Quantitative methods of physician scheduling at hospitals

Masteroppgave i industriell økonomi og informasjonsledelse 2010 – Universitetet i Agder, GrimstadStaff scheduling at hospitals is a widely studied area within the fields of operation research and management science because of the cost pressure on hospitals. There is an interest to find procedures on how to run a hospital more economically and efficient. Many of the studies about staff scheduling at hospital have been done about nurses, which work under common labor law restrictions. The goal of nurse scheduling is to minimize the staffing cost and maximizing their preferences. While the operation rooms are the engine of the hospitals, the physicians are the fueling for the hospitals. Without the physicians the patients would not be treated well and the hospital would not earn money. This thesis studies the physician scheduling problem, which has not been studied so widely as the nurse scheduling problem. A limited number of literatures about this theme have been studied to answer the main research question: How can we categorize physician scheduling at hospitals? Studying the physician rostering problem on the search for efficiency and cost savings is an intricate process. One can read a lot about this theme develop a lot of models; and shape and test different hypotheses. However, to increase efficiency it is wise to make a plan of information to consider. The categories searched for within this literature review are the level of experience, the planning period, the field of specialty, the type of shifts, whether cyclic or acyclic schedules are used and also which models and methods are used to solve this problem. Level of experience was first divided between residents - that are still under education, and physicians - which are fully licensed. Physicians are medical trained doctors that provide medical treatment rather than surgical treatment in hospitals. After medical school, they have accomplished between three to seven years of residential internship before they obtain their license. The residents are still under education and must therefore participate in a number of assorted activities and patient treatments during their resident period to acquire their license. This situation for resident makes scheduling unique as they are in a learning period and staffing the hospital at the same time. The planning period is a category that is divided in three levels; short-term which lasts up to a month, midterm which lasts from one month up to six months and a long-term that lasts from six months up to one year. The field of specialty is divided between the specialties of the physicians. In the numerous departments at a hospital, the work is distinctive from one another. A normal workday in a department that is only open during the day can be quite different from a workday in an emergency department. Working in a hospital is unlike other type of jobs. A hospital or at least different departments in a hospital are open all day long, every day of the year. As a result, the hospital must be staffed all the time. The need for staffing varies during the day, the day of week; and during the different seasons, due to the fluctuation of the demands. An example for a solution is a variety of broad types of shifts. Scheduling these shift types can be made cyclic or acyclic. Qualitative method has been used in this master’s thesis. The research question is a typically quantitative method starting with “how”. And to answer it, this thesis builds on a definite number of case studies. These case studies are limited to concern only about physician and resident scheduling problem written in English. These cases are primarily scientific articles and conference handouts. The cases are read - and interesting information is registered in a case study database. The findings have shown different use of planning period after the level of experience. Few studies have been done with short-term planning period; physicians are mostly scheduled for a midterm planning period, whereas residents are mostly scheduled with a long-term planning period. Most studies have scheduled physicians and residents for a day, evening and night shift, often in a combination with some kind of on-call shift. The field of specialty that is most studied is within emergency medicine. As the work in an emergency department is stressful, it is a complex task to make good schedules that satisfies the physicians and residents working there. Exact approaches are the most used modeling technique used for physician scheduling

