Capacity Planning And Pricing Of The Referral System With Delay-sensitive Patients

To address the problems of accessibility and affordability for the medical resource, China builds up a two-tier health care system. With this system, patients are supposed to be diagnosed and treated at clinics, and referred to hospitals for further treatments if necessary. Many patients, however, do not behave as expected such that the medical resource utilization in hospitals is much higher than that in clinics. Hence, patient behavior plays an important role in designing an effective health care system that allocates the medical resource rationally, and incorporating the patient response into the system design is an interesting issue both in academe and in practice.Motivated by the imbalance of the medical resource usage between clinics and hospital, we consider an integrated model of the queuing and game theory to understand how patients behave in the two-tier health care system. Based on the patient behavior, we further study the service capacity and price design problem for the system, with patients’delay sensitivity homogeneous and heterogeneous respectively.We first study the problem with a clinic, a hospital and homogenous patients. The clinic and hospital is modelled as an M/M/1 queueing system, respectively. The clinic, which receives subsidy from the government, aims to serve patients as more as possible via choosing its capacity, while the hospital’s objective is to maximize the profit via choosing the price with a price limit set by the government. The interaction among the patients, clinic and hospital is modelled as a Stackelberg game. The equilibrium shows that the clinic capacity is increasing in the subsidy; when the subsidy is low, the hospital chooses the price limit as the optimal price; otherwise, the hospital chooses a price that is below the price limit.We then consider the heterogeneous patients case, in which patients’delay sensitivity follows a continuous distribution. When the subsidy increases, the clinic’ capacity is increasing. And, when the subsidy is sufficiently large such that the clinic’s capacity is greater than the hospital’s, the clinic’s effective arrival rate is increasing and the hospital’s effective arrival rate, price and profit are decreasing in the subsidy. Next, we extend the model by allowing the hospital to decide its price. The result indicates that the subsidy helps increase the clinic’s and total effective arrival rate, and decrease the hospital’s effective arrival rate and price.Next, we study the impact of the patients’heterogeneity in service value and delay sensitivity on the system design. Patients are classified into two classes with high (low) service value patients having low (high) delay sensitivity, and no priority is provided to them. We consider a multi-objective optimization problem that incorporates the subsidy minimization and profit maximization, and apply genetic algorithm to solve the problem. The result shows that the presence of the heterogeneity in service value makes a significant difference to the system design.Finally, we are interested in the impact of the current referral mechanism in which patients who are referred from the clinic have priority of being served in the hospital. We derive the patients’expected delay and further capture the patient behavior and the hospital’s optimal referral mechanism design. Interestingly, we show that when the referral rate is low, offering priority not only improves the hospital’s profit, but also increase the effective arrival rate of the clinic; when the referral rate is high, no priority should be offered.