A Markov decision optimization of medical service resources for two-class patient queues in emergency departments via particle swarm optimization algorithm
Abstract In the modern healthcare system, the rational allocation of emergency department (ED) resources is crucial for enhancing emergency response efficiency, ensuring patient safety, and improving the quality of medical services. This paper focuses on the issue of ED resource allocation and desig...
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Nature Portfolio
2025-01-01
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| Online Access: | https://doi.org/10.1038/s41598-025-86158-w |
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| author | Chia-Hung Wang Rong Tian Kun Hu Yu-Tin Chen Tien-Hsiung Ku |
| author_facet | Chia-Hung Wang Rong Tian Kun Hu Yu-Tin Chen Tien-Hsiung Ku |
| author_sort | Chia-Hung Wang |
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| description | Abstract In the modern healthcare system, the rational allocation of emergency department (ED) resources is crucial for enhancing emergency response efficiency, ensuring patient safety, and improving the quality of medical services. This paper focuses on the issue of ED resource allocation and designs a priority sorting system for ED patients. The system classifies patients into two queues: urgent and routine. Considering different service rates, a multi-server preemptive priority queueing model $$(M/M/c_{1}/K)$$ and a multi-server non-preemptive priority queueing model $$(M/M/c_{2}/\infty )$$ are constructed. Additionally, the number of beds, K, is introduced as the capacity of the urgent queue. By comprehensively considering the costs associated with patient waiting time, the cost of rejecting the most critical patients, and the total costs of beds and servers, a mixed-integer programming model was constructed with the objective of minimizing the total cost. The particle swarm optimization algorithm was applied to determine the optimal number of servers, service rate, and number of beds. Compared with the model proposed by Alipour-Vaezi et al., our model significantly improves patient waiting times and queue lengths using the same data set: the waiting time $$W_{q}^{1}$$ decreased by 74.44%, $$W_{q}^{3}$$ by 5.79%, and $$W_{q}^{4}$$ by 1.13%; the queue length $$L_{q}^{1}$$ decreased by 78% and $$L_{q}^{3}$$ by 3.33%. Our model effectively reduces patient waiting times and queue lengths while controlling costs, identifies the optimal number of beds, and achieves optimized resource allocation. Finally, we conducted a sensitivity analysis and provided some valuable management insights. |
| format | Article |
| id | doaj-art-d3dda68501384e2dad96481ceffebecf |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
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| spelling | doaj-art-d3dda68501384e2dad96481ceffebecf2025-01-26T12:31:45ZengNature PortfolioScientific Reports2045-23222025-01-0115112910.1038/s41598-025-86158-wA Markov decision optimization of medical service resources for two-class patient queues in emergency departments via particle swarm optimization algorithmChia-Hung Wang0Rong Tian1Kun Hu2Yu-Tin Chen3Tien-Hsiung Ku4College of Computer Science and Mathematics, Fujian University of TechnologyCollege of Computer Science and Mathematics, Fujian University of TechnologyCollege of Computer Science and Mathematics, Fujian University of TechnologyDepartment of Information Management, Lunghwa University of Science and TechnologyDepartment of Anesthesiology, Changhua Christian HospitalAbstract In the modern healthcare system, the rational allocation of emergency department (ED) resources is crucial for enhancing emergency response efficiency, ensuring patient safety, and improving the quality of medical services. This paper focuses on the issue of ED resource allocation and designs a priority sorting system for ED patients. The system classifies patients into two queues: urgent and routine. Considering different service rates, a multi-server preemptive priority queueing model $$(M/M/c_{1}/K)$$ and a multi-server non-preemptive priority queueing model $$(M/M/c_{2}/\infty )$$ are constructed. Additionally, the number of beds, K, is introduced as the capacity of the urgent queue. By comprehensively considering the costs associated with patient waiting time, the cost of rejecting the most critical patients, and the total costs of beds and servers, a mixed-integer programming model was constructed with the objective of minimizing the total cost. The particle swarm optimization algorithm was applied to determine the optimal number of servers, service rate, and number of beds. Compared with the model proposed by Alipour-Vaezi et al., our model significantly improves patient waiting times and queue lengths using the same data set: the waiting time $$W_{q}^{1}$$ decreased by 74.44%, $$W_{q}^{3}$$ by 5.79%, and $$W_{q}^{4}$$ by 1.13%; the queue length $$L_{q}^{1}$$ decreased by 78% and $$L_{q}^{3}$$ by 3.33%. Our model effectively reduces patient waiting times and queue lengths while controlling costs, identifies the optimal number of beds, and achieves optimized resource allocation. Finally, we conducted a sensitivity analysis and provided some valuable management insights.https://doi.org/10.1038/s41598-025-86158-wQueueing systemWaiting timeHospital bed capacityEmergency departmentParticle swarm optimizationHealthcare service quality |
| spellingShingle | Chia-Hung Wang Rong Tian Kun Hu Yu-Tin Chen Tien-Hsiung Ku A Markov decision optimization of medical service resources for two-class patient queues in emergency departments via particle swarm optimization algorithm Scientific Reports Queueing system Waiting time Hospital bed capacity Emergency department Particle swarm optimization Healthcare service quality |
| title | A Markov decision optimization of medical service resources for two-class patient queues in emergency departments via particle swarm optimization algorithm |
| title_full | A Markov decision optimization of medical service resources for two-class patient queues in emergency departments via particle swarm optimization algorithm |
| title_fullStr | A Markov decision optimization of medical service resources for two-class patient queues in emergency departments via particle swarm optimization algorithm |
| title_full_unstemmed | A Markov decision optimization of medical service resources for two-class patient queues in emergency departments via particle swarm optimization algorithm |
| title_short | A Markov decision optimization of medical service resources for two-class patient queues in emergency departments via particle swarm optimization algorithm |
| title_sort | markov decision optimization of medical service resources for two class patient queues in emergency departments via particle swarm optimization algorithm |
| topic | Queueing system Waiting time Hospital bed capacity Emergency department Particle swarm optimization Healthcare service quality |
| url | https://doi.org/10.1038/s41598-025-86158-w |
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