A heuristic algorithm for nurse scheduling with balanced preference satisfaction

This paper tackles the nurse scheduling problem with balanced preference satisfaction which consists of generating an assignment of shifts to nurses over a given time horizon and ensuring that the satisfaction of nurses personal preferences for shifts is as even as possible in order to ensure fairness. We propose a heuristic algorithm based on successive resolutions of the bottleneck assignment problem. The algorithm has two phases. In the first phase, the algorithm constructs an initial solution by solving successive bottleneck assignment problems. In the second phase, two improvement procedures based on reassignment steps are applied. Computational tests are carried out using instances from the standard benchmark dataset NSPLib. Our experiments indicate that the proposed method is effective and efficient, reducing discrepancies (hence improving fairness) between the individual rosters

A heuristic algorithm for nurse scheduling with balanced preference satisfaction

This paper tackles the nurse scheduling problem with balanced preference satisfaction which consists of generating an assignment of shifts to nurses over a given time horizon and ensuring that the satisfaction of nurses personal preferences for shifts is as even as possible in order to ensure fairness. We propose a heuristic algorithm based on successive resolutions of the bottleneck assignment problem. The algorithm has two phases. In the first phase, the algorithm constructs an initial solution by solving successive bottleneck assignment problems. In the second phase, two improvement procedures based on reassignment steps are applied. Computational tests are carried out using instances from the standard benchmark dataset NSPLib. Our experiments indicate that the proposed method is effective and efficient, reducing discrepancies (hence improving fairness) between the individual rosters

Course Scheduling Optiimization with Zero-One Linear Goal Programming Method

Abstrak Penjadwalan perkuliahan di perguruan tinggi membutuhkan model matematik yang dapat memaksimumkan kepuasan dosen dan mahasiswa. Penelitian ini menggunakan Zero-One Linear Goal Programming (0-1 LGP) untuk mengoptimasi penjadwalan perkuliahan di sebuah perguruan tinggi di Jakarta. Pendapat 50 orang responden yang terdiri dari mahasiswa dan dosen, diolah dengan metode AHP, untuk mendapatkan prioritas kriteria dalam penyusunan penjadwalan perkuliahan. Penelitian ini membuktikan metode 0-1 LGP secara efektif dapat digunakan untuk meningkatkan kepuasan dosen dan mahasiswa terhadap jadwal perkuliahan. Kata kunci: penjadwalan mata kuliah, kriteria, metode AHP, prioritas, metode Zero-One Linear Goal Programming, tingkat kepuasan  Abstract University course scheduling requires mathematical model to maximize the student and lecturer satisfaction. This research uses  Zero-One Linear Goal Programming (0-1 LGP) to optimize the course scheduling in a university in Jakarta. The data colletted from fifty students and lecturers was processed by using AHP to get the priority kriteria of course scheduling. This reseach shows that 01 LGP can be used for effective course scheduling which to improve the student and lecturer satiscation level. Keywords: courses scheduling, criteria, AHP, Priority, Zero One Linear Goal Programming, satisfation leve

Revisión de literatura sobre los modelos de optimización en programación de turnos de enfermería

Siendo la programación de turnos de enfermería (NSP) un componente esencial en la calidad del servicio de salud y debido al gran número de investigaciones desarrolladas sobre NSP en la literatura, se desarrolla una revisión de literatura sobre los artículos sobre NSP realizados desde 2003 hasta la fecha. A partir de este trabajo se logran identificar la tendencia y las necesidades propias de este problema, las cuales se caracterizan por (1) la necesidad de cerrar la brecha entre academia y práctica mediante el desarrollo de modelos objetivos de representación del problema y (2), desarrollar investigación sobre técnicas de solución capaces de tratar modelos de gran complejidad, sin sacrificar el recurso computacional. Este artículo presenta una revisión de literatura sobre los modelos de optimización en la programación de turnos de enfermería, publicados desde 2003 a la fecha.B Being the nurse shift scheduling an essential component of the quality of the health service and due to the big amount of research conducted regarding the Nurse Scheduling Problem (NSP), a literature review is carried out concerning articles on NSP published from 2003 up to now. As a result of this work, we were able to highlight the tendencies and own needs of this problem, which are characterized by: (1) the need to close the gap between academy and practice through the development of objective models that represent the problem and (2) research about solution techniques capable of processing models of great complexity, without sacrificing the computational resource. This article presents a literature review on optimization models in the NSP published since 2003

