The performance of a generalized Bailey-Welch rule for outpatient appointment scheduling under inpatient and emergency demand

We are considering the problem of scheduling a given number of outpatients to a medical service facility with two resources servicing outpatients, inpatients, and emergency patients. Each of the three patient classes has associated class-specific arrival processes and cost-figures. The objective is to maximize the total expected reward which is made of revenues for served patients, costs for letting patients wait, and costs for denial of service. For this problem we propose a generalization of the well-known Bailey-Welch rule as well as a neighborhood search heuristic. We analyze the impact of different problem parameters on the total reward and the structure of the derived appointment schedules and address the question of the number of outpatients to be scheduled. The results show that the generalized Bailey-Welch rule performs astonishingly well over a wide range of problem parameters.