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

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

Optimisation de roulements de chauffeurs d’autobus

RÉSUMÉ: Le problème de roulements de chauffeurs d’autobus vise à déterminer les horaires de travail des chauffeurs d’autobus sur un horizon donné. Il s’agit d’un problème où des séquences de jours de repos et de journées de travail sont construites. Les journées de travail sont générées lors de la résolution du problème de construction de journées de travail. Ce problème a pour objectif de générer des journées de travail anonymes afin d’assurer, à un coût minimum, la couverture complète des horaires d’autobus. Plusieurs règles doivent être respectées lors de la résolution, entre autres, l’amplitude maximale ou minimale d’une journée de travail, le temps maximal ou minimal de travail, etc. Lorsque les journées de travail sont déterminées, elles sont affectées aux différents chauffeurs disponibles et les roulements des chauffeurs sont construits à cette étape. Les journées de travail sont affectées en respectant un ensemble de règles dérivées des conventions collectives, et chaque journée de travail est effectuée par un chauffeur durant un jour de la semaine. Dans notre contexte, les roulements de chauffeurs d’autobus sont cycliques et définis sur une semaine pour un certain horizon de planification. Ainsi les journées de travail peuvent varier d’un jour à l’autre mais se répètent d’une semaine à une autre. Le problème de roulements avec jours de repos fixés vise à affecter les journées de travail aux différents chauffeurs dans les jours de travail (c’est-à-dire, les jours qui ne sont pas des jours de repos). Nous proposons, d’abord, une nouvelle formulation forte en nombres entiers du problème de roulements avec repos fixés. Les règles d’affectation des journées de travail sont diverses et compliquées, surtout qu’elles impliquent des contraintes de repos de nuit entre deux journées de travail et des contraintes qui s’étendent sur plusieurs jours et parfois sur plusieurs semaines. La fonction objectif vise à équilibrer le plus possible la charge de travail entre tous les chauffeurs. Ceci a été traduit par la minimisation des déviations positives par rapport à la moyenne des charges de travail totale par semaine de toutes les journées de travail. Différentes modélisations des contraintes de repos de nuit ont été proposées, ainsi qu’une deuxième formulation de la fonction objectif, mais qui vise aussi à équilibrer la charge de travail entre les chauffeurs d’autobus. Nous avons montré que la nouvelle formulation permet de reserrer l’espace de recherche lors du branchement, ce qui permet d’avoir des solutions entières plus rapidement. Ensuite, une approche est proposée pour résoudre le problème de roulements intégré de construction de jours de repos et d’affectation de journées de travail. Le problème est modélisé comme un programme linéaire mixte en nombres entiers. Étant donné que le problème ne contient pas de règles de quarts de travail ni de règles souples (des préférences par exemple), le problème présente beaucoup de symétrie. Le modèle s’est avéré très difficile à résoudre à l’optimalité avec le solveur commercial CPLEX malgré l’ajustement très poussé des paramètres et l’utilisation des méthodes avancées de programmation en nombres entiers (fixation de variables, branchement priorisé, ...). Sur la base de ce modèle, nous avons introduit une matheuristique à deux étapes qui permet de trouver des solutions de très bonne qualité. En utilisant une telle solution comme donnée d’entrée dans un solveur commercial, le modèle intégré peut être résolu beaucoup plus rapidement. Nos expériences de calcul testées sur des instances réelles de grande taille ont montré l’efficacité de la matheuristique. Des solutions optimales ont été obtenues dans des temps de calcul relativement courts (3.5 heures pour le cas impliquant jusqu’à 333 chauffeurs). En outre, en fournissant ces solutions comme solutions initiales au solveur CPLEX, de grandes accélérations (jusqu’à 99%) ont été obtenues pour résoudre le problème intégré avec une optimalité prouvée. L’article intitulé "Integrated and sequential solution methods for the cyclic bus driver rostering problem" traitant cet objectif a été publié dans la revue "Journal of the Operational Research Society" Finalement, nous avons intégré des règles relatives aux préférences des chauffeurs dans le modèle de roulements. Le nouveau modèle vise à affecter les journées de travail aux différents chauffeurs sur un horizon prédéfini, tout en respectant les règles strictes d’affectation, en équilibrant la charge de travail entre les chauffeurs et en minimisant le plus possible les violations des règles souples (les préférences). Deux nouvelles matheuristiques ont été proposées. La première limite l’espace de recherche en pré-assignant les journées de travail aux roulements avec des jours de repos fixés. La deuxième matheuristique utilise un problème de partitionnement d’ensemble pour décomposer les roulements de grande taille en sous-roulements de tailles petites à moyennes. Dans une série d’expériences de calcul menées sur des instances réelles, nous montrons que ces matheuristiques peuvent être utilisées pour produire des solutions de bonne qualité pour des grandes instances (333 chauffeurs et 1509 journées de travail) dans des temps de calcul relativement courts. L’article intitulé "Preference-based bus driver rostering problem with fixed days off" traitant cet objectif a été soumis à la revue "Public Transport"---------ABSTRACT:The bus driver rostering problem aims at building the work schedules of bus drivers over a given period of time. Solving such problem results in sequences of days off and duties. The duties are constructed via the duty scheduling problem, which creates anonymous duties in order to ensure, at a minimum cost, complete coverage of a set of bus trips. Several rules must be respected while solving this problem, i.e. maximum or minimum span of a duty, maximum or minimum working time, etc. The resulting duties must then be assigned to the different available drivers, creating their rosters. This process complies with a set of rules derived from collective agreements. Every duty is performed by one driver on one day of the week. Here in this context, bus driver rosters are cyclic, and defined over a week for a certain planning horizon. Thus, duties may vary from a day to another, but they are repeated weekly. The rostering problem with fixed days off aims at assigning duties to drivers in working days. First, a new mixed integer formulation of the problem is proposed. The assignment rules are diverse and complicated, especially since they involve night rest constraints between two duties and constraints that are extended over several days, and sometimes over several weeks. The objective function is to balance the workload among all the drivers. This has been achieved by minimizing positive deviations from the average total workload per week. Furthermore, different formulations of the night rest constraints are presented, as well as, a second formulation of the objective function that minimizes the sum of the absolute values of the deviations from the average workload per week. It is shown that the first proposed formulation makes it possible to tighten the search space during the branch-and-bound process and, consequently, helps finding integer solutions more rapidly. Next, an approach is proposed to solve the integrated days off scheduling and rostering problem. First the problem is modeled as a mixed integer linear program. In this problem, there are no shifts, and therefore, no shift related rules that reduce the solution space, nor shift related preferences that can reduce symmetry in the branch-and-bound process and ease the search for integer solutions. This model turns out to be very hard to solve to optimality without providing an initial solution. Based on this model, we introduce a new two-step matheuristic that can compute high-quality solutions. Using such a solution as an input to a commercial solver, the integrated model can be solved much more rapidly. Our computational results obtained on real-world instances involving up to 333 drivers and 1509 duties show that these initial solutions are optimal in most cases and, consequently, that the proposed matheuristic is very efficient by itself. Finally, we integrated the bus driver preference rules to the rostering problem. The new model aims at assigning duties to different drivers over a predefined cyclic horizon, while respecting a set of rules (hard constraints), balancing the workload among the drivers and satisfying as much as possible the driver preferences (soft constraints). We first model the problem as a mixed integer linear program that minimizes the number of preference violations while maintaining the workload balance of the solutions within a certain margin relative to the optimal one. Since this model is hard to solve for large instances, we propose two new matheuristics. The first one restricts the search space by preassigning duties to rosters based on an optimal solution to the duty assignment problem with fixed days off. The second algorithm makes use of a set partitioning problem to decompose rosters consisting of a large number of positions into sub-rosters of smaller sizes. In a series of computational experiments conducted on real-world instances, we show that these matheuristics can be used to produce high-quality solutions for large instances of the problem, within short computational times

