In Germany, around 40% of the hospitals do not generate an annual surplus. This leads to an increasing pressure on hospitals’ management to reorganize and restructure their processes and resources to decrease the upcoming costs and become profitable. Since personnel, especially physicians, generates a major part of the arising costs, assigning staff efficiently provides an opportunity to decrease associated costs. Up to now, experienced physicians create rosters manually which is cost and time intense due to the problem’s complexity and especially the fluctuation in demand. To circumvent this difficulty, it is our main aim to create a new mathematical modeling approach to implement additional flexibility in the rostering process to better match supply and demand. Therefore, we formulate the problem as mixed-integer programming model with the objective to minimize occurring labor costs of physicians over the considered planning horizon subject to coverage of demand to make flexibility monetarily evaluable. In our approach, full flexibility in terms of patterns of working days, shift types, and the placement of the break is provided. To solve the problem under consideration, a column generation heuristic is presented. In our experimental study, the performance of the provided solution approach as well as the effect of additional flexibility in the rostering process are evaluated using real life data. Results indicate the significant impact of implementing flexibility in the scheduling process on the salary costs of the number of required physicians and evidence the superior quality of our solution approach.

在德国，大约40％的医院没有产生年度盈余。这给医院的管理人员带来了越来越大的压力，要求其重组和重组其流程和资源以降低即将发生的成本并实现盈利。由于人员（尤其是医生）占了产生费用的主要部分，因此有效分配人员可提供降低相关费用的机会。迄今为止，由于问题的复杂性，尤其是需求的波动，经验丰富的医生手动创建花名册，这是费时和费力的。为了克服这一困难，我们的主要目标是创建一种新的数学建模方法，以在排班过程中实现更大的灵活性，以更好地匹配供需关系。所以，我们将问题表述为混合整数规划模型，其目的是在考虑需求范围的前提下，在考虑的规划范围内最大限度地减少医师的人工成本，以使灵活性在货币上可评估。在我们的方法中，在工作日模式，轮班类型和休息位置方面提供了充分的灵活性。为了解决所考虑的问题，提出了一种列生成启发式方法。在我们的实验研究中，使用实际数据评估了提供的解决方案方法的性能以及排班过程中额外灵活性的影响。结果表明，在调度过程中实施灵活性对所需医生数量的薪资成本具有重大影响，并证明了我们解决方案的卓越质量。