| At present,most countries and regions are facing the problem of shortage of medical resources and uneven quality of medical services.In China,this problem is particularly prominent.The countdown of per capita medical resources,the prominent problem of aging,and the wrong concept of medical treatment of the people have led to overcrowding in high-level hospitals and idleness in primary hospitals.In order to alleviate the imbalance of medical resources,the state proposed to establish a hierarchical diagnosis and treatment system,piloted and implemented hierarchical diagnosis and treatment in multiple provinces,and achieved very good results.However,at present,the imbalance of medical resource utilization in China’s hierarchical diagnosis and treatment system is still common.The rational allocation of medical resources is related to people’s livelihood and health,and is closely related to social equity and residents’ happiness.It is of great significance to the implementation of the Healthy China strategy.The problem of referral has also been widely concerned by the academic community,but there are few articles on the relative advantages and disadvantages of different referral mechanisms.This paper studies the service capability design and pricing of single-way referral and two-way referral systems for stationary queuing systems and blocking systems.The service performance of the two referral mechanisms is compared to provide decision support for resource coordination in different situations.For the stationary queuing system,firstly,based on the decentralized situation,the profit maximization models under two centralized decision-making situations of singleway referral and two-way referral are established,and the optimal capacity,price strategy and optimal profit are determined.Secondly,based on the perspective of hospitals and patients,the benefits of cooperation and the relative advantages and disadvantages of different referral mechanisms are analyzed.Finally,the profit allocation of the alliance is studied.In the blocking system,we consider a more general case where the capacity of the hospital is fixed,the arrival rate of the high-level hospital is greater than the service rate,and the patient’s arrival rate is related to the referral mechanism.We use the probability model to establish the objective function in each case of non-cooperation,single-way referral and two-way referral.Then,through numerical simulation and sensitivity analysis,the optimal referral mechanism is given based on the hospital perspective,and the influence of different parameters on the optimal profit is discussed.This paper draws the following main conclusions.First,in the practice of referral,emphasis should be placed on guiding common patients to the community healthcare center for the first diagnosis,so as to improve the efficiency of the medical system and form a positive feedback to the community healthcare center.Second,in the absence of external intervention,the alliance between hospitals at different levels can also be reached,and the construction of the medical consortium can promote the formation of a win-win situation among general hospitals,community healthcare centers and patients.The profit allocation within the alliance should be based on the actual arrival rate of each hospital.Third,in the stable queuing system,the single-way referral mechanism is superior to the non-cooperative and two-way referral mechanism,which is manifested in bringing higher profits to the hospital and saving the waiting time of patients.In the case of congestion,the two-way referral mechanism is better.When implementing referral within the medical consortium,the appropriate referral plan should be selected according to the actual situation. |