Tabea Krabs: Robust Hospital Management

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Hospital beds are the most basic resources in hospitals. Tabea Krabs studies the patientto-room assignment problem. She first considered the allocation of elective patients on one ward to available beds. She proved that this problem is already NP-hard for two-bed rooms and an assignment for just one day, if some patients are not allowed to share a room. Increasing the time horizon and dropping conflicts between patients, she showed that at most one transfer from one room to another is necessary in an optimal schedule which minimises the number of transfers. This is in the literature often assumed without evidence. She also developed several algorithms to solve this problem in case no transfers are necessary. In contrast to elective patients, emergency patients arrive without notice and need to be assigned to the most appropriate ward. For some cases, e.g., if the assignment of the patient to ward is unique, she developed a polynomial algorithm. Currently, Krabs works on more general cases of the emergency assignment problem. In a next step, the combination of both problems will be studied with a focus on uncertain patient lengths and arrival dates. In order to integrate these uncertainties into the optimisation process, a recoverable robust approach according to the length of stay and a recovery action by delaying the admission of elective patients or an early discharge is considered.