To Solve Hospital Overcrowding, Think Like a Mathematician

An operations management specialist is applying lessons from statistics to help free up hospital beds. It’s working.

  • Many hospitals have struggled to figure out how best to allocate resources to handle the ebb and flow of patient demand.

    Visual: mathisworks/Getty Images

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The emergency department where I see patients can get pretty crowded. Sometimes, when we run out of rooms, we examine patients in the hