Patient referral strategy and cost sharing for a medical consortium

In this paper, we investigate the problem of sharing medical resources through patient referrals for hospitals in a medical consortium. We address two main issues. One is to derive the optimal patient referral strategy for the consortium to minimize the total costs of the consortium; the other is to determine a fair cost allocation scheme to ensure the stability of the medical consortium. We first consider a general setting wherein patients can be referred between any two hospitals in the medical consortium. Then, we extend our analysis to the special setting wherein patient referrals are only allowed between hospitals in different categories. We formulate the patient referral problem as a convex optimization problem, and discuss the properties of the optimal patient referral strategy. We apply the framework of cooperative game theory to allocate the total costs arising from the medical consortium to the member hospitals. We propose a dual-price cost allocation scheme and show that it is in the core of the corresponding cooperative game. Numerical studies are conducted to further examine the proposed cost allocation schemes and to investigate the impact of parameters on the efficiency of a medical consortium.