DFG Research Grants Project 405488489: Resident scheduling in teaching hospitals with the use of quantitative methods

© Universität Augsburg

This research project mainly deals with the strategic and tactical-operative scheduling of medical residents. In addition to relieving the medical staff who are currently responsible for the planning process, this research project increases the predictability of structured training. This gives hospitals the opportunity to increase the quality of their training and, consequently, their attractiveness to other hospitals. In addition, supervisors from different departments can better assess the knowledge of residents and thus to keep the level of service, which is particularly important in hospitals, permanently high even when changing residents.


16.03.2020: Poster presentation of “Rotation Design for Residents” at the QBWL 2020
Sebastian Kraul travels to Königswinter and presents new research results of our research project “Rotation design for task-related resident scheduling problems”. The poster shows that rotations can be applied to task-related resident scheduling problems. Additionally, a new bound for the maximum number of assignments to one department is derived.


16.01.2020: Survey on the satisfaction of residents
The research team of Prof. Dr. Jens O. Brunner and Prof. Dr. Manfred Blobner is conducting a long-term study on the satisfaction of residents in anesthesiology. The online questionnaire is sent to prospective specialists in anesthesiology with the support of the Bavarian Medical Association. The survey aims to obtain conclusions, especially on fairness, workload, and organization within the resident program.


02.12.2019: Organization of a Session at IFORS 2020 in Seoul
Prof. Dr. Jens O. Brunner is organizing the session "Personnel scheduling with training in health care" of the Health Planning Stream at IFORS 2020 in Korea. The conference will be held on June 21-26, 2020 in Seoul. IFORS is an international conference held every three years to bring together academia, practitioners and experts in the field of Management Science from more than 60 countries and to contribute to its development through mutual academic and information exchange. Since its inaugural meeting in the United Kingdom in 1957, this conference has become a large international academic conference involving more than 2,000 professionals from the United States, Europe, Asia, Oceania and South America.


04.09.2019: Presentation of “A Two-Stage Formulation for the Strategic Resident Scheduling Problem” at the OR 2019
Sebastian Kraul travels to Dresden and presents the research results of our research project “Strategic task-related resident scheduling with uncertainty”. The presentation shows possibilities of the applicability of rotation plans even for task-related programs. A subsequent discussion led to possible solution methods for the problem.


02.07.2019: "Annual scheduling for anesthesiology medicine residents in task-related programs with a focus on continuity of care" accepted for publication in Flexible Services and Manufacturing Journal
Sebastian Kraul will publish new results of resident scheduling in teaching hospitals with the use of quantitative methods in Flexible Services and Manufacturing Journal. He presents a new formulation of scheduling residents in a task-related setting and analyzes the effect of a fair training progress on continuity of care.


05.03.2019: Presentation of „A robust framework for task-related resident scheduling” at Ghent University
Prof. Dr. Jens O. Brunner travels to Ghent and presents the first publication of our project “Strategic task-related resident scheduling with uncertainty”. A focus of the presentation is the integration of robustness in our mathematical formulation and the resulting insights of the problem. Subsequent to the presentation, new possibilities for resident scheduling are discussed using the methods of Operations Research.


14.01.2019: “A Robust Framework for Task-Related Resident Scheduling” accepted for publication in the European Journal of Operational Research
The research team of Prof. Dr. Jens O. Brunner and Prof. Dr. Manfred Blobner will publish first results of resident scheduling in teaching hospitals with the use of quantitative methods in the European Journal of Operational Research. They present a new formulation of scheduling residents in a task-related setting with uncertainty in interventions. They show that ignoring uncertainty in interventions leads to a large increase in the duration of a resident program.


12.09.2018: Presentation of “Annual Scheduling for Anesthesia Residents in Task-Related Programs with a Focus on Continuity of Care” at the OR 2018
Sebastian Kraul travels to Brussel and presents the research results of our research project “Tactical task-related resident scheduling focusing on continuity of care”. The presentation highlights key-performance indicators for continuity of care and how to integrate them into a mathematical formulation.


21.08.2018: First Meeting
The research team of Prof. Dr. Jens O. Brunner and Prof. Dr. Manfred Blobner have a first meeting to identify organizational tasks before the project starts.


17.07.2018: Presentation of “A robust framework for task-related resident scheduling” at the Bergische Universität Wuppertal
Prof. Dr. Jens O. Brunner travels to the Bergische Universität Wuppertal and presents the research results of our project “Strategic task-related resident scheduling with uncertainty”. In the talk, he presents the influence of interventions on resident programs.


