A Major Medical Center Gets a Cheaper, Fairer Way to Assign Doctors

Model tells schedulers which anesthesiologists should be on call or on-site at specific times

Anesthesiology staffing is an important aspect in managing operating rooms in hospitals, as its propensity to leave doctors sitting idle or, alternatively, collecting overtime seems ripe for cost cutting. The problem — very prevalent across hospital systems — is typically addressed with cost optimization models that focus on how many doctors should be assigned in hospitals or on call at any given time. 

A new scheduling protocol takes the next step by pairing cost optimization modeling with real doctors across a large health system with several hospitals. In using the model to assign actual named staff to actual schedule openings, one major medical center has already booked significant savings, according to a study by its designers. 

University of Pittsburgh Medical Center reports saving more than $2,000 a day, or some $15,570 a week on average, in its first few months with the new protocol in 2024. Annual savings are estimated at about $800,000, which represents a 12% cost reduction from prior years. The protocol and results are detailed in a study, forthcoming in the journal Operations Research, by the Indian School of Business’s Sandeep Rath, UCLA Anderson’s Kumar Rajaram and UPMC physicians Mark E. Hudson and Aman Mahajan. 

Keeping the Talent Happy

The research team was tasked with cutting costs by changing the way it scheduled anesthesiologists across UPMC’s 11 hospitals. The organization on average staffs 84 anesthesiologists daily and sometimes more than 100 a day. Importantly, the team needed to avoid potential solutions that the doctors themselves would not appreciate, such as last-minute schedule changes or excessive call duty.

The model is designed to assign specific anesthesiologists to schedules in the most cost-effective and objectively fair ways. Savings come from reducing overtime and idle time. Both efforts help maintain goodwill among the staff, the researchers report. 

Across U.S. hospitals, about half of all surgeries are scheduled with less than three days’ notice. But staff assignments, including on-call duties, ideally are set weeks in advance. That means scheduling operating staff without knowing the full extent of how many and what types of surgeries will be needed or how long each will last. In order to avoid tragedies caused by understaffing, most hospitals end up paying large sums for anesthesiologists to be on-site when there is no work for them or, on other days, overtime for those on duty. 

At hospitals, some portion of operating room staff is always assigned to on-call duty to cover unexpected situations, and physicians generally accept that these assignments are part of the job, the researchers write. It’s common for a hospital to pay a fee on top of salary to doctors that end up actually working while on call. But frustration grows when on-call or on-duty assignments seem pointless — when they have to be at work but no one needs their skills — or the time and day of assignments seem unfair. Hospital schedulers often handle fairness issues by manually changing software-generated schedules. 

Many researchers have addressed this problem using aggregate-level staff-planning optimization models to test how various scheduling protocols affect costs at a single hospital. Rajaram, for example, built one at the UCLA Ronald Reagan Medical Center, which demonstrated cost savings about six years ago. 

Results from aggregate models give users data-backed advice on what to strive for in creating schedules, such as how many anesthesiologists should be on call for a particular location. But they do not give directions on how the scheduler can fill these times using the only doctors available to her to assign. While hospitals often use software to help with this, these programs don’t consider the costs of different scheduling decisions.   

Getting Personal

The UPMC team built an optimization model that goes well beyond such high level suggestions. This model considers rules both general to the anesthesiology staff — no one should be assigned back-to-back shifts, for example — as well as those specific to each individual anesthesiologist in the system. Perhaps Dr. X works only at these two hospitals, and Dr. Y is permanently assigned to one specific hospital on Tuesdays. Dr. Z never works Wednesdays. It assigns anesthesiologists to every slot, in every schedule, accordingly.

Assignments are done in stages to allow for updating as details of the day’s surgeries become clearer.

Six weeks prior to the date, all available anesthesiologists are assigned to specific hospitals or the on-call pool. These assignments account for a variety of system-specific factors. Maybe everyone has to take call at times, but no more than seven days a year. 

Three days prior, schedulers decide how many and which anesthesiologists should be pulled from the on-call list and assigned to specific hospitals. The rest of the on-call pool keeps that assignment.

Not Reaching for the Last Dollar

Interestingly, UPMC rejected some potential changes to the model that could have saved it significantly more money on anesthesiology staffing. For example, taking out the provision that assigns on-call duty in a round-robin fashion — each doctor is moved to the bottom of the duty pool immediately after serving one — could cut costs an additional 8.6% a year, according to the study. It also is an agnostic system that removes concerns of favoritism in scheduling. 

But without the round-robin constraint, anesthesiologists who have agreed to work at multiple locations serve more time on call than others. That happens because their flexibility reduces overtime and idle time more than a doctor who works for a single hospital, the researchers note. Because the round-robin approach would seem more fair to its staff — there’s no room for favoritism in scheduling — UPMC chose instead to address the problem by increasing the number of doctors who work at multiple hospitals.

Perceived fairness in scheduling is perhaps a necessary cost as about a third of anesthesiologists working in the U.S. are older than 60 years, and the industry expects large shortages of these specialists as they retire, the researchers note.