot be applied directly due to variability preferences and conflicting interest and objectives between nurses and hospital. The main objective of this research study is to find the optimal solution that can deal with varying preferences in term of skill categories, flexible constraint parameters, flexible coverage and varying the size of nurses. A combination of heuristic ordering and particle swarm optimization (HOPSO) has been proposed to achieve the objectives. The capability of PSO algorithm is enhanced by emphasizing the use of information on the constraints and heuristic ordering for searching optimal solution in both the feasible and infeasible solution spaces. The constraints are adapted to the evaluation function that iteratively evaluates all the solutions. The solution with lowest violation penalty cost is selected and will compare to a new solution. Before the particles update its position, variable neighborhood search (VNS) is applied in order to enhanced the diversity before being trapped in a local optima. The performance of the proposed method is tested on the real problem benchmark dataset in Malaysia public hospital, Universti Kebangsaan Malaysia Medical Centre (UKMMC) that had 8 datasets with the different number of nurses. The comparison of the result of HOPSO, harmony search algorithm (HSA) and heuristic variable neighborhood search (HVNS) is presented. The result show that the proposed HOPSO can generate the schedule in the range between one to twenty-six seconds computational time, followed by the HSA which range between one hundred and eighty-five to three hundred and forty-five seconds and HVNS takes one hundred and thirty-one to eight hundred and twenty seconds. HOPSO can decrease the penalty cost into ninety seven percent improvement than the HSA which is less than fifty percent of improvement. Computational results show that the proposed HOPSO based algorithm is performed better than HSA and HVNS in order to provide a practical solution to the problem
Exact and non-exact procedures for solving the response time variability problem (RTVP)
Premi extraordinari doctorat curs 2009-2010, à mbit d’Enginyeria IndustrialCuando se ha de compartir un recurso entre demandas (de productos, clientes, tareas, etc.) competitivas que requieren una atención regular, es importante programar el derecho al acceso del recurso de alguna forma justa de manera que cada producto, cliente o tarea reciba un acceso al recurso proporcional a su demanda relativa al total de las demandas competitivas. Este tipo de problemas de secuenciación pueden ser generalizados bajo el siguiente esquema. Dados n sÃmbolos, cada uno con demanda di (i = 1,...,n), se ha de generar una secuencia justa o regular donde cada sÃmbolo aparezca di veces. No existe una definición universal de justicia, ya que puede haber varias métricas razonables para medirla según el problema especÃfico considerado. En el Problema de Variabilidad en el Tiempo de Respuesta, o Response Time Variability Problem (RTVP) en inglés, la injusticia o irregularidad de una secuencia es medida como la suma, para todos los sÃmbolos, de sus variabilidades en las distancias en que las copias de cada sÃmbolo son secuenciados. AsÃ, el objetivo del RTVP es encontrar la secuencia que minimice la variabilidad total. En otras palabras, el objetivo del RTVP es minimizar la variabilidad de los instantes en que los productos, clientes o trabajos reciben el recurso necesario. Este problema aparece en una amplia variedad de situaciones de la vida real; entre otras, secuenciación en lÃneas de modelo-mixto bajo just-in-time (JIT), en asignación de recursos en sistemas computacionales multi-hilo como sistemas operativos, servidores de red y aplicaciones mutimedia, en el mantenimiento periódico de maquinaria, en la recolección de basura, en la programación de comerciales en televisión y en el diseño de rutas para agentes comerciales con múltiples visitas a un mismo cliente. En algunos de estos problemas la regularidad no es una propiedad deseable por sà misma, si no que ayuda a minimizar costes. De hecho, cuando los costes son proporcionales al cuadrado de las distancias, el problema de minimizar costes y el RTVP son equivalentes. El RTVP es muy difÃcil de resolver (se ha demostrado que es NP-hard). El tamaño de las instancias del RTVP que pueden ser resueltas óptimamente con el mejor método exacto existente en la literatura tiene un lÃmite práctico de 40 unidades. Por otro lado, los métodos no exactos propuestos en la literatura para resolver instancias mayores consisten en heurÃsticos simples que obtienen soluciones rápidamente, pero cuya calidad puede ser mejorada. Por tanto, los métodos de resolución existentes en la literatura son insuficientes. El principal objetivo de esta tesis es mejorar la resolución del RTVP. Este objetivo se divide en los dos siguientes subobjetivos : 1) aumentar el tamaño de las instancias del RTVP que puedan ser resueltas de forma óptima en un tiempo de computación práctico, y 2) obtener de forma eficiente soluciones lo más cercanas a las óptimas para instancias mayores. Además, la tesis tiene los dos siguientes objetivos secundarios: a) investigar el uso de metaheurÃsticos bajo el esquema de los hiper-heurÃsticos, y b) diseñar un procedimiento sistemático y automático para fijar los valores adecuados a los parámetros de los algoritmos. Se han desarrollado diversos métodos para alcanzar los objetivos anteriormente descritos. Para la resolución del RTVP se ha diseñado un método exacto basado en la técnica branch and bound y el tamaño de las instancias que pueden