09.07.2018: Funding received
Prof. Dr. Jens O. Brunner and Prof. Dr. Manfred Blobner are informed by the DFG that their research grants project “Resident scheduling in teaching hospitals with the use of quantitative methods” will be funded.

WP 1: Data & Experts
Throughout the whole project, the relevant data is gathered and anonymized from the cooperation partner to form a building block for the planning process of residents. To identify criteria of fairness and stability as well as potential weaknesses experts are interviewed and the results are used to generate mathematical models. Additionally, also interviews with residents are done to evaluate their satisfaction and receive feedback for the project. The insights of these interviews are used to point out and react to the strengths and weaknesses of the project and thus support the achievement of intended goals.


WP 2: Demand & Capacity
In the first step, it is important to clearly define demands and capacities for surgeries, not only for shifts but also regarding the different types of physicians. This is necessary since the number of surgeries that a resident can perform within a time period and a certain clinic is an elementary component of fulfilling the different stages of education. Therefore realistic predictions help to plan the duration of the different stages.


WP 3: Key Figures & Evaluation
Key figures are an essential operational instrument for comparison and regulation as well as for the measurement of target achievement. Therefore it is tried to derive key figures from other service areas, use them for the modeling of objectives and evaluate interdependencies. In this context, thresholds should help with evaluating the fitness of the key figures. In collaboration with the project partner, a method for tracking these key figures within the daily routine is developed.


WP 4: Implementation & Guideline
In order to implement the insights of the project to hospitals, a suitable interface for personnel planning software is necessary. Therefore the correlations between education and personnel planning are analyzed and mapped to an interdependency matrix. This also helps with identifying and avoiding potential problems and intends to simplify future research.
Additionally, a guideline for researchers and practitioners sums up the arising problems in resident planning to help them understand the complexity of planning.


WP 5: Models & Methods
A clear educational structure and reliable planning improves a hospitals reputation for attractive and efficient education and thus providing a competitive advantage in employing physicians. However, hospitals need to consider high service levels and the effective use of human resources. Paying attention to all of these aspects means in a first step to determine the optimal number of education appointments with consideration of resource and capacity limitations. Due to the planning complexity, mathematical models and methods are used to first determine the optimal number of resident jobs along with the appropriate education schedules. Therefore a mixed integer problem is formulated and solved with OR/MS algorithms, like column generation, branch, price and cut or Benders decomposition. The developed methods are tested within simulations as well as case studies at the cooperation partner.


WP 6: Stochastic & Robustness
After developing the mathematical model for resident scheduling, the problem is expanded by stochastic factors that occur in reality and affect demands and capacities. Therefore on the one hand Markov decision processes are used and on the other hand a two-stage stochastic programming approach, which intends to provide more ex-ante information. The formerly developed methods need to be adapted to these topics.
However, uncertainties occur not only within the strategical planning but also within the tactical planning level, where the educational schedule is transformed into a concrete working roster. In this context, certainty measurements help to avoid unfairness in terms of steady progress or number of clinic transitions.
Overall the uncertainties regarding the number of surgeries are intended to be met by a robustness concept in order to improve planning reliability and lower the number of roster changes.


WP 7: Fairness & Stability
Since fairness directly affects employees satisfaction and thus the quality of work, different fairness concepts are defined and their influence on personnel planning is evaluated. In this context, especially the number of clinic transitions and the intended influence on the continuity of care is considered. Therefore the developed models are adapted and solved heuristically, for example with local search heuristics.

Strategic task-related resident scheduling with uncertainty
Sebastian Kraul; Andreas Fügener; Jens O. Brunner; Manfred Blobner