Optimisation methods for staff scheduling and rostering: an employee-friendly approach

The growth in the global call centre industry over the last twenty years has been huge. The main motivating factor for businesses to introduce call centres as their main vehicle for handling customer contacts has been that call centres are inherently efficient. Since the mid-1980's, UK businesses have sought to establish competitive advantage by using call centres to reduce the cost of managing their customer contacts. Over the last decade or so, however, an alternative strategy has emerged based not on cost-reduction and efficiency, but on revenue generation and service quality. This new strategy places high value on customer and staff retention. This thesis is concerned with the operations management task of employee rostering. We argue that traditional models for producing rosters for call centre employees are designed to support the older efficiency-based culture, and are inappropriate for call centres adopting the more recent quality-based culture. We show how the use of methods and models drawn from conflicting management philosophies contributes to the high level of employee turnover, and inhibits the drive for service quality. Our primary contributions are to identify a set of rostering goals which reflect the interests of the employees, and to quantitatively represent these goals in a system of mathematical rostering models designed to support the revenue generation strategy. Our models are implemented using the robust Mixed Integer Programming methodology. In addition, we adapt our model to address the related problem of nurse rostering, and solve two benchmark problems to optimality. We demonstrate that our model generates rosters of a higher quality than the alternatives, at no additional cost

Generalized Algorithms for Crew Planning: Survey and Future Directions for Railways

This paper studies the crew planning problem as observed in the transportation industry. We first survey the existing literature on crew scheduling applications in railways and airlines. Next, we identify the synergies in the two domains and propose new directions for railway crew scheduling inspired from the applications in airlines

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

A tabu search approach with embedded nurse preferences for solving nurse rostering problem

This paper presents an intelligent tabu search (TS) approach for solving a complex real-world nurse rostering problem (NRP). Previous study has suggested that improvement on neighborhoods and smart intensification of a TS could produce faster and fitted solution. In order to enhance the TS, this paper introduces an improvement to the neighborhoods and explores on the neighborhoods exploitations of TS to solve the NRP. The methodology consists of two phases: initialization and neighborhood. The semi-random initialization is employed for finding a good initial solution during the initialization phase which avoids the violation of hard constraints, while the neighborhood phase is established for further improving the solution quality with a special representation and innovative neighborhood generations within TS algorithm. The aim is to move sample points towards a high-quality solution while avoiding local optima by utilising a calculated force value. It is observed that the enhancement strategy could improve the solution quality of the constructed roster. It is concluded that the TS with enhancements approach is able to assign effective and efficient shift duties for the NRP especially when related with real-world working regulations and nurses preference

A Tabu Search Approach with Embedded Nurse Preferences for Solving Nurse Rostering Problem

This paper presents an intelligent tabu search (TS) approach for solving a complex real-world nurse rostering problem (NRP). Previous study has suggested that improvement on neighborhoods and smart intensification of a TS could produce faster and fitted solution. In order to enhance the TS, this paper introduces an improvement to the neighborhoods and explores on the neighborhoods exploitations of TS to solve the NRP. The methodology consists of two phases: initialization and neighborhood. The semi-random initialization is employed for finding a good initial solution during the initialization phase which avoids the violation of hard constraints, while the neighborhood phase is established for further improving the solution quality with a special representation and innovative neighborhood generations within TS algorithm. The aim is to move sample points towards a high-quality solution while avoiding local optima by utilising a calculated force value. It is observed that the enhancement strategy could improve the solution quality of the constructed roster. It is concluded that the TS with enhancements approach is able to assign effective and efficient shift duties for the NRP especially when related with real-world working regulations and nurses preference