Nurse rostering

This paper presents a new methodology to solve the cyclic preference scheduling problem for hourly workers. The focus is on nurse rostering but is applicable to any organization in which the midterm scheduling decision must take into account a complex of legal, institutional, and preferential constraints. The objective is to strike a balance between satisfying individual preferences and minimizing personnel costs. The common practice is to consider each planning period independently and to generate new rosters at the beginning of each. To reduce some of the instability in the process, there is a growing trend toward cyclic schedules, which are easier to manage and are generally perceived to be more equitable. To address this problem, a new integer programming model is presented that combines the elements of both cyclic and preference scheduling. To find solutions, a branch-and-price algorithm is developed that makes use of several branching rules and an extremely effective rounding heuristic. A unique feature of the formulation is that the master problem contains integer rather than binary variables. Computational results are reported for problem instances with up to 200 nurses. Most were solved within 10 minutes and many within 3 minutes when a double aggregation approach was applicable.

Despite decades of research into automated methods for nurse rostering and some academic successes, one may notice that there is no consistency in the knowledge that has been built up over the years and that many healthcare institutions still resort to manual practices. One of the possible reasons for this gap between the nurse rostering theory and practice is that often the academic community focuses on the development of new techniques rather than developing systems for healthcare institutions. In addition, methods suitable for one problem are usually not easily transferable to other problems. In real-world healthcare environments, a personnel manager cannot afford to model a problem and construct a roster using available approaches in order to quantitatively determine which one suits best. There is a lack of criteria for the comparison of approaches to provide a clear picture about their advantages and disadvantages and therefore their suitability to a problem in hand. This paper introduces seven criteria: expressive power, flexibility, algorithmic power, learning capabilities, maintenance, rescheduling capabilities, and parameter tuning, that may offer guidance to researchers and developers of systems for nurse rostering. Two approaches to nurse rostering, which are of very different nature, are evaluated and compared against the introduced criteria. One approach is based on meta-heuristics, while the other employs case-based reasoning.

Nurse rostering is a complex scheduling problem that affects hospital personnel on a daily basis all over the world. The need for quality software solutions is acute for a number of reasons. In particular, it is very important to efficiently utilise time and effort, to evenly balance the workload among people and to attempt to satisfy personnel preferences. A high quality roster can lead to a more contented and thus more effective workforce.

The Nurse Rostering Problem (NRP) is one of the NP-hard problems that are difficult to solve for optimality. NRP deals with the distribution of working shifts to the staff nurses at healthcare organizations under given rules. Normally, NRP aims at generating a duty roster that satisfies all of the hard constraints (mandatory) and as many soft constraints (optional) as possible. This work introduces a greedy constructive heuristic algorithm, based on building two patterns of two-week's duration that satisfies all of the hard constraints and several soft constraints. The first pattern is designed mainly to fulfill the night shift coverage whilst the second pattern is concerned with morning and evening shifts only. If the solution is not feasible (for example the coverage is not met), a repairing mechanism algorithm is applied until a feasible solution is reached. Simulated Annealing (SA) is then used to improve the constructed solution. A real dataset from Universiti Kebangsaan Malaysia Medical Center (UKMMC) is used in this work to test the proposed approach. Currently, the duty roster at UKMMC is still constructed manually. Promising results have been obtained and presented in this paper.

A novel nurse rostering model is developed to represent real world problem instances more accurately. The proposed model is generic in the sense that it allows modelling of essentially different problem instances. Novel local search neighbourhoods are implemented to take advantage of the problem properties represented by the model. These neighbourhoods are used in a variable neighbourhood search and in an adaptive large neighbourhood search algorithm. The performance of the solution method is evaluated empirically on real world data. The proposed model is open to further extensions for covering personnel planning problems in different sectors and countries.