resolverse en un tiempo práctico se ha incrementado a 55 unidades. Para instancias mayores, se han diseñado métodos heurÃsticos, metaheurÃsticos e hiper-heurÃsticos, los cuales pueden obtener soluciones óptimas o casi óptimas rápidamente. Además, se ha propuesto un procedimiento sistemático y automático para tunear parámetros que aprovecha las ventajas de dos procedimientos existentes (el algoritmo Nelder & Mead y CALIBRA).When a resource must be shared between competing demands (of products, clients, jobs, etc.) that require regular attention, it is important to schedule the access right to the resource in some fair manner so that each product, client or job receives a share of the resource that is proportional to its demand relative to the total of the competing demands. These types of sequencing problems can be generalized under the following scheme. Given n symbols, each one with demand di (i = 1,...,n), a fair or regular sequence must be built in which each symbol appears di times. There is not a universal definition of fairness, as several reasonable metrics to measure it can be defined according to the specific considered problem. In the Response Time Variability Problem (RTVP), the unfairness or the irregularity of a sequence is measured by the sum, for all symbols, of their variabilities in the positions at which the copies of each symbol are sequenced. Thus, the objective of the RTVP is to find the sequence that minimises the total variability. In other words, the RTVP objective is to minimise the variability in the instants at which products, clients or jobs receive the necessary resource. This problem appears in a broad range of real-world areas. Applications include sequencing of mixed-model assembly lines under just-in-time (JIT), resource allocation in computer multi-threaded systems such as operating systems, network servers and media-based applications, periodic machine maintenance, waste collection, scheduling commercial videotapes for television and designing of salespeople's routes with multiple visits, among others. In some of these problems the regularity is not a property desirable by itself, but it helps to minimise costs. In fact, when the costs are proportional to the square of the distances, the problem of minimising costs and the RTVP are equivalent. The RTVP is very hard to be solved (it has been demonstrated that it is NP-hard). The size of the RTVP instances that can be solved optimally with the best exact method existing in the literature has a practical limit of 40 units. On the other hand, the non-exact methods proposed in the literature to solve larger instances are simple heuristics that obtains solutions quickly, but the quality of the obtained solutions can be improved. Thus, the solution methods existing in the literature are not enough to solve the RTVP. The main objective of this thesis is to improve the resolution of the RTVP. This objective is split in the two following sub-objectives: 1) to increase the size of the RTVP instances that can be solved optimally in a practical computing time; and 2) to obtain efficiently near-optimal solutions for larger instances. Moreover, the thesis has the following two secondary objectives: a) to research the use of metaheuristics under the scheme of hyper-heuristics, and b) to design a systematic, hands-off procedure to set the suitable values of the algorithm parameters. To achieve the aforementioned objectives, several procedures have been developed. To solve the RTVP an exact procedure based on the branch and bound technique has been designed and the size of the instances that can be solved in a practical time has been increased to 55 units. For larger instances, heuristic, heuristic, metaheuristic and hyper-heuristic procedures have been designed, which can obtain optimal or near-optimal solutions quickly. Moreover, a systematic, hands-off fine-tuning method that takes advantage of the two existing ones (Nelder & Mead algorithm and CALIBRA) has been proposed.Award-winningPostprint (published version
Real-Life Optimum Shift Scheduling Design
In many industries, manpower shift scheduling poses problems that require immediate solutions. The fundamental need in this domain is to ensure that all shifts are assigned to cover all or as many jobs as possible. The shifts should additionally be planned with minimum manpower utilization, minimum manpower idleness and enhanced adaptability of employee schedules. The approach used in this study was to utilize an existing manpower prediction method to decide the minimum manpower required to complete all jobs. Based on the minimum manpower number and shift criteria, the shifts were assigned to form schedules using random pick and criteria-based selection methods. The potential schedules were then optimized and the best ones selected. Based on several realistic test instances, the proposed heuristic approach appears to offer promising solutions for shift scheduling as it improves shift idle time, complies with better shift starting time and significantly reduces the manpower needed and the time spent on creating schedules, regardless of data size
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
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Resource constrained routing and scheduling: Review and research prospects
