Managing Patient Service in a Diagnostic Medical Facility

A simple formula using available data shows how best to schedule patients for medical services involving costly equipment.
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The Idea

A simple formula using available data shows how best to schedule patients for medical services involving costly equipment.

The Research

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.


Practical Applications

Hospital managers

This research offers a method for you to manage your facility for MRI or any other expensive medical service. If outpatients, inpatients and emergency patients come with different revenues and costs, and if there are penalties for some patients held over another day, then the formula can help you increase profitability or reduce patient waiting time. If your facility matches the example in the study, you can apply directly the formula derived from these research results.

Linda Green

Professor Green earned her doctorate in Operations Research from Yale University. Her research, which has focused on the development and application of mathematical models of service systems, has resulted in dozens of publications in the premier technical journals such as Operations Research and Management Science as well as prominent healthcare journals such as Health Services Research, Inquiry and Academic...

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Linda Green, Sergei Savin, Ben Wang

"Managing Patient Service in a Diagnostic Medical Facility"


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