This paper describes the Rostering Engine (RE) that we have developed for the Hospital Authority (HA), Hong Kong as part of their Staff Rostering System (SRS) using AI constraint-programming techniques. The Hospital Authority manages over 40 public hospitals in Hong Kong. With close to 1500 wards total, the amount of resources needed to produce weekly staff rosters for each ward

Penjadwalan atau rostering tenaga kerja dapat dilakukan untuk mengalokasikan sumber daya dengan ukuran yang tepat terhadap beragam permintaan. Penjawalan kerja minimal dilakukan terhadap permintaan jasa yang minimal, sebaliknya penjadwalan kerja maksimal di sesuaikan dengan tingginya permintaan supaya ongkos produksi tidak terlalu tinggi. Penjadwalan kerja jasa di sesuaikan dengan aturan kerja perusahaan dan kepentingan staff terhadap penyesuai kerja dengan kepentingannya, artinya jawal kerja yang sudah di buat masih bisa di rubah sesuai dengan konsep fairness, acceptability and compliance to the policy.

Personnel rostering has received ample attention in recent years. Due to its social and economic relevance and due to its intrinsic complexity, it has become a major subject for scheduling and timetabling researchers. Among the personnel rostering problems, nurse rostering turned out to be particularly complex and difficult. In this paper, we propose a notation for nurse rostering problems along the lines of the α|β|γ notation for scheduling. The system allows extension as well as refinement. It is the aim of the notation to facilitate problem description, classification and systematic study. It enables authors to position the problems in the vaster body of research on the subject. By developing this notation for nurse rostering, we hope that an extension of it will be applicable to a broader domain of personnel rostering.

Hospitals need to repeatedly produce duty rosters for its nursing staff. The good scheduling of nurses has impact on the quality of health care, the recruitment of nurses, the development of budgets and other nursing functions. The nurse rostering problem (NRP) has been the subject of much study. This paper presents a brief overview, in the form of a bibliographic survey, of the many models and methodologies available to solve the NRP.

Constructing timetables of work for personnel in healthcare institutions is a highly constrained and difficult problem to solve. In this chapter, we will present an overview of our development of the algorithms that underpin a commercial nurse rostering decision support system that is in use in over 40 hospitals in Belgium. As such, we are particularly concerned with the real world regulations and requirements of Belgian institutions. We have concentrated upon short term rostering which involves assigning tasks to nurses in a hospital ward. Of course, the over-riding requirement of our algorithms is to assure a permanent level of care for the patients. However, our approaches are also required to consider administrative requirements, the nurses' contracts and their personal preferences.

Hospitals need to repeatedly produce duty rosters for its nursing staff. The good scheduling of nurses has impact on the quality of health care, the recruitment of nurses, the development of budgets and other nursing functions. The nurse rostering problem (NRP) has been the subject of much study. This paper presents a brief overview, in the form of a bibliographic survey, of the many models and methodologies available to solve the NRP.

Personnel rostering problems are highly constrained resource allocation prob- lems. Human rostering experts have many years of experience in making rostering de- cisions which re∞ect their individual goals and objectives. We present a novel method for capturing nurse rostering decisions and adapting them to solve new problems using the Case-Based Reasoning (CBR) paradigm. This method stores examples of previously encountered

This paper presents a new methodology to solve the cyclic preference scheduling problem for hourly workers. The focus is on nurse rostering but is applicable to any organization in which the midterm scheduling decision must take into account a complex of legal, institutional, and preferential constraints. The objective is to strike a balance between satisfying individual preferences and minimizing personnel costs. The common practice is to consider each planning period independently and to generate new rosters at the beginning of each. To reduce some of the instability in the process, there is a growing trend toward cyclic schedules, which are easier to manage and are generally perceived to be more equitable. To address this problem, a new integer programming model is presented that combines the elements of both cyclic and preference scheduling. To find solutions, a branch-and-price algorithm is developed that makes use of several branching rules and an extremely effective rounding heuristic. A unique feature of the formulation is that the master problem contains integer rather than binary variables. Computational results are reported for problem instances with up to 200 nurses. Most were solved within 10 minutes and many within 3 minutes when a double aggregation approach was applicable.

