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A Stochastic Queueing Model for Capacity Allocation in the Hierarchical Healthcare Delivery System

Author

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  • Jianpei Wen

    (Department of Industrial Engineering and Management, Peking University, Beijing 100871, P. R. China)

  • Hanyu Jiang

    (Department of Biomedical Engineering, Peking University, Beijing 100871, P. R. China)

  • Jie Song

    (Department of Industrial Engineering and Management, Peking University, Beijing 100871, P. R. China)

Abstract

We use the capacity allocation as a demand management tool to optimize the patient flow distribution on a hierarchical healthcare delivery system, which is a mixture of patient choice and gatekeeping. Capacity allocation for such service system can be challenging because of the inherent stochastic referral process and patients’ heterogeneous delay sensitivities. In this research, a stochastic queueing-based model is proposed to find the optimal allocation of the limited service capacity of the second level of experts. Considering the impact of the deficiency of the skill level and the amount of gatekeepers, the stochastic referral process is modeled with a tandem queue. By solving a fixed-point problem, we show that there is an unique optimal allocation and corresponding equilibrium demand. We carry out numerical studies and find that providing two alternatives for patients can be better than gatekeeper system, when the capacity of the gatekeeper is moderate compared to patients’ potential demand. Results also indicate that the optimal allocation is robust in terms of the referral rate and the mistreatment rate when two rates are less than corresponding thresholds.

Suggested Citation

  • Jianpei Wen & Hanyu Jiang & Jie Song, 2019. "A Stochastic Queueing Model for Capacity Allocation in the Hierarchical Healthcare Delivery System," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(01), pages 1-24, February.
    • Handle: RePEc:wsi:apjorx:v:36:y:2019:i:01:n:s0217595919500052
    DOI: 10.1142/S0217595919500052
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    1. Jie Xu & Si Zhang & Edward Huang & Chun-Hung Chen & Loo Hay Lee & Nurcin Celik, 2016. "MO2TOS: Multi-Fidelity Optimization with Ordinal Transformation and Optimal Sampling," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(03), pages 1-26, June.
    2. Jeff Hong, L. & Xu, Xiaowei & Zhang, Sheng Hao, 2015. "Capacity reservation for time-sensitive service providers: An application in seaport management," European Journal of Operational Research, Elsevier, vol. 245(2), pages 470-479.
    3. Brekke, Kurt R. & Nuscheler, Robert & Straume, Odd Rune, 2007. "Gatekeeping in health care," Journal of Health Economics, Elsevier, vol. 26(1), pages 149-170, January.
    4. Jie Song & Jianpei Wen, 2015. "A non-cooperative game with incomplete information to improve patient hospital choice," International Journal of Production Research, Taylor & Francis Journals, vol. 53(24), pages 7360-7375, December.
    5. Godager, Geir & Iversen, Tor & Ma, Ching-to Albert, 2015. "Competition, gatekeeping, and health care access," Journal of Health Economics, Elsevier, vol. 39(C), pages 159-170.
    6. Tamer Boyaci & Saibal Ray, 2003. "Product Differentiation and Capacity Cost Interaction in Time and Price Sensitive Markets," Manufacturing & Service Operations Management, INFORMS, vol. 5(1), pages 18-36, May.
    7. Joseph Abate & Gagan L. Choudhury & Ward Whitt, 1996. "Exponential Approximations for Tail Probabilities in Queues II: Sojourn Time and Workload," Operations Research, INFORMS, vol. 44(5), pages 758-763, October.
    8. Pangburn, Michael S. & Stavrulaki, Euthemia, 2008. "Capacity and price setting for dispersed, time-sensitive customer segments," European Journal of Operational Research, Elsevier, vol. 184(3), pages 1100-1121, February.
    9. Robert A. Shumsky & Edieal J. Pinker, 2003. "Gatekeepers and Referrals in Services," Management Science, INFORMS, vol. 49(7), pages 839-856, July.
    10. Weixin Shang & Liming Liu, 2011. "Promised Delivery Time and Capacity Games in Time-Based Competition," Management Science, INFORMS, vol. 57(3), pages 599-610, March.
    11. Zhongsheng Hua & Wuhua Chen & Zhe George Zhang, 2016. "Competition and Coordination in Two-Tier Public Service Systems under Government Fiscal Policy," Production and Operations Management, Production and Operations Management Society, vol. 25(8), pages 1430-1448, August.
    12. Anthony M. Kwasnica & Euthemia Stavrulaki, 2008. "Competitive location and capacity decisions for firms serving time‐sensitive customers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(7), pages 704-721, October.
    13. Kyle Cattani & Glen M. Schmidt, 2005. "The Pooling Principle," INFORMS Transactions on Education, INFORMS, vol. 5(2), pages 17-24, January.
    14. Yue Zhang & Oded Berman & Patrice Marcotte & Vedat Verter, 2010. "A bilevel model for preventive healthcare facility network design with congestion," IISE Transactions, Taylor & Francis Journals, vol. 42(12), pages 865-880.
    15. Office of Health Economics, 2007. "The Economics of Health Care," For School 001490, Office of Health Economics.
    16. Xiaoyu Liu & Xiaoqiang Cai & Ruiqing Zhao & Yanfei Lan, 2015. "Mutual referral policy for coordinating health care systems of different scales," International Journal of Production Research, Taylor & Francis Journals, vol. 53(24), pages 7411-7433, December.
    17. Marianov, Vladimir & Rí­os, Miguel & Icaza, Manuel José, 2008. "Facility location for market capture when users rank facilities by shorter travel and waiting times," European Journal of Operational Research, Elsevier, vol. 191(1), pages 32-44, November.
    18. Jie Xu & Edward Huang & Chun-Hung Chen & Loo Hay Lee, 2015. "Simulation Optimization: A Review and Exploration in the New Era of Cloud Computing and Big Data," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(03), pages 1-34.
    19. Andritsos, Dimitrios A. & Tang, Christopher S., 2014. "Introducing competition in healthcare services: The role of private care and increased patient mobility," European Journal of Operational Research, Elsevier, vol. 234(3), pages 898-909.
    20. Dimitrios Andritsos & Christopher S. Tang, 2014. "Introducing competition in healthcare services: The role of private care and increased patient mobility," Post-Print hal-00977175, HAL.
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