Flowing through hospitals

Due to an aging population and increased healthcare costs, hospitals are forced to use their resources more efficiently, meaning that the same amount of patients has to be treated with less resources or more patients with the same amount of resources. Practitioners in hospitals often think that by using resources more efficiently, the quality of care will decrease. On the contrary, the reduction achieved by improving the efficiency may also improve the quality of care as, e.g., unnecessary waiting time is reduced or even eliminated. In this thesis it is shown that the efficiency of healthcare can be improved by carefully scheduling and planning the processes at the departments the patient visits during his stay. Procedures or appointments should be scheduled such that, e.g., (1) the waiting time for the patients is minimized, (2) the schedule is robust against changes in the procedure or appointment time, and (3) the arrival of emergency patients is accounted for. For some of the considered problems, some of these objectives are more important than the other objectives, and sometimes, the objectives are even conflicting. Therefore, often a balanced trade-off between different (conflicting) objectives has to be made. Another challenging aspect of improving the efficiency in hospitals is that many uncertainties have to be taken into account. Including these uncertainties in the modeling process often leads to complex models that need to be simplified in order to solve them within a reasonable amount of time. Moreover, the considered problems are often already NP-hard without including uncertainty. To be able to get solutions for such problems, we either may approximate some part of the model and solve the resulting problem to optimality or we may use heuristics to solve the complete problem. Both approaches lead to suboptimal solutions as the first approach does not solve the original problem and the second approach often ends in a local optimum instead of a global optimum. Nevertheless, the results of the thesis show that approaches developed in this way form a good first step in solving these complex problems.