Hybrid optimization and discrete-event simulation model to reduce waiting times in a primary health center

Abstract

In the early stages of health attention, such as in the examination rooms, patients are generally treated using a First In First Treat (FIFT) logic. This treatment style is inefficient from an operational view as it leads to long waiting times for critical patients. Based on optimization and discrete-event simulation, this paper introduces a hybrid model to assign patients priorities and exam rooms. Patients arrive to the system following a probability function, and for every discrete interval, a mixed-integer linear optimization model is used to allocate patients, considering health priority, preparation times, and availability of time and resources. Instances of the problem are defined using information from a health system in Mexico. Additional to the linear model, a heuristic algorithm is proposed, composed of two phases and aims to provide good, feasible, and fast solutions without ensuring optimality. Computational experiments showed that the linear model is more appropriate for small instances since the heuristic is faster and the relative deviations with respect to the linear model are below five percent. Finally, the discrete-event simulation is run for two cases: (1) with a FIFT logic and (2) using the optimization model. The hybrid model reduces the global waiting times up to 90% and the number of high health priority patients who are not treated up to 100%.