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.

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).