A novel mathematical optimization model for a preemptive multi-priority M/M/C queueing system of emergency department’s patients, a real case study in Iran

Abstract The Covid-19 pandemic crisis has caused many difficulties worldwide. One of the most critical problems is that the emergency departments (EDs) have become overcrowded. Because this problem can increase patients’ queue length and waiting times in EDs, this paper provides a mixed-integer non-linear mathematical model considering a preemptive M/M/C queueing system to solve the problem and optimize a benefit function concerning the number of servers and treatment rate. In this model, different patient priorities, which are modified according to Covid-19 patients, are considered. This model is then solved using an exact approach and a meta-heuristic algorithm, the grasshopper optimization algorithm, for two shifts of the ED of a hospital in order to consider non stationery arrival rate in Varamin, Iran. The results of both algorithms confirmed the effectiveness of the proposed model. Moreover, to justify using the preemptive model, a comparison between the preemptive and non-preemptive models is conducted. An extensive sensitivity analysis is presented, and finally, a list of managerial insights is provided for managers to improve their service system further.