A fuzzy programming approach for the multi-objective patient appointment scheduling problem under uncertainty in a large hospital

Abstract

Inspired by a real case of a large regional hospital in Argentina, this research presents an integer linear programming (ILP) model for the patient appointment scheduling problem. The mathematical formulation allows to plan the admission of patients belonging to a waiting list according to a week-hospital modality where all the prescribed clinical procedures to a patient have to be performed during a short hospitalization time no longer than one week. For modeling purposes, each day of the planning horizon is divided in two blocks which, in turn, are discretized into a number of time slots where the different clinical services are carried out. Key features of the model include limited clinical services availability in each time slot and a reduced number of beds and armchairs for hospitalization of patients. The two main goals pursued in the scheduling problem are to provide early patients’ admissions, especially for those with high clinical priority (i.e., minimize the admission dates), and reducing the hospital stay per patient (i.e., minimize the length of stay). Since there exists a significant uncertainty in the available amount of clinical services in each time slot, a fuzzy programming approach was adopted to solve the resulting multi-objective problem. According to the obtained results, such an approach conciliates in a natural way decision maker expectations and constraint fuzziness conducting to balanced schedules.