In the service industry, it is crucial to efficiently allocate scarce resources to perform tasks and meet particular service requirements. What considerably complicates matters is when these resources, for example skilled technicians, nurses, and home carers have to visit different customer locations. This paper provides a comprehensive survey on resource constrained routing and scheduling that unveils the problem characteristics with respect to resource qualifications, service requirements and problem objectives. It also identifies the most effective exact and heuristic algorithms for this class of problems. The paper closes with several research prospects
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
Exact and non-exact procedures for solving the response time variability problem (RTVP)
Cuando se ha de compartir un recurso entre demandas (de productos, clientes, tareas, etc.) competitivas que requieren una atención regular, es importante programar el derecho al acceso del recurso de alguna forma justa de manera que cada producto, cliente o tarea reciba un acceso al recurso proporcional a su demanda relativa al total de las demandas competitivas. Este tipo de problemas de secuenciación pueden ser generalizados bajo el siguiente esquema. Dados n sÃmbolos, cada uno con demanda di (i = 1,...,n), se ha de generar una secuencia justa o regular donde cada sÃmbolo aparezca di veces. No existe una definición universal de justicia, ya que puede haber varias métricas razonables para medirla según el problema especÃfico considerado. En el Problema de Variabilidad en el Tiempo de Respuesta, o Response Time Variability Problem (RTVP) en inglés, la injusticia o irregularidad de una secuencia es medida como la suma, para todos los sÃmbolos, de sus variabilidades en las distancias en que las copias de cada sÃmbolo son secuenciados. AsÃ, el objetivo del RTVP es encontrar la secuencia que minimice la variabilidad total. En otras palabras, el objetivo del RTVP es minimizar la variabilidad de los instantes en que los productos, clientes o trabajos reciben el recurso necesario. Este problema aparece en una amplia variedad de situaciones de la vida real; entre otras, secuenciación en lÃneas de modelo-mixto bajo just-in-time (JIT), en asignación de recursos en sistemas computacionales multi-hilo como sistemas operativos, servidores de red y aplicaciones mutimedia, en el mantenimiento periódico de maquinaria, en la recolección de basura, en la programación de comerciales en televisión y en el diseño de rutas para agentes comerciales con múltiples visitas a un mismo cliente. En algunos de estos problemas la regularidad no es una propiedad deseable por sà misma, si no que ayuda a minimizar costes. De hecho, cuando los costes son proporcionales al cuadrado de las distancias, el problema de minimizar costes y el RTVP son equivalentes. El RTVP es muy difÃcil de resolver (se ha demostrado que es NP-hard). El tamaño de las instancias del RTVP que pueden ser resueltas óptimamente con el mejor método exacto existente en la literatura tiene un lÃmite práctico de 40 unidades. Por otro lado, los métodos no exactos propuestos en la literatura para resolver instancias mayores consisten en heurÃsticos simples que obtienen soluciones rápidamente, pero cuya calidad puede ser mejorada. Por tanto, los métodos de resolución existentes en la literatura son insuficientes. El principal objetivo de esta tesis es mejorar la resolución del RTVP. Este objetivo se divide en los dos siguientes subobjetivos : 1) aumentar el tamaño de las instancias del RTVP que puedan ser resueltas de forma óptima en un tiempo de computación práctico, y 2) obtener de forma eficiente soluciones lo más cercanas a las óptimas para instancias mayores. Además, la tesis tiene los dos siguientes objetivos secundarios: a) investigar el uso de metaheurÃsticos bajo el esquema de los hiper-heurÃsticos, y b) diseñar un procedimiento sistemático y automático para fijar los valores adecuados a los parámetros de los algoritmos. Se han desarrollado diversos métodos para alcanzar los objetivos anteriormente descritos. Para la resolución del RTVP se ha diseñado un método exacto basado en la técnica branch and bound y el tamaño de las instancias que pueden resolverse en un tiempo práctico se ha incrementado a 55 unidades. Para instancias mayores, se han diseñado métodos heurÃsticos, metaheurÃsticos e hiper-heurÃsticos, los cuales pueden obtener soluciones óptimas o casi óptimas rápidamente. Además, se ha propuesto un procedimiento sistemático y automático para tunear parámetros que aprovecha las ventajas de dos procedimientos existentes (el algoritmo Nelder & Mead y CALIBRA).When a resource must be shared between competing demands (of products, clients, jobs, etc.) that require regular attention, it is important to schedule the access right to the resource in some fair manner so that each product, client or job receives a share of the resource that is proportional to its demand relative to the total of the competing demands. These types of sequencing problems can be generalized under the following scheme. Given n symbols, each one with demand di (i = 1,...,n), a fair or regular sequence must be built in which each symbol appears di times. There is not a universal definition of fairness, as several reasonable metrics to measure it can be defined according to the specific considered problem. In the Response Time Variability Problem (RTVP), the unfairness or the irregularity of a sequence is measured by the sum, for all symbols, of their variabilities in the positions at which the copies of each symbol are sequenced. Thus, the objective of the RTVP is to find the sequence that minimises the total variability. In other words, the RTVP objective is to minimise the variability in the instants at which products, clients or jobs receive the necessary resource. This problem appears in a