Rostering Research Articles

Less Quick Returns — Greater Well-being

The aim of this study was to design ergonomically improved shift schedules for nurses in primary health care shift work in order to enhance their health and well-being. The main change made was the reduction of quick returns (i.e., no more morning shifts immediately after an evening shift) in order to ensure more recovery time between work shifts. Six municipal hospital units participated in the intervention. Our aim was to maintain or improve the well-being and work ability of aged workers. The subjects (n=75) were divided into three age groups: 20-40, 41-52, and 53-62 yr. The introduction of more recovery time between evening and morning shifts significantly improved the subjects' sleep and alertness, well-being at work, perceived health, and leisure-time activities independently of their age. The effect on social and family life was also positive. Working in shifts was the most disruptive for the youngest group of nurses. The Work Ability Index score depended on the age group: it was lowest among the oldest age group, and did not change during the intervention. Ergonomic working time arrangements show positive effects on the well-being of health care workers of all ages.

Nurse scheduling using fuzzy modeling approach

Nurse scheduling is a complex scheduling problem and involves generating a schedule for each nurse that consists of shift duties and days off within a short-term planning period. In real world applications, multiple sources of uncertainties are needed to be treated in providing higher quality schedules. This paper presents a seminal research on the application of fuzzy set theory to the nurse scheduling problem (NSP) to treat uncertainties in the target values of the hospital management and nurses’ preferences. More specifically, a new multi-objective integer programming model for the NSP is developed. Then, based on this model three fuzzy goal programming models are developed using different fuzzy solution approaches. A real world application is presented to confirm the viability of the proposed models. Also, to provide the decision maker for a more confident solution set for policy decision making, a sensitivity analysis is performed. Additionally, to show the efficiency of the proposed model, it is applied to several problem instances. The paper contributes to the literature by revealing that fuzzy modeling approaches can effectively be used in the NSP in providing schedules which are more personalized and equitable for nurses, and more satisfying for hospital management.

A Constraint-directed Local Search Approach to Nurse Rostering Problems

In this paper, we investigate the hybridization of constraint programming and local search techniques within a large neighbourhood search scheme for solving highly constrained nurse rostering problems. As identified by the research, a crucial part of the large neighbourhood search is the selection of the fragment (neighbourhood, i.e. the set of variables), to be relaxed and re-optimized iteratively. The success of the large neighbourhood search depends on the adequacy of this identified neighbourhood with regard to the problematic part of the solution assignment and the choice of the neighbourhood size. We investigate three strategies to choose the fragment of different sizes within the large neighbourhood search scheme. The first two strategies are tailored concerning the problem properties. The third strategy is more general, using the information of the cost from the soft constraint violations and their propagation as the indicator to choose the variables added into the fragment. The three strategies are analyzed and compared upon a benchmark nurse rostering problem. Promising results demonstrate the possibility of future work in the hybrid approach.

Elaboração automática da escala periódica de trabalho dos profissionais de enfermagem por meio de um software específico

To elaborate the nursing staff periodic schedule always was an arduous task for the nurses, because besides complex, it is a delayed task, taking them a lot of your precious time. Despite of this necessity, the software was developed based on the Internet, that it is capable to generate it in fast and simple way. The Software tries to elaborate a nursing staff schedule to get all the requests of the employees related to theirs desires of work days and time off, thus minimizing the displeasure and quarrels regarding the monthly work schedule.

A Component-Based Heuristic Search Method with Evolutionary Eliminations for Hospital Personnel Scheduling

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 the 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 for them to remain there. This demonstration employs an evaluation function that evaluates how well each component contributes toward the final objective. Two elimination steps are then applied: the first elimination removes 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.

