MOHFDQ: A metaheuristic approach to optimizing hospital patient registration with a fuzzy double-orbit queueing model

Queueing management is applied across sectors such as airlines, banking, healthcare, and telecommunications. However, there are very few queueing model-based approaches to managing patient waiting times, particularly in healthcare systems. Patients often reattempt to access services when they are initially unable to receive care upon arrival. If the registration desk is busy, an arriving patient may choose to join either the regulaor execuwaiting area. In this study, we consider two types of patients: premium/emergency patients who receive additional services based on payment and ordinary/non-emergency patients, who do not pay extra. However, if an ordinary patient becomes dissatisfied with the service, the registration desk may provide additional support. To address this, the MOHFDQ framework a three-phase approach integrating queueing theory, fuzzy theory, and stochastic optimization developed. In the first phase, the MOHFDQ model is analyzed and key performance metrics such as patient queue length, waiting time, and throughput are established. In the second phase, the crisp model is extended to a fuzzy model for a double orbit system, and α-cut and parametric nonlinear programming (PNLP) techniques are used to derive various fuzzified metrics. Finally, in the third phase, to enhance productivity and ensure high quality of service (QoS), a metaheuristic genetic algorithm (GA) and a deterministic golden section search (GSS) method are implemented to determine the optimal service parameters by minimizing the total system cost.