Referral strategy, incentive scheme, and network externalities in a multisite service system

In Hong Kong, the public hospital system consists of seven clusters, and each patient is expected to receive service either from his home public hospital or from a private hospital. Hong Kong Hospital Authority (HKHA) manages the public system and faces two major challenges. First, the waiting times vary significantly across clusters and HKHA starts to refer a patient from a heavy-loaded cluster to another low-loaded one. How should HKHA make the referral decisions and when does referral strategy reduce the system cost effectively? Second, HKHA starts to cooperate with private hospitals and partially subsidizes patients who receive services from private hospitals. What is the impact of the subsidy? We analyze a multisite service system wherein a customer can accept service at his home station, or switch to another station under a switching cost, or reject the service under a rejection cost, observing the system workload. We show the optimal referral strategy follows some switching curves, and identify conditions under which referral is effective in reducing system cost. Providing subsidy can better align individual patient’s routing decision with the system optimal one and hence reduce system cost, but full coordination cannot be achieved due to network externalities.