Scheduling trainees at a hospital department using a branch-and-price approach.

Scheduling trainees (graduate students) is a complicated problem that has to be solved frequently in many hospital departments. We will describe a trainee scheduling problem encountered in practice (at the ophthalmology department of the university hospital Gasthuisberg, Leuven). In this problem a department has a certain number of trainees at its disposal, which assist specialists in their activities (surgery, consultation, etc.). For each trainee one has to schedule the activities in which (s)he will assist during a certain time horizon, usually one year. Typically, these kind of scheduling problems are characterized by both hard and soft constraints. The hard constraints consist of both work covering constraints and formation requirements, whereas the soft constraints include trainees' preferences and setup restrictions. In this paper we will describe an exact branch-and-price method to solve the problem to optimality.Branch-and-price; Constraint; Health care; Problems; Requirements; Scheduling; Staff scheduling; Time; University;

Exact and Heuristic Methodologies for Scheduling in Hospitals: Problems, Formulations and Algorithms..

Dit proefschrift handelt over een aantal exacte en heuristische pro cedures voor planningsproblemen die opduiken binnen ziekenhuizen. H et materiaal kan opgedeeld worden in drie delen. Het eerste deel richt z ich op personeelsplanning. We introduceren een nieuwe formulering en ont ledingsbenadering voor een probleem dat het opstellen van een assistente nplanning op lange termijn behelst. De benadering ontleedt het probleem op basis van de activiteiten en maakt gebruik van kolomgeneratie om een optimale oplossing te bekomen. Het resulterende vertak-en-prijs algoritm e werd geïmplementeerd in een applicatie, aangevuld met heuristische zoe kprocedures en getest op een aantal praktijkproblemen. Onze experimentel e resultaten tonen een belangrijke toename in efficiëntie aan, vergeleke n met de traditionele benaderingen die het probleem ontleden op basis va n de stafleden. Het tweede deel van deze thesis handelt over het plannen van het operati ekwartier. Eerst stellen we een model en computerprogramma voor om het g ebruik van diverse hulpmiddelen in functie van de cyclische hoofdplannin g van het operatiekwartier te visualiseren. Vervolgens stellen we een aa ntal modellen en algoritmes voor om planningen te genereren met een afge vlakte, resulterende bedbezetting. Onze ideeën werden getest op praktijk data in twee gevalstudies. In het derde deel combineren we de kennis verkregen uit de eerste twee d elen in een geïntegreerd model voor de planning van het personeel en het operatiekwartier. Het model wordt opgelost door een vertak-en-prijs alg oritme dat herhaaldelijk twee verschillende subproblemen oplost. Het eer ste behelst het genereren van een individuele planning van een personeel slid d.m.v. dynamische programmering. In het tweede subprobleem zoeken w e naar een planning van het operatiekwartier met een bijhorende ben odigde personeelsbezetting die goed past bij de gegenereerde set va n individuele planningen. Dit gebeurt via het oplossen van een geheeltal lig programmeringsprobleem. We hebben mooie rekenresultaten bekomen voor dit moeilijke probleem. Tenslotte wordt er aangetoond hoe onze benaderi ng gebruikt kan worden om verschillende ziekenhuizen te vergelijken. Con creet illustreren we hoe de resultaten geïnterpreteerd kunnen worden om de bronnen van verspilling in het personeelsbeleid van een ziekenhuis te detecteren.

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

Heuristic branch-and-price for building long term trainee schedules.

Branch-and-price is an increasingly important technique for solving large integer programming models. Staff scheduling has been a particularly fruitful area since these problems typically exhibit a decomposable structure. Beside computational efficiency branch-and-price produces two other important advantages in comparison with pure integer programming. Firstly, it often allows for a more accurate problem statement since many constraints which are hard to formulate in the integer program could be easily incorporated in the column generator. Secondly, a branch-and-price algorithm can easily be turned into an effective heuristic when optimality is no major concern. We illustrate these advantages for a medical trainee scheduling problem encountered at Oogziekenhuis Gasthuisberg Leuven and present some computational results together with implementation issues.Advantages; Area; Branch-and-price; Constraint; Efficiency; Heuristic; Integer programming; Model; Models; Problems; Research; Scheduling; Staff scheduling; Structure;

On the trade-off between staff-decomposed and activity-decomposed column generation for a staff scheduling problem.