In this project, we investigate the effects of uncertainty regarding interventions on the total number of residents that a hospital can employ without violating the program length.
We consider the training phase of physicians after finishing medical school. They specialize in a common field like ophthalmology or anesthesiology and are called residents. Technological progress in health care leads to increasing complexity in the requirements of physician training. As a consequence, those programs are often not only time-related but also task-related. Task-related means that residents should perform a given number of different interventions in their program. Typically, a resident will follow a rotation across different clinical departments, where the number of performed interventions per period may be estimated. Predicting the exact number of interventions is usually not possible. Accordingly, a resident might not be able to perform all of the required interventions during the planned rotation, resulting in an extension of the program. In this project, a new model is presented that calculates the number of residents a hospital can reliably train on a strategic level. Our model also provides the corresponding training schedule. It considers minimum requirements of both time-related stays in specific departments as well as task-related interventions that have to be performed. The robustness of the model can be set by management to handle uncertainties in interventions. A Dantzig-Wolfe decomposition is used to accelerate the solution process, and a new pattern generation approach that can construct multiple patterns out of one solution is developed. The termination of the column generation algorithm is accelerated significantly by this method. The model is evaluated using real-world data from a resident program for anesthesiology in a German university hospital. The results demonstrate that near-optimal solutions with an average optimality gap of below five percent can be achieved within computation times of few minutes.


Rotation design for task-related resident scheduling problems


In this project, we investigate the transferability of rotations from time-dependent resident programs like the US to task-related programs.
We present a novel formulation for designing rotation schedules in task-related resident programs. Additionally, we propose a new bound for the maximum number of assignments to a department per resident, which is crucial for the design of rotations. Since the bound ensures feasibility at an operational level and is, in general, defined by the hospital management, it must be made comprehensible to them. We evaluate the newly designed rotations with a resident scheduling model, which can be used for both task-related and rotation-based systems. In order to solve the problem, we make use of a combinatorial relaxation and embed the model in an algorithm guaranteeing optimality of the original problem. In our study, we show the variability between different rotation schedules. Besides, we can use our models to derive bottlenecks in the context of resident training.


Tactical task-related resident scheduling focusing on continuity of care
Sebastian Kraul


In this project, we investigate the impact of continuity of care and fair training progress for annual schedules.
This project presents a new model for constructing annual schedules for medical residents based on the regulations of a German teaching hospital as well as the program restrictions of the German Medical Association. Since resident programs of physicians do not only vary between disciplines but also between countries, it is essential to evaluate the main characteristics of the program. The main difference between the already well-studied resident programs in the US and the one of this project is the task-related structure. Residents need to perform different interventions several times to become specialists. This study will focus on Germany since there was a judgment in 2015 that hospital management needs training schedules guaranteeing the success of the resident program in time. Therefore, a new formulation of a tactical resident scheduling problem is presented. The problem is formulated in two stages considering the total number of interventions, equal progress in training as well as continuity of care. As the second stage of our formulation is a quadratic program and even by linearization standard solvers are not able to generate high-quality solutions within 24 hours, a genetic algorithm using standard crossovers is developed for the second stage constructing annual schedules for an existing stock of residents. We evaluate our algorithm by comparing the solutions of the genetic algorithm and standard software with a real-world situation of a German training hospital from 2016.


Training priorities in annual scheduling of residents in task-related programs

In this project, we investigate the effects of training priorities in the annual scheduling of residents in task-related programs.
This project presents a novel, two-stage stochastic approach for the annual resident scheduling problem. In our formulation, we combine the tactical planning of residents with the operational level of daily and duty rostering. Uncertainty is defined in terms of the availability of residents. In order to provide as much information as possible, we develop a novel formulation taking different priorities for tactical scheduling into account. The priorities are used to provide the residents with more than one department in the tactical plan to which they can be assigned. This allows the residents to better prepare for possible department changes. We develop for the formulation of a robust dual bound, which is up to 30% superior to the LP bound. In addition, we develop an efficient algorithm for solving the stochastic program using a sample average approximation.


Sebastian Kraul
2020 | 2019


Sebastian Kraul
Annual scheduling for anesthesiology medicine residents in task-related programs with a focus on continuity of care

BibTeX | RIS | DOI


Sebastian Kraul, Andreas Fügener, Jens O. Brunner and Manfred Blobner
A robust framework for task-related resident scheduling

BibTeX | RIS | DOI



Prof. Dr. Jens O. Brunner
Chair of Health Care Operations/Health Information Management, Faculty of Business and Economics, University of Augsburg, Neusässer Straße 47, Augsburg 86156, Germany


Prof. Dr. Manfred Blobner
Department of Anaesthesiology, School of Medicine, Technical University of Munich, Klinikum rechts der Isar, Ismaninger Straße 22, Munich 81675, Germany


Responsible Project Member

Wissenschaftlicher Mitarbeiter
Prof. Dr. Jens O. Brunner: Health Care Operations / Health Information Management
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