An optimization model for multi-appointment scheduling in an outpatient cardiology setting

In this paper, we tackle the problem of outpatient scheduling in the cardiology department of a large medical center. The outpatients have to go through a number of diagnostic tests and treatments before they are able to complete the final interventional procedure or surgery. We develop an integer programming (IP) formulation to ensure that the outpatients will go through the necessary procedures on time, that they will have enough time to recover after each step, and that their availability will be taken into account. Our goal is to schedule appointments that are convenient for the outpatients, by minimizing the number of visits that the patients have to make to the hospital and the time they spend waiting in the hospital. We propose formulation improvements and introduce valid inequalities to the IP, which help the running times to decrease significantly. Furthermore, we investigate whether scheduling outpatients in groups can lead to better schedules for the patients. This would require coordination between the different members of the scheduling staff within the cardiology department. The results show improvements in the total objective value over a period of one month, ranging from 0.45% to 2.33% on average, depending on the scenario taken into account.