Bundled vs. unbundled : impact of payment scheme on performance in a healthcare downstream referral program

Healthcare downstream referral programs, where patients are transferred to a community hospital after surgical treatment in a tertiary hospital for rehabilitation treatment, have been widely advocated. However, no appropriate payment scheme aligns incentives to promote the program. This paper mainly compares two payment schemes: bundled and unbundled, which refer to packaged versus separate payments for surgery and rehabilitation treatment. By establishing a three-stage Stackelberg game within a M/Cox-2/1 queuing framework, our paper considers a payer maximizing social welfare in the base model and a payer maximizing the system's long-term surplus in the extension. The base model finds that: (i) the payer pays less under the bundled payment scheme when the potential arrival rate is low and the delay cost is high; otherwise, in most cases, the payer pays more under the bundled payment scheme. (ii) The bundled payment scheme yields greater referral volume and a higher level of effort. (iii) The bundled payment scheme is a weak Pareto improvement (PI hereafter) when both the potential arrival rate and the delay cost are high; the unbundled payment scheme is a PI when the delay cost is moderate and the potential arrival rate is relatively low; otherwise, there is no PI. However, when the payer aims to maximize the system's long-term surplus with a limited budget, several different results are obtained. These results can provide practical insights for policy-makers to coordinate downstream referral programs.