Flexible staffing of physicians with column generation

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.