When applying evolutionary algorithms to difficult real-world problems, the fitness function routinely needs evaluating for a very high number of intermediary cases. The paper is concerned with real-world nurse rostering problems with highly constrained resources. We consider a particular approach, which allows for a quick evaluation and is general enough to deal with other kinds of resource planning problems with

Recently, many healthcare institutions became interested in automating the process of personnel scheduli ng. Nurse Rostering is a difficult scheduling problem, which is defined as generating rosters by assigning working shifts to a number of nurses over a certain planning period, such that a predefined set of constraints is satisfied. There is a high demand to automate this process, since many healthcare institutions still make nurse rosters manually . In this research we design a scheduling tool that is based on a Genetic Algorithm (GA) approach to solve the nurse rostering problem for the surgical unit in a Riyadh hospital. Our GA-based tool will automatically create a schedule while taking into account a number of difficult constraints. Some constraints are specified by the hospital, and mainly relate to maximizing the coverage of shifts and adhering to workload requirements and certain shift succession patterns. Other constraints relate to preferences of the nurses regarding t h...

In this paper, an empirical study on self-generating multimeme memetic algorithms is presented. A set of well known benchmark functions is used during the experiments. Moreover, a heuristic template is introduced for solving timetabling problems. The heuristics designed based on this template can utilize a set of constraint-based hill climbers in a cooperative manner. Two such adaptive heuristics are described. Memetic algorithms utilizing each one as if a single hill climber are experimented on a set of random nurse rostering problem instances. Additionally, simple genetic algorithm and two self-generating multimeme memetic algorithms are compared to the proposed memetic algorithms and a previous study.

This paper proposes a new memetic evolutionary algorithm to achieve explicit learning in rule-based nurse rostering, which involves applying a set of heuristic rules for each nurse’s assignment. The main framework of the algorithm is an estimation of distribution algorithm, in which an ant-miner methodology improves the individual solutions produced in each generation. Unlike our previous work (where learning is implicit), the learning in the memetic estimation of distribution algorithm is explicit, that is, we are able to identify building
blocks directly. The overall approach learns by building a probabilistic model, that is, an estimation of the
probability distribution of individual nurse–rule pairs that are used to construct schedules. The local search
processor (ie the ant-miner) reinforces nurse–rule pairs that receive higher rewards. A challenging real-world
nurse rostering problem is used as the test problem. Computational results show that the proposed approach
outperforms most existing approaches. It is suggested that the learning methodologies suggested in this paper
may be applied to other scheduling problems where schedules are built systematically according to specific rules.

Matrix models are ubiquitous for constraint problems. Many such problems have a matrix of variables M, with the same constraint defined by a finitestate automaton A on each row of M and a global cardinality constraint gcc on each column of M. We give two methods for deriving, by double counting, necessary conditions on the cardinality variables of the gcc constraints from the automaton A. The first method yields linear necessary conditions and simple arithmetic constraints. The second method introduces the cardinality automaton, which abstracts the overall behaviour of all the row automata and can be encoded by a set of linear constraints. We evaluate the impact of our methods on a large set of nurse rostering problem instances.

There is considerable interest in the use of genetic algorithms to solve problems arising in the areas of scheduling and timetabling. However, the classical genetic algorithm paradigm is not well equipped to handle the conflict between objectives and constraints that typically occurs in such problems. In order to overcome this, successful implementations frequently make use of problem specific knowledge. This paper is concerned with the development of a GA for a nurse rostering problem at a major UK hospital. The structure of the constraints is used as the basis for a co-evolutionary strategy using cooperating sub-populations. Problem specific knowledge is also used to define a system of incentives and disincentives, and a complementary mutation operator. Empirical results based on 52 weeks of live data show how these features are able to improve an unsuccessful canonical GA to the point where it is able to provide a practical solution to the problem.

Nurse rostering is a complex scheduling problem that affects hospital personnel on a daily basis all over the world. The need for quality software solutions is acute for a number of reasons. In particular, it is very important to efficiently utilise time and effort, to evenly balance the workload among people and to attempt to satisfy personnel preferences. A high quality roster can lead to a more contented and thus more effective workforce. In this review, we discuss nurse rostering within the global personnel scheduling problem in healthcare. We begin by briefly discussing the review and overview papers that have appeared in the literature and by noting the role that nurse rostering plays within the wider context of longer term hospital personnel planning. The main body of the paper describes and critically evaluates solution approaches which span the interdisciplinary spectrum from operations research techniques to artificial intelligence methods. We conclude by drawing on the strengths and weaknesses of the literature to outline the key issues that need addressing in future nurse rostering research.