In this paper a comparison is made between two decomposition techniques to solve a staff scheduling problem with column generation. In the first approach, decomposition takes place on the staff members, whereas in the second approach decomposition takes place on the activities that have to be performed by the staff members. The resulting master LP is respectively a set partitioning problem and a capacitated multi-commodity flow problem. Both approaches have been implemented in a branch-and-price algorithm. We show a trade-off between modeling power and computation times of both techniques.decomposition; staff scheduling; set partitioning; multi-commodity flow; branch-and-price; branch-and-price; programs;

Reducing access times for an endoscopy department by an iterative combination of computer simulation and Linear Programming

de Wit, J.; Struben, V.M.D.; Overbeek, B.J.H.; Fockens, P.; Elkhuizen, S.G. General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Abstract To reduce the access times of an endoscopy department, we developed an iterative combination of Discrete Event simulation and Integer Linear Programming. We developed the method in the Endoscopy Department of the Academic Medical Center in Amsterdam and compared different scenarios to reduce the access times for the department. The results show that by a more effective allocation of the current capacity, all procedure types will meet their corresponding performance targets in contrast to the current situation. This improvement can be accomplished without requiring additional equipment and staff. Currently, our recommendations are implemented

A heuristic procedure to solve the project staffing problem with discrete time/resource trade-offs and personnel scheduling constraints

Highlights • Project staffing with discrete time/resource trade-offs and calendar constraints. • An iterated local search procedure is proposed. • Different problem decomposition techniques are applied. Abstract When scheduling projects under resource constraints, assumptions are typically made with respect to the resource availability and activities are planned each with its own duration and resource requirements. In resource scheduling, important assumptions are made with respect to the staffing requirements. Both problems are typically solved in a sequential manner leading to a suboptimal outcome. We integrate these two interrelated scheduling problems to determine the optimal personnel budget that minimises the overall cost. Integrating these problems increases the scheduling flexibility, which improves the overall performance. In addition, we consider some resource demand flexibility in this research as an activity can be performed in multiple modes. In this paper, we present an iterated local search procedure for the integrated multi-mode project scheduling and personnel staffing problem. Detailed computational experiments are presented to evaluate different decomposition heuristics and comparison is made with alternative optimisation techniques

Model Penjadwalan Calon Tenaga Dokter (Dokter Muda/Koas) Mempertimbangkan Faktor Ergonomi Di Rumah Sakit Pendidikan

Industri jasa pelayanan kesehatan dituntut untuk terus memperbaiki performa dan pelayanan kepada masyarakat. Perbaikan tersebut bisa dilakukan dengan perbaikan kinerja calon dokter. Calon dokter harus melayani seluruh pasien dengan baik, tepat waktu dan tepat sasaran selama 24 jam. Agar pelayanan tersebut terlaksana selama 24 jam, butuh penjadwalan calon dokter. Penjadwalan calon dokter merupakan pengalokasian calon dokter ke stase/bagian klinik tertentu selama periode tertentu sehingga dapat memenuhi batasan yang diberikan. Penelitian ini bertujuan membuat model penjadwalan calon dokter mempertimbangkan faktor ergonomi. Ergonomi berkontribusi dalam pembuatan penjadwalan, rotasi kerja, serta penentuan jam istirahat pada sebuah organisasi atau industri agar tercipta kesesuaian antara manusia, lingkungan fisik dan karakteristik pekerjaan. Objek yang diteliti yaitu calon dokter dari Universitas Hang Tuah sejumlah 179 orang (26 kelompok), selama dua tahun yang akan dijadwalkan di 16 stase. Penelitian dilakukan dengan membuat permodelan matematika (Integer Nonlinear Programming) untuk merumuskan persoalan penjadwalan dengan mempertimbangkan faktor ergonomi, kemudian permodelan matematika tersebut diselesaikan dengan metode Branch and Bound menggunakan software LINGO, dan pada tahap terakhir yaitu percobaan numerik dan Analisa hasil =============================================================================================== The health care industry is required to improve its performance and services continuously. One improvement alternative that can be carried out is by improving the performance of medical trainees. The medical trainees must serve every patient well, timely, and on target for 24 hours. In order for services to be well carried out for 24 hours, it requires medical trainees scheduling. Medical trainees scheduling is an act of allocation medical trainees to specific clinic for a specific period of time in order to satisfy the limit given. This study aims to create a medical trainees scheduling model considering ergonomic factors. Ergonomics contributes in developing of a schedule, job rotation and determining rest hours in an organization or industry to create conformity and harmony among human, physical environments and job characteristics. The object of this study is Medical Trainees of Hang Tuah University (179 persons in 26 groups), for two years and will be scheduled at 16 clinics. The study was preceded by making mathematical modelling (Integer Nonlinear Programming) to formulate scheduling problems by considering ergonomic factors, then mathematical modelling is solved by branch and bound method using LINGO software, and at the last stage is numerical experiments and results analysi