Implicit shift scheduling with multiple breaks and work stretch duration restrictions

This paper considers a shift scheduling problem that includes different forms of flexibility in terms of shift starting times, break lengths and break placement. Two particular forms are studied: fractionable breaks and work stretch duration restrictions. Unlike standard breaks, fractionable breaks are not required to be attributed as a whole. They can be divided into fractions of breaks under some conditions. The distribution of breaks within a shift is done with respect to work stretch duration restrictions to ensure a correct mix of periods of work and rest. Two implicit models are proposed. They extend previous work on implicit modeling of break placement to incorporate the concepts of fractionable breaks and work stretch duration restrictions. In this context, we show the merits of using the so-called forward and backward constraints to model work stretch duration restrictions. We also introduce a new formulation of the forward and backward constraints and demonstrate that it considerably reduces the density of the constraint matrix of the two proposed models. Finally, we study the impact of fractionable breaks and work stretch duration restrictions and show that, for some instances, the use of these concepts considerably reduces the workforce size when compared to other traditional approaches.

On the characterization and generation of nurse scheduling problem instances

Due to its complexity and relevance in practice, many different procedures have been proposed in the operations research literature to solve the well-known nurse scheduling problem (NSP). The NSP assigns nurses to shifts per day maximizing the overall quality of the roster while taking various constraints into account. The often highly case-specific workplace conditions in hospital departments have resulted in the development of dedicated (meta-)heuristics to find a workable schedule in an acceptable time limit. However, in spite of research community posing a growing need for benchmarking, these procedures lack any base for comparison. In this paper, we propose a range of complexity indicators which characterize nurse scheduling problem instances, and a problem generator in order to construct a comparative test framework for various solution procedures for the NSP. We show that the different complexity indicators for the NSP presented in this paper predict the computational effort of a particular NSP instance for a particular solution procedure. Moreover, the comparison of procedures and good predictions of their performance allow the a priori selection of the best solution procedure, based on the simple calculation of the indicators. Hence, with the developed NSP generator those indicators can facilitate the evaluation of existing and future research techniques. Tests on a simple IP model illustrate the use of the proposed indicators.

Flexible shift scheduling of physicians

This research addresses a shift scheduling problem in which physicians at a German university hospital are assigned to demand periods over a planning horizon that can extend up to several weeks. When performing the scheduling it is necessary to take into account a variety of legal and institutional constraints that are imposed by a national labor agreement, which governs all physicians in German university hospitals. Currently, most medical departments develop their staff schedules manually at great cost and time. To solve the problem, a new modeling approach is developed that requires shifts to be generated implicitly. Rather than beginning with a predetermined number of shift types and start times, shifts are allowed to start at every pre-defined period in the planning horizon and extend up to 13 h with an hour-long break included. The objective is to find an assignment such that the total hours that have to be paid out as overtime are minimal under the restrictions given by the labor agreement. The problem is formulated as a mixed-integer program and solved with CPLEX. During the solution process individual lines-of-work are constructed for each physician. Using data from an anesthesia department, computational results indicate that high quality schedules can be obtained much more quickly than by current practice.

A shift sequence based approach for nurse scheduling and a new benchmark dataset

This paper investigates an adaptive constructive method for solving nurse rostering problems. The constraints considered in the problems are categorised into three classes: those that are sequence related, those that are nurse schedule related and those that are roster related. We propose a decomposition approach (to construct solutions) that consists of two stages: (1) to construct high quality sequences for nurses by only considering the sequence constraints, and (2) to iteratively construct schedules for nurses and the overall rosters, based on the sequences built and considering the schedule and roster constraints. In the second stage of the schedule construction, nurses are ordered and selected adaptively according to the quality of the schedules they were assigned to in the last iteration. Greedy local search is carried out during and after the roster construction, in order to improve the (partial) rosters built. We show that the local search heuristic during the roster construction can further improve the constructed solutions for the benchmark problems tested. In addition, we introduce new benchmark nurse rostering datasets which are based upon real world data. The data sets represent a variety of real world constraints. The publication of this problem data to the research community is aimed at closing the gap between theory and practice in nurse scheduling research. One of the main objectives is to encourage more research on these data sets.