The problem of finding a high quality timetable for personnel in a hospital ward has been addressed by many researchers, personnel managers and schedulers over a number of years. Nevertheless, automated nurse rostering practice is not common yet in hospitals. Many head nurses are currently still spending several days per month on constructing their rosters by hand. In recent years, the emergence of larger and more constrained problems has presented a real challenge because finding good quality solutions can lead to a higher level of personnel satisfaction and to flexible organisational procedures. Compared to many industrial situations (where personnel schedules normally consist of stable periodic morning-day-night cycles) health care institutions often require more flexibility in terms of hours and shift types. The motivation for the research presented in this paper has been provided by real world hospital administrators/schedulers and the approach that we describe has been implemented in over 40 hospitals in Belgium. This paper consists of two main contributions:

Abstract: Users of hospital personnel planning software cope with the complex task of translating their needs into several constraints of a very different nature and with differing cost parameters. We present a multi criteria evolutionary approach, which overcomes some of the practical difficulties that personnel schedulers in hospitals often face.

Users of hospital personnel planning software cope with the complex task of translating their needs into several constraints of a very different nature and with differing cost parameters. We present a multi criteria evolutionary approach, which overcomes some of the practical difficulties that personnel schedulers in hospitals often face.

This paper deals with the problem of nurse rostering in Belgian hospitals. This is a highly constrained real world problem that was (until the results of this research were applied) tackled manually. The problem basically concerns the assignment of duties to a set of people with different qualifications, work regulations and preferences. Constraint programming and linear programming techniques can produce feasible solutions for this problem. However, the reality in Belgian hospitals forced us to use heuristics to deal with the over constrained schedules. An important reason for this decision is the calculation time, which the users prefer to reduce. The algorithms presented in this paper are a commercial nurse rostering product developed for the Belgian hospital market, entitled Plane.

ORTEC is a Netherlands-based software company selling decision support systems based on operations research models. One of her products is HARMONY, a workforce scheduling package. We developed a model to predict its return on investment for a specific customer. The model uses a database of reference implementations to find organizations that are similar to the prospective customer’s organization. The costs and benefits have been broken down into several factors and we use this detailed information from the reference implementations to create a prediction of the return on investment for the workforce scheduling package. Using the information from the reference set allows us to move from industry-averages for potential savings to a prediction of potential savings based on the actual experiences from similar organizations. This also makes the model transparent: the outcomes can be traced to the elements that were selected from the reference set and a detailed description of the model i...

Hospitals need to repeatedly produce duty rosters for its nursing staff. The good scheduling of nurses has impact on the quality of health care, the recruitment of nurses, the development of budgets and other nursing functions. The nurse rostering problem (NRP) has been the subject of much study. This paper presents a brief overview, in the form of a bibliographic survey, of the many models and methodologies available to solve the NRP.

Nurse rostering problems represent a subclass of scheduling problems that are hard to solve. The goal is finding high quality shift and resource assignments, satisfying the needs and requirements of employees as well as the employers in healthcare institutions. In this paper, a real case of a nurse rostering problem is introduced. Memetic Algorithms utilizing different type of promising genetic operators and a self adaptive violation directed hierarchical hill climbing method are presented based on a previously proposed framework.

Optimization in sports is a field of increasing interest. Combinatorial optimization techniques have been applied e.g. to game scheduling and playoff elimination. A common problem usually found in sports management is the assignment of referees to games already scheduled. There are a number of rules and objectives that should be taken into account when referees are assigned to games. We address a simplified version of a referee assignment problem common to many amateur leagues of sports such as soccer, baseball, and basketball. The problem is formulated by integer programming and its decision version is proved to be NP-complete. To tackle real-life large instances of the referee assignment problem, we propose a three-phase heuristic approach based on a constructive procedure, a repair heuristic to make solutions feasible, and a local search heuristic to improve feasible solutions. Numerical results on realistic instances are presented and discussed.