Optimisation stochastique de problèmes d’ordonnancement en santé

RÉSUMÉ : Les problèmes d'ordonnancement en santé sont complexes, car ils portent sur la fabrication d'ordonnancements qui absorbent les perturbations survenant dans le futur. Par exemple, les nouveaux patients urgents ont besoin d’être intégrés rapidement dans le planning courant. Cette thèse s'attaque à ces problèmes d'ordonnancement en santé avec de l'optimisation stochastique afin de construire des ordonnancements flexibles. Nous étudions en premier lieu la fabrication d'horaires pour deux types d’équipes d’infirmières: l’équipe régulière qui s'occupe des unités de soins et l’équipe volante qui couvre les pénuries d’infirmières à l’hôpital. Quand les gestionnaires considèrent ce problème, soit ils utilisent une approche manuelle, soit ils investissent dans un logiciel commercial. Nous proposons une approche heuristique simple, flexible et suffisamment facile à utiliser pour être implémentée dans un tableur et qui ne requiert presque aucun investissement. Cette approche permet de simplifier le processus de fabrication et d'obtenir des horaires de grande qualité pour les infirmières. Nous présentons un modèle multi-objectif, des heuristiques, ainsi que des analyses pour comparer les performances de toutes ces méthodes. Nous montrons enfin que notre approche se compare très bien avec un logiciel commercial (CPLEX), peut être implémentée à moindre coût, et comble finalement le manque de choix entre les solutions manuelles et les logiciels commerciaux qui coûtent extrêmement cher. Cette thèse s'attaque aussi à l'ordonnancement des chirurgies dans un bloc opératoire, fonctionnant avec un maximum de deux chirurgiens et de deux salles, en tenant compte de l'incertitude des durées d'opérations. Nous résolvons en premier lieu une version déterministe, qui utilise la programmation par contraintes, puis une version stochastique, qui encapsule le programme précédent dans un schéma de type ``sample average approximation''. Ce schéma produit des plannings plus robustes qui s’adaptent mieux aux variations des durées de chirurgies. Cette thèse présente le problème de prise de rendez-vous en temps réel dans un centre de radiothérapie. La gestion efficace d'un tel centre dépend principalement de l'optimisation de l'utilisation des machines de traitement. En collaboration avec le Centre Intégré de Cancérologie de Laval, nous faisons la planification des rendez-vous patients en tenant compte de leur priorité, du temps d'attente maximale et de la durée de traitement, le tout en intégrant l'incertitude reliée à l'arrivée des patients au centre. Nous développons une méthode hybride alliant optimisation stochastique et optimisation en temps réel pour mieux répondre aux besoins de planification du centre. Nous utilisons donc l'information des arrivées futures de patients pour dresser le portrait le plus fidèle possible de l'utilisation attendue des ressources. Des résultats sur des données réelles montrent que notre méthode dépasse les stratégies typiquement utilisées dans les centres. Par la suite, afin de proposer un algorithme stochastique et en temps réel pour des problèmes d'allocation de ressources, nous généralisons et étendons la méthode hybride précédente. Ces problèmes sont naturellement très complexes, car un opérateur doit prendre dans un temps très limité des décisions irrévocables avec peu d'information sur les futures requêtes. Nous proposons un cadre théorique, basé sur la programmation mathématique, pour tenir compte de toutes les prévisions disponibles sur les futures requêtes et utilisant peu de temps de calcul. Nous combinons la décomposition de Benders, qui permet de mesurer l'impact futur de chaque décision, et celle de Dantzig-Wolfe, qui permet de s'attaquer à des problèmes combinatoires. Nous illustrons le processus de modélisation et démontrons l’efficacité d'un tel cadre théorique sur des données réelles pour deux applications: la prise de rendez-vous et l'ordonnancement d'un centre de radiothérapie, puis l'assignation de tâches à des employés et leur routage à travers l’entrepôt.----------ABSTRACT : Scheduling problems are very challenging in healthcare as they must involve the production of plannings that absorb perturbations which arise in the future. For example, new high-priority patients needs to be quickly added in the computed plannings. This thesis tackles these scheduling problems in healthcare with stochastic optimization such as to build flexible plannings. We first study the scheduling process for two types of nursing teams, regular teams from care units and the float team that covers for shortages in the hospital. When managers address this problem, they either use a manual approach or have to invest in expensive commercial tool. We propose a simple heuristic approach, flexible and easy enough to be implemented on spreadsheets, and requiring almost no investment. The approach leads to streamlined process and higher-quality schedules for nurses. %improves both the process and the quality of the resulting schedule. The multi-objective model and heuristics are presented, and additional analysis is performed to compare the performance of the approach. We show that our approach compares very well with an optimization software (CPLEX solver) and may be implemented at no cost. It addresses the lack of choice between either manual solution method or a commercial package at a high cost. This thesis tackles also the scheduling of surgical procedures in an operating theatre containing up to two operating rooms and two surgeons. We first solve a deterministic version that uses the constraint programming paradigm and then a stochastic version which embeds the former in a sample average approximation scheme. The latter produces more robust schedules that cope better with the surgeries' time variability. This thesis presents an online appointment booking problem for a radiotherapy center. The effective management of such facility depends mainly on optimizing the use of the linear accelerators. We schedule patients on these machines taking into account their priority for treatment, the maximum waiting time before the first treatment, and the treatment duration. We collaborate with the Centre Intégré de Cancérologie de Laval to determine the best scheduling policy. Furthermore, we integrate the uncertainty related to the arrival of patients at the center. We develop a hybrid method combining stochastic optimization and online optimization to better meet the needs of central planning. We use information on the future arrivals of patients to provide an accurate picture of the expected utilization of resources. Results based on real data show that our method outperforms the policies typically used in treatment centers. We generalize and extend the previous hybrid method to propose a general online stochastic algorithm for resource allocation problems. These problems are very difficult in their nature as one operator should take irrevocable decisions with a limited (or inexistent) information on future requests and under a very restricted computational time. We propose a mathematical programming-based framework taking advantage of all available forecasts of future requests and limited computational time. We combine Benders decomposition, which allows to measure the expected future impact of each decision, and Dantzig-Wolfe decomposition, which can tackle a wide range of combinatorial problems. We illustrate the modelling process and demonstrate the efficiency of this framework on real data sets for two applications: the appointment booking and scheduling problem in a radiotherapy center and the task assignment and routing problem in a warehouse

