A Stochastic Queueing Model for the Pricing of Time-Sensitive Services in the Demand-Sharing Alliance

Abstract

The medical alliance has developed rapidly in recent years. This kind of alliance established by multiple hospitals can alleviate the imbalance of medical resources. We investigate the benefit of demand sharing between a hospital with large demand (HD) and another hospital with large supply (HS). Two hospitals are modeled as queueing systems with finite service rates. Both hospitals set prices to maximize the revenues by serving their time-sensitive patients. We adopt a cooperative game theoretic framework to determine when demand sharing is beneficial. We also propose an optimal allocation of this benefit through a commission fee, which makes the alliance stable. We find that demand sharing may not be beneficial even if HS has a low capacity utilization. Demand sharing becomes beneficial for both hospitals only when the idle service capacity of HS exceeds a threshold, which depends on the potential demand rate of the HS and the unit waiting cost of hospitals. Furthermore, if the idle service capacity of HS is smaller than another threshold, which depends on the potential demand of the two hospitals and the service capacity of HD, then the benefit of demand sharing will be independent of the service capacity and potential demand of HD. We also examine the effect of system parameters on revenue gains due to demand sharing.