Linda Green, Sergei Savin and Ben Wang conducted the first detailed study of how to manage a hospital’s facility for magnetic resonance imaging (MRI). The equipment for an MRI costs $2 million to buy and $2 million to install, so it must keep busy to recoup the expense. This research used data from a major urban hospital for three types of patients: outpatients, scheduled in advance; inpatients, scheduled randomly during the day; and emergency patients, scheduled immediately. Each type of patient entails different costs and revenues — for example, the hospital typically receives no extra payment from the insurer when an inpatient has to wait an extra day for an MRI, and an emergency patient who has to stay overnight becomes a more expensive inpatient. The study took the differences in cost and revenue among the different types of patients and developed a mathematical formula for scheduling MRIs.
The result is a set of scheduling rules that yields the most patients for the lowest cost and highest revenue. The full formula includes the probability of arrival, revenue, waiting cost and end-of-day penalty for outpatients, inpatients and emergency patients. But some rules that work in most situations require even fewer data elements. For example, filling all appointments with outpatients and giving priority to critical cases works well except when costs are very high for keeping an inpatient or an emergency patient in the hospital for an extra day. The formula can also be used to determine how to reduce patient waiting time.