An Online approach for the scheduling of treatment modalities in a rehabilitation department

We analyze the treatment modalities booking system of a rehabilitation Department. We want to assign to each patient the physical therapies the physician had prescript to him/her, choosing them from the available testament modalities turn. The problem is formulated as a deterministic scheduling problem where the couples (therapy machineries-therapists) are the “machines” and patients represent the “jobs”. We tackle the online approach which simulates what the secretary really does to make a reservation and we formulate suitable algorithms, with the objective of minimizing the machines average idle time. Finally we implement the algorithms to a real case showing that the online algorithm leads to a better solution with respect to the one computed by hand as it simultaneously reduces the Department costs (system idle time and computation time) and improves the service to patients (quicker booking queues at the counter and shorter waiting-list.