A branch-and-price approach for integrating nurse and surgery scheduling

A common problem at hospitals is the extreme variation in daily (even hourly) workload pressure for nurses. The operating room is considered to be the main engine and hence the main generator of variance in the hospital. The purpose of this paper is threefold. First of all, we present a concrete model that integrates both the nurse and the operating room scheduling process. Second, we show how the column generation technique approach, one of the most employed exact methods for solving nurse scheduling problems, can easily cope with this model extension. Third, by means of a large number of computational experiments we provide an idea of the cost saving opportunities and required solution times.

Application of evidence- based nursing in preventing adverse effect of air - pocket tourniquet

Objective To lower the incidence of adverse effect of Air - pocket tourniquet application in nursing practice based on best evidences. Methods Clinical datas of 453 patients for retrospective analysis and 498 patients for usual care. Using evidence - based nursing program, a nursing schedule is established and implemented by means of referring documents and records on relative nursing problems found in datas adoptted in this paper, analyzing and summarizing the direct and indirect evidences, and clinical practice. Results The incidence of adverse effect of air - pocket tourniquet was obviously decreased after application of evidence - based nursing. Conclusion Application of evidence - based nursing can improve the quality of nursing practice and promote the development of nursing care delivery. Key words: Air-pocket tourniquet; Evidence-based nursing; Adverse effect

A hybrid heuristic ordering and variable neighbourhood search for the nurse rostering problem

This paper is concerned with the development of intelligent decision support methodologies for nurse rostering problems in large modern hospital environments. We present an approach which hybridises heuristic ordering with variable neighbourhood search. We show that the search can be extended and the solution quality can be significantly improved by the careful combination and repeated use of heuristic ordering, variable neighbourhood search and back-tracking. The amount of computational time that is allowed plays a significant role and we analyse and discuss this. The algorithms are evaluated against a commercial Genetic Algorithm on commercial data. We demonstrate that this methodology can significantly outperform the commercial algorithm. This paper is one of the few in the scientific nurse rostering literature which deal with commercial data and which compare against a commercially implemented algorithm.

Topics in real-time fleet management

This is a summary of the author’s Ph.D. thesis, supervised by Gianpaolo Ghiani and Barrett W. Thomas and defended on 21 February 2008, at the Università degli Studi della Calabria. The thesis is written in English and is available from the author upon request. In this work, various tactical and operational issues concerning real-time fleet management are studied. First, we introduce the Dynamic and Stochastic Traveling Salesman Problem and propose an optimal policy through a Markov Decision Process as well as develop lower and upper bounds on the optimal policy cost. Then, we present several strategies for implementing a priori routes, and we identify situations in which the use of more involved a priori strategies can give some benefit. Next, we consider the Dynamic and Stochastic Vehicle Dispatching Problem with Pickups and Deliveries, for which we develop anticipatory algorithms that evaluate alternative solutions through a short-term demand sampling and a fully sequential procedure for indifference zone selection. Finally, we propose Approximated Neighborhood Evaluation procedures for the same-day Courier Shift Scheduling Problem, a tactical problem which amounts to minimizing the staffing cost subject to probabilistic service level requirements.

A Bayesian Optimization Algorithm for Nurse Scheduling

Our research has shown that schedules can be built mimicking a human scheduler by using a set of rules that involve domain knowledge. This chapter presents a Bayesian Optimization Algorithm (BOA) for the nurse scheduling problem that chooses such suitable scheduling rules from a set for each nurse’s assignment. Based on the idea of using probabilistic models, the BOA builds a Bayesian network for the set of promising solutions and samples these networks to generate new candidate solutions. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed algorithm may be suitable for other scheduling problems.