Development and implementation of a computer-aided method for planning resident shifts in a hospital

Ce mémoire propose une formulation pour le problème de confection d'horaire pour résidents, un problème peu étudiée dans la litérature. Les services hospitaliers mentionnés dans ce mémoire sont le service de pédiatrie du CHUL (Centre Hospitalier de l'Université Laval) et le service des urgences de l'Hôpital Enfant-Jésus à Québec. La contribution principale de ce mémoîre est la proposition d'un cadre d'analyse pour l’analyse de techniques manuelles utilisées dans des problèmes de confection d'horaires, souvent décrits comme des problèmes d'optimisation très complexes. Nous montrons qu'il est possible d'utiliser des techniques manuelles pour établir un ensemble réduit de contraintes sur lequel la recherche d’optimisation va se focaliser. Les techniques utilisées peuvent varier d’un horaire à l’autre et vont déterminer la qualité finale de l’horaire. La qualité d’un horaire est influencée par les choix qu’un planificateur fait dans l’utilisation de techniques spécifiques; cette technique reflète alors la perception du planificateur de la notion qualité de l’horaire. Le cadre d’analyse montre qu'un planificateur est capable de sélectionner un ensemble réduit de contraintes, lui permettant d’obtenir des horaires de très bonne qualité. Le fait que l'approche du planificateur est efficace devient clair lorsque ses horaires sont comparés aux solutions heuristiques. Pour ce faire, nous avons transposées les techniques manuelles en un algorithme afin de comparer les résultats avec les solutions manuelles. Mots clés: Confection d’horaires, Confection d’horaires pour résidents, Creation manuelle d’horaires, Heuristiques de confection d’horaires, Méthodes de recherche localeThis thesis provides a problem formulation for the resident scheduling problem, a problem on which very little research has been done. The hospital departments mentioned in this thesis are the paediatrics department of the CHUL (Centre Hospitalier de l’Université Laval) and the emergency department of the Hôpital Enfant-Jésus in Québec City. The main contribution of this thesis is the proposal of a framework for the analysis of manual techniques used in scheduling problems, often described as highly constrained optimisation problems. We show that it is possible to use manual scheduling techniques to establish a reduced set of constraints to focus the search on. The techniques used can differ from one schedule type to another and will determine the quality of the final solution. Since a scheduler manually makes the schedule, the techniques used reflect the scheduler’s notion of schedule quality. The framework shows that a scheduler is capable of selecting a reduced set of constraints, producing manual schedules that often are of very high quality. The fact that a scheduler’s approach is efficient becomes clear when his schedules are compared to heuristics solutions. We therefore translated the manual techniques into an algorithm so that the scheduler’s notion of schedule quality was used for the local search and show the results that were obtained. Key words: Timetable scheduling, Resident scheduling, Manual scheduling, Heuristic schedule generation, Local search method