DFG Research Grants Project 438507036: Modeling physician scheduling for high-cost areas in hospitals

© Universität Augsburg

Two of the most important scarce resources in hospitals are operating rooms and physicians, since more than half of the operating costs are staff-related. Consequently, efficient and effective  scheduling of both of these resources is one of the most relevant planning tasks within hospitals since it directly affects operating costs as well as patient and staff satisfaction and thus the quality of care.


This research project deals with the formulation of sophisticated integer programming algorithms in the sector of health care operations in terms of physician scheduling as well as providing decision support systems. Through the work of this project, efficient and effective ways of mid-term and short-term physician scheduling with integrated operating room planning shall be investigated.

31.08.2023: Presentation of "Continuous Integrated Task Assignment and Personnel Scheduling" and "A branch and price approach for integrated surgery and staff scheduling in operating theatres on a daily planning level" at the OR 2023

Gerriet Fuchs and Stefanie Ebel travel to Hamburg and present their current research.


16.02.2023: Presentation of "Personalplanung im Krankenhaus unter Berücksichtigung von Fairness" at the GOR AG HCM 2023

Gerriet Fuchs travels to Hildesheim to present his current results on the consideration of preferences and fairness in staff scheduling.


08.09.2022: Presentation of "Integrated Personnel and Task Planning" and "A branch and price approach for integrated surgery and staff scheduling in operating theatres on the operational level" at the OR 2022

Gerriet Fuchs and Stefanie Ebel travel to Karlsruhe and present their current research. The presentations show their current methodologies on integrated modeling and solution approaches.


29.03.2022: Presentation of „Integrated surgery and staff scheduling in operating theatres on the operational level“ at the QBWL 2022

Stefanie Ebel takes part in the digital QBWL workshop and presents first results of an approach for integrated surgery sequencing and staff assignment. The presentation shows a mathematical formulation and a solution approach along with an outline for further research.


11.06.2021: First meeting 

The research team of Prof. Dr. Jens O. Brunner and Prof. Dr. Katja Schimmelpfeng have a first meeting to identify organizational tasks and discuss first research projects.


01.05.2021: Occupation of research project

Stefanie Ebel and Gerriet Fuchs start working for this research project at the chairs of Prof. Dr. Jens O. Brunner and Prof. Dr. Katja Schimmelpfeng


16.03.2020: Funding received
Prof. Dr. Jens O. Brunner and Prof. Dr. Katja Schimmelpfeng are informed by the DFG that their research grants project “Modeling physician scheduling for high-cost areas in hospitals” will be funded.

At the end of the project, two main contributions will be provided:


1. Development of a framework for physician scheduling to enable the possibility of organizing the planning problems into modules in combination with their interdependencies to other areas. In this context, the main drivers for physicians’ satisfaction will be investigated and furthermore elaborated how to translate these into economically efficient schedules and patient service levels


2. Optimization of physician scheduling by including preferences and fairness aspects and furthermore creating more efficient and more effective scheduling decisions by solving physician and operating room scheduling simultaneously


The result of this research should on the one hand side represent an improvement in the quality of care (e.g. due to the consideration of preferences and fairness aspects), as well as facilitate scheduling decisions.


© Universität Augsburg

Module 1: Setting the basis and developing a planning framework for physician scheduling


1. Data collection and preferences/fairness

Relevant data is collected by cooperating partners and afterwards analyzed using descriptive and inductive statistics. To draw up general guidelines for physician scheduling, questionnaires and interviews are conducted to formulate generic mathematical models. In addition, surveys are done to elaborate different fairness measures and preference components. These can then be integrated into the mathematical models in terms of weights in the objective function that are important to formalize violations of fairness and preference constraints.


2. Demand modeling and shift design

The demand is defined per period and will not be linked to shift profiles. In addition, demand stochasticity will be integrated in the models. After reviewing different shift assumptions from hospitals as well as union and general labor contracts, ideas will be developed that allow a use of automated scheduling models and methods hospital-wide efficiently.


3. Identification of pitfalls in physician scheduling

Usually, the mean demand over one period is taken to solve the physician scheduling. However, this approach does not consider the stochasticity in terms of variance and therefore, the availability is lower than expected, due to a lower quality of care and satisfaction of the physicians. This problem will be circumvented by providing guidelines for demand modeling, statement of realistic models, development, and implementation of algorithms as well as the evaluation of final schedules.


4. Planning framework for physician scheduling

This package aims to create a holistic approach considering planning interpendencies in terms of  scheduling. Therefore, coherent demand and operations planning problems will be identified, described, and structured, which results in creating a coherent planning matrix among others. This planning architecture then will ensure the foundation of advanced decision support systems which also will be used in a practical environment.


© Universität Augsburg

Module 2: Modeling and solving the physician scheduling problem


5. Development of a modeling toolkit for physician scheduling including fairness aspects, preference considerations, and break assignments

In this working package two types of constraints are determined: On the one hand side, general constraints, that are mandatory in all physician scheduling problems (e.g. demand coverage) and on the other side constraints whose consideration depends on the hospital setting. To automatically consider relevant constraints depending on the type of objective function, a toolbox will be developed to combine constraints into different optimization models depending on the specifics of the considered problem. In addition, the model will be extended by considering satisfaction of the physicians and the fairness aspect of the schedule as well as the assignment of mandatory breaks within the schedule.


6. Integrated physician and operating room scheduling

Nowadays, the creation of a so called Master Surgery Schedule (MSS) is commonly used in theory as well as in practice. This MSS then usually is applied cyclically and repeatedly as long as there is no major change that requires a rescheduling. Here, often interdependencies with other areas occur (e.g. physicians’ shift as well as required availability of adjacent resources). Therefore, a solution is sought by integrating both described problems and solving them in one model by considering further influencing factors like residents’ training.


7. Robust physician scheduling

By considering stochasticity of demand, it’s possible to simultaneously increase the predictability of physician working hours, maintain high service levels, and increase employee satisfaction. Therefore, the models are tested to robust planning to ensure a high quality of care by reaching a balance of over- and understaffing when considering stochasticity in terms of demand fluctuation. Furthermore, it is planned to counteract the issue of stochasticity by e.g. using a float pool of physicians or identify lower and upper bounds for the uncertainty interval. These approaches then will be analyzed by simulations to measure its effectiveness.


8. Efficient algorithms for physician scheduling

After setting up the introduced models, sophisticated integer programming algorithms are designed to solve these kinds of scheduling issues. The focus here is on new branching strategies, sophisticated stabilization procedures, efficient subproblem algorithms, and fast primal bound procedures. Furthermore, all approaches will be performed by using real-world data to be analyzed afterwards in terms of performance (e.g. deviations from the optimal solution) as well as in a practical perspective (e.g. amount of planning time).




Prof. Dr. Jens O. Brunner
Health Care Operations/Health Information Management, Faculty of Business and Economics, University of Augsburg, Eichleitnerstraße 30, Augsburg 86159, Germany


Prof. Dr. Katja Schimmelpfeng
Department of Business Administration -     Procurement and Production, Faculty of  Business, Economics and Social Sciences, University of Hohenheim, Schwerzstraße 40, Stuttgart 70599, Germany


Responsible Project Members

Stefanie Ebel, M.Sc.


Gerriet Fuchs, M.Sc.