An Integrated Framework for Staffing and Shift Scheduling in Hospitals

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

A mathematical programming model for scheduling of nurses' labor shifts

PubMedID: 20703701In this study, a mathematical programming model is proposed for scheduling problem of nurses' labor shifts. The developed mathematical programming model's aim is to minimize nurses' total idle waiting time during a week planning horizon. In this model, investigated constraints are as follows: (1) Maximum total working time a week for each nurse must not be exceeded. (2) After a nurse works a shift, the nurse can be assigned to another shift after two shifts at least. This constraints-set ensures resting of the nurse after the nurse works a shift. (3) Total number of nurses worked for each shift must be controlled with maximum and minimum bounds given for number of nurses for each shift. In this manner, total number of nurses worked for each shift is between maximum and minimum limit-values given for each shift. This constraint ensures flexibility to the user to determine number of nurses for each shift. (4) The decision variable that shows nurse-shift assignment pairs is 0 or 1. In this study, maximum total working time a week for a nurse, total number of nurses in a health service, maximum and minimum numbers of nurses worked a shift are user-specified parameters. In this way, this model can be adapted for the studies with different values of these parameters. In this study, the developed model is illustrated using a numerical example and then LINGO8.0 software is used to ensure the global optimum solution of the developed model. Results and also sensitivity analysis carried out for this example are presented in the study. © Springer Science+Business Media, LLC 2010