Multi-appointment outpatient scheduling in cardiology

We study the problem of scheduling outpatients for appointments required by the cardiology department in a hospital. These are outpatients going through interventions or surgery, which require a number of tests or treatments to be completed before the patient is allowed to go through the final procedure. The outpatients visit the hospital on multiple occasions and may wait at the hospital in between appointments in order to go through all of the required steps. We propose an Integer Programming (IP) formulation that will schedule each patient with the objective of minimizing the number of visits to the hospital and the idle time that the patient spends in the hospital waiting for appointments. At the same time, the IP will ensure that no more than the available resources will be used, that the availability of the outpatients will be taken into consideration, and that the necessary recovery time will be provided to the patients. Improvements to the initial formulation are proposed in order to obtain an optimal solution faster.