Solution approaches to large shift scheduling problems

This paper considers large shift scheduling problems with different shift start times and lengths, fractionable breaks and work stretch duration restrictions. Two solution approaches are proposed to solve the problems over a multiple-day planning horizon. The first approach is based on a local branching strategy and the second one is based on a temporal decomposition of the problem. Local branching is very efficient in finding good feasible solutions when compared to a classical branch-and-bound procedure. However, the decomposition approach has the advantage of yielding feasible solutions in short computing times, even for difficult instances.

An agent-based nurse rostering system under minimal staffing conditions

Nurse rostering is a complex problem. We propose a new heuristic using a competitive agent-based negotiation that focuses on nurse preferences called competitive nurse rostering (CNR). Unlike the existing literature, CNR models each nurse's preference functions separately and separates the cost minimization and preference maximization problems. CNR produces quality nurse rosters even though it cannot leverage extra staffing. As an agent system, CNR can distribute computational requirements over several computer systems, include other solution methods at various points in of the rostering problem, and act as a real-time scheduling system. These benefits are not naturally inherent in centralized heuristic solutions.

The Effect of Consistent Nursing Shifts on Teamwork and Continuity of Care

To attract nurses to the workforce, scheduling of nurses on patient care units has evolved into a mixture of 4-, 6-, 8-, and 12-hour shifts. The result is chaotic as staff members come and go at varying times, creating the need for multiple handoffs and reassignment of patients. Effective teamwork and continuity of care are difficult, if not impossible, to achieve under these circumstances. The authors describe the effect of using just 1 shift length for all nursing staff.

Workforce Design with Movement Restrictions Between Workstation Groups

This paper is concerned with the problem of determining the optimal size and composition of a permanent workforce needed to run a facility when demand is specified by a workstation group (WSG) for up to 24 hours a day, 7 days a week. For full-time employees, a solution is characterized by a bid job, which consists of a five-day-a-week schedule, a lunch break for all shifts, and a set of WSG task assignments for each of the half-hour periods in a shift. In contrast, each part-time employee may be given anywhere from one to six shifts during the week, and each shift may vary from four to eight hours in length. To facilitate supervision, all employees must be assigned to a home WSG, but when idle time exists in their schedules, they can be redeployed to other WSGs for a portion of the day. One of the complicating and unique factors addressed in this paper is the existence of nonsymmetric movement restrictions between WSGs. For example, an employee whose home base is A may be permitted to perform tasks at B, but not vice versa. Because the full problem could not be reduced to a single model, a multistage solution approach was developed. In the first stage, an extended shift-scheduling problem is solved to determine the optimal number of employees and their shifts. The results are postprocessed in subsequent stages to obtain lunch breaks, days off, and task assignments under WSG movement restrictions. In the implementation of the multistage approach, two alternatives were explored. The first was based on the idea of partitioning the WSGs into manageable clusters and then solving them in series. The second involved the direct solution of an integer programming formulation of the task assignment problem with home-base restrictions and WSG movement restrictions, but for a fixed workforce. An iterative scheme was used to adjust the size of the workforce until all constraints were satisfied and overall optimality was achieved. Testing was done with data provided by the U.S. Postal Service (USPS) mail processing and distribution center (P&DC) in Dallas. The computations showed that the second alternative always yielded the smaller workforce and was always able to find good solutions within 30 minutes.

Development of a Generation Method of Evaluation Functions for the Nurse Scheduling Support System

Development of a Generation Method of Evaluation Functions for the Nurse Scheduling Support System

Comparison and hybridization of crossover operators for the nurse scheduling problem

In this paper, we present a hybrid genetic algorithm for the well-known nurse scheduling problem (NSP). The NSP involves the construction of roster schedules for nursing staff in order to maximize the quality of the roster schedule subject to various hard constraints. In the literature, several genetic algorithms have been proposed to solve the NSP under various assumptions. The contribution of this paper is twofold. First, we extensively compare the various crossover operators and test them on a standard dataset in a solitary approach. Second, we propose several options to hybridize the various crossover operators.