VNS-Lagrangean Heuristics for Scheduling of Patients in Hospitals

We address the real world problem of how to schedule the treatments of the resident patients in hospitals. The problem considers the patients who have to be subjected to a certain kind of treatment on a given day. Each kind of treatment consists of different number of procedures which have to be done in a strictly prescribed sequence. Each procedure is performed on a certain medical machine. Treatments of specific patients have different levels of priority. Exactly one physician has to be assigned to each medical machine on which there is a treatment being performed in that moment. We model the problem as 0 - 1 integer programming problem and propose a heuristics based on Variable Neighborhood Search and Lagrangean relaxation.