The scheduling of the medical staff of a hospital is the problem of allocating to the many different services the appropriate and available resources: we address it developing a suitable integer programming based model.
In a typical scenario, the priorities are to ensure that each service is covered by doctors licensed to carry out that task and to guarantee enough days of rest due to particular services (as for example night shifts).
The mathematical model also takes into account holydays, trying to satisfy the demands in an optimal way.
As a showcase, we tested the model on real data coming from the scheduling of the shifts of a medical team of 12 persons with five different qualifications.
For the implementation of the solution, we chose to couple Scilab with the GLPK library (GNU Linear Programming Kit), allowing to keep the whole model open.
The presented solution represents a first glance at our strategy of exploration of open source techniques to solve combinatorial optimization problems.