broad range of real-world areas. Applications include sequencing of mixed-model assembly lines under just-in-time (JIT), resource allocation in computer multi-threaded systems such as operating systems, network servers and media-based applications, periodic machine maintenance, waste collection, scheduling commercial videotapes for television and designing of salespeople's routes with multiple visits, among others. In some of these problems the regularity is not a property desirable by itself, but it helps to minimise costs. In fact, when the costs are proportional to the square of the distances, the problem of minimising costs and the RTVP are equivalent. The RTVP is very hard to be solved (it has been demonstrated that it is NP-hard). The size of the RTVP instances that can be solved optimally with the best exact method existing in the literature has a practical limit of 40 units. On the other hand, the non-exact methods proposed in the literature to solve larger instances are simple heuristics that obtains solutions quickly, but the quality of the obtained solutions can be improved. Thus, the solution methods existing in the literature are not enough to solve the RTVP. The main objective of this thesis is to improve the resolution of the RTVP. This objective is split in the two following sub-objectives: 1) to increase the size of the RTVP instances that can be solved optimally in a practical computing time; and 2) to obtain efficiently near-optimal solutions for larger instances. Moreover, the thesis has the following two secondary objectives: a) to research the use of metaheuristics under the scheme of hyper-heuristics, and b) to design a systematic, hands-off procedure to set the suitable values of the algorithm parameters. To achieve the aforementioned objectives, several procedures have been developed. To solve the RTVP an exact procedure based on the branch and bound technique has been designed and the size of the instances that can be solved in a practical time has been increased to 55 units. For larger instances, heuristic, heuristic, metaheuristic and hyper-heuristic procedures have been designed, which can obtain optimal or near-optimal solutions quickly. Moreover, a systematic, hands-off fine-tuning method that takes advantage of the two existing ones (Nelder & Mead algorithm and CALIBRA) has been proposed
Metaheuristic Design Patterns: New Perspectives for Larger-Scale Search Architectures
Design patterns capture the essentials of recurring best practice in an abstract form. Their merits are well established in domains as diverse as architecture and software development. They offer significant benefits, not least a common conceptual vocabulary for designers, enabling greater communication of high-level concerns and increased software reuse. Inspired by the success of software design patterns, this chapter seeks to promote the merits of a pattern-based method to the development of metaheuristic search software components. To achieve this, a catalog of patterns is presented, organized into the families of structural, behavioral, methodological and component-based patterns. As an alternative to the increasing specialization associated with individual metaheuristic search components, the authors encourage computer scientists to embrace the ‘cross cutting' benefits of a pattern-based perspective to optimization algorithms. Some ways in which the patterns might form the basis of further larger-scale metaheuristic component design automation are also discussed
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
Novel heuristic and metaheuristic approaches to the automated scheduling of healthcare personnel
This thesis is concerned with automated personnel scheduling in healthcare organisations; in particular, nurse rostering. Over the past forty years the nurse rostering problem has received a large amount of research. This can be mostly attributed to its practical applications and the scientific challenges of solving such a complex problem. The benefits of automating the rostering process include reducing the planner’s workload and associated costs and being able to create higher quality and more flexible schedules. This has become more important recently in order to retain nurses and attract more people into the profession. Better quality rosters also reduce fatigue and stress due to overwork and poor scheduling and help to maximise the use of leisure time by satisfying more requests. A more contented workforce will lead to higher productivity, increased quality of patient service and a better level of healthcare.
Basically stated, the nurse rostering problem requires the assignment of shifts to personnel to ensure that sufficient employees are present to perform the duties required. There are usually a number of constraints such as working regulations and legal requirements and a number of objectives such as maximising the nurses working preferences. When formulated mathematically this problem can be shown to belong to a class of problems which are considered intractable. The work presented in this thesis expands upon the research that has already been conducted to try and provide higher quality solutions to these challenging problems in shorter computation times.
The thesis is broadly structured into three sections. 1) An investigation into a nurse rostering problem provided by an industrial collaborator. 2) A framework to aid research in nurse rostering. 3) The development of a number of advanced algorithms for solving highly complex, real world problems
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