This paper presents our work on decomposing a specific nurse rostering problem by cyclically assigning blocks of shifts, which are designed considering both hard and soft constraints, to groups of nurses. The rest of the shifts are then assigned to the nurses to construct a schedule based on the one cyclically generated by blocks. The schedules obtained by decomposition and

This paper presents our work on decomposing a specific nurse rostering problem by cyclically assigning blocks of shifts, which are designed considering both hard and soft constraints, to groups of nurses. The rest of the shifts are then assigned to the nurses to construct a schedule based on the one cyclically generated by blocks. The schedules obtained by decomposition and construction can be further improved by a variable neighborhood search. Significant results are obtained and compared with a genetic algorithm and a variable neighborhood search approach on a problem that was presented to us by our collaborator, ORTEC bv, The Netherlands. We believe that the approach has the potential to be further extended to solve a wider range of nurse rostering problems.

Nurse rostering is a complex scheduling problem that affects hospital personnel on a daily basis all over the world. This paper presents a new component-based approach with evolutionary eliminations, for a nurse scheduling problem arising at a major UK hospital. The main idea behind this technique is to decompose a schedule into its components (i.e. the allocated shift pattern of each nurse), and then to
implement two evolutionary elimination strategies mimicking natural selection and natural mutation process on these components respectively to iteratively deliver better schedules. The worthiness of all components in the schedule has to be continuously demonstrated in order for them to remain there. This demonstration employs an evaluation function which evaluates how well each component contributes towards the final objective. Two elimination steps are then applied: the first elimination eliminates a number of components that are deemed not worthy to stay in the current schedule; the second elimination may also throw out, with a low level of probability, some worthy components. The eliminated components are replenished with new ones using a set of constructive heuristics using local optimality criteria. Computational results using 52 data instances demonstrate the applicability of the proposed
approach in solving real-world problems.

This paper addresses the problem of developing cyclic schedules for nurses while taking into account the quality of individual rosters. In this context, quality is gauged by the absence of certain undesirable shift patterns. The problem is formulated as an integer program (IP) and then decomposed using Lagrangian relaxation. Two approaches were explored, the first based on the relaxation of the preference constraints and the second based on the relaxation of the demand constraints. A theoretical examination of the first approach indicated that it was not likely to yield good bounds. The second approach showed more promise and was subsequently used to develop a solution methodology that combined subgradient optimization, the bundle method, heuristics, and variable fixing. After the Lagrangian dual problem was solved, though, there was no obvious way to perform branch and bound when a duality gap existed between the lower bound and the best objective function value provided by an IP-b...

... AI techniques model a nurse rostering problem as CSP. In terms of modeling flexibility and ease of extending search methods, it is an adequate approach (Chun, 1997; Andy Chun et al., 2000; Lazaro and Aristondo, 1995; Weil et al., 1995) with a rich set of basic CP tools. ...

There is an undeniable global shortage of skillful nurses. This is a problem of high priority, which is correlated to workforce management issues. These issues can be palliated by increasing nurses' satisfaction based on flexible rosters using automated nurse rostering. This paper in concerned with nurse rostering based on constraint programming by satisfying global constraints, such as REGULAR, which is powerful but requires devising au-tomata of acceptable states. It was proven that REGULAR is reformulatable to SLIDE. En route to reformulate a REGULAR-based into SLIDE-based solution to nurse rostering, and through elaboration of Minizinc implementation , the author of this paper proposes a couple of metaphors namely the gamut and time arrow to model the nurse rostering. A gamut is a whole-subset of objects, such as within a given color-space or by an output device. The time arrow may refer to the direction of time as comprehended in physics. The paper in hand elucidates the new formulation based on these two metaphors, and presents implementation in Minizinc.

Healthcare organization is very important for community in delivering a healthy life. Nurse is the person in charge that will handle the healthcare organization wisely. The nurses should get their duty roster with a wide hand to deliver a good service. There are some issue related to that needs to be classified such as the modes of operation and constraints. The most desirable environment for the nurses is the balance workload roster that will consider any preferences from them that is possible to achieve due to aim to give a respect and care about. Besides that, the solution approach that can be applied in their field must be clarified. In this paper, we will discuss the entire thing about the nurse rostering problem such as its constraints, the modes of operation, the process to complete a roster and the solution approach to this problem.

