Hospital referral and capacity strategies in the two-tier healthcare systems

Jian Jun Wang, Zhong Ping Li, Jim (Junmin) Shi, Ai Chih (Jasmine) Chang

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


Healthcare referral has been widely advocated and adopted through the implementation of the two-tier healthcare systems whereby patients are transferred from a comprehensive hospital provider (CHP) to a primary hospital provider (PHP). However, operationally, exactly how to implement the healthcare referral program remains a challenging research question, especially when considering the possibility of patient revisits and the coordination needed between the CHP and PHP. To address such a challenge, this paper considers the two-tier healthcare systems consisting of a CHP and a PHP. By establishing a three-stage Stackelberg game within a queuing framework among the CHP, the PHP, and their patients, we first investigate the equilibrium strategy in terms of the CHP's referral rate and the PHP's capacity level, and then examine the impact of revisit rates and referral payments (RP) on the healthcare system and the equilibrium outcomes (e.g., expected utility, social welfare, and waiting times). Two major findings of our study are: (1) both the equilibrium referral rate and the equilibrium capacity first increase and then decrease according to the revisit rate; in addition, the patient referral process always improves the PHP's performance but is likely to sacrifice the social welfare of the CHP. (2) There exists an RP threshold value such that if the RP is below the threshold, then all the permitted patients should be referred and the system performance will be enhanced, in which case a win-win situation in terms of expected utilities can be attained that benefits all the stakeholders, i.e., the CHP, the PHP, and the patients. Otherwise, only a portion of the permitted patients can be referred, and an increase in RP always reduces the efficiency of the healthcare delivery system, i.e., a higher RP mitigates the operational performance of the healthcare system. Our analysis sheds light on how to implement a healthcare referral scheme.

Original languageEnglish (US)
Article number102229
JournalOmega (United Kingdom)
StatePublished - Apr 2021

All Science Journal Classification (ASJC) codes

  • Strategy and Management
  • Management Science and Operations Research
  • Information Systems and Management


  • Capacity
  • Healthcare operations
  • Queuing-game
  • Referral payment
  • Referral rate
  • Two-tier healthcare systems


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