This paper presents a new methodology to solve the cyclic preference scheduling problem for hourly workers. The focus is on nurse rostering but is applicable to any organization in which the midterm scheduling decision must take into account a complex of legal, institutional, and preferential constraints. The objective is to strike a balance between satisfying individual preferences and minimizing personnel costs. The common practice is to consider each planning period independently and to generate new rosters at the beginning of each. To reduce some of the instability in the process, there is a growing trend toward cyclic schedules, which are easier to manage and are generally perceived to be more equitable. To address this problem, a new integer programming model is presented that combines the elements of both cyclic and preference scheduling. To find solutions, a branch-and-price algorithm is developed that makes use of several branching rules and an extremely effective rounding heuristic. A unique feature of the formulation is that the master problem contains integer rather than binary variables. Computational results are reported for problem instances with up to 200 nurses. Most were solved within 10 minutes and many within 3 minutes when a double aggregation approach was applicable. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007.

We investigate the applicability of an existing framework for algorithm runtime prediction to the field of metaheuristics, in particular applied to the real world problem of nurse rostering. Apart from predicting the runtime, we look at other performance criteria as well. These so called empirical hardness models are based on readily computable features of the problem instances. These problem features are basic properties or characteristics that are thought to be influencing the complexity of the problem instances. We follow two approaches, one in a domain specific setting, and later in a more general setting where problems are represented using a Propositional Satisfiability (SAT) formulation. Both approaches lead to accurate prediction models in a small proof-of-concept problem distribution. The framework can be used to help understanding the complexity, build algorithm portfolios and allow for quick quality approximation when the resources for computing a solution are not available.

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This contribution deals with the distributed version of the nurse rostering problem. It is considered in a hospital with many separated wards. The nurse rostering problem within a ward is 'the local problem', rosters within a ward are 'local rosters'. At any time in the process, i.e. at the time of the construction of a roster for a certain time period as well as in the course of this time period when unexpected events cause rescheduling, wards may call in the help of their peers. At this level negotiation will take place. The details of the local rosters do not necessarily enter this negotiation level, and when they do, they may be translated from a local representation to a generally accepted vocabulary. After a motivation for a distributed approach, a general architecture is proposed and a negotiation protocol is described.

Hospital personnel scheduling deals with a large number of constraints of a different nature, some of which need to be satisfied at all costs. It is, for example, unacceptable not to fully support patient care needs and therefore a sufficient number of skilled personnel has to be scheduled at any time. In addition to personnel coverage constraints, nurse rostering problems deal with time related constraints arranging work load, free time, and personal requests for the staff. Real-world nurse rostering problems are usually over-constrained but schedulers in hospitals manage to produce solutions anyway. In practice, coverage constraints, which are generally defined as hard constraints, are often relaxed by the head nurse or personnel manager. The work presented in this paper builds upon a previously developed nurse rostering system that is used in several Belgian hospitals. In order to deal with widely varying problems and objectives, all the data in the model are modifiable by the users. We introduce a set of specific algorithms for handling and even relaxing coverage constraints, some of which were not supposed to be violated in the original model The motivation is that such practices are common in real scheduling environments. Relaxations enable the generation of better quality schedules without enlarging the search space nor the computation time.

When applying evolutionary algorithms to difficult real-world problems, the fitness function routinely needs evaluating for a very high number of intermediary cases. This paper is concerned with real-world nurse rostering problems with highly constrained resources. We consider a particular approach, which allows for a quick evaluation and is general enough to deal with other kinds of resource planning problems with time-related constraints. The model developed for this approach handles the constraints in a modular way and the addition of new constraints is relatively straightforward. Simple constraints (such as those affecting the personal wishes of employees) and global constraints (such as balancing the workload among people) can be formulated easily using this approach. Our approach can also handle very complex time-related constraints as well as conditions that are related to previously planned work. Moreover, it provides clear feedback about violation of constraints. The approach has been implemented successfully in a nurse rostering program entitled "Plane" which is used in hospitals all over Belgium. It can tackle a high number of specific and modifiable constraints of a very different nature. The benefits from this approach (in terms of software requirements) are small memory use and a computationally simple, single evaluation function allowing for the simultaneous rostering of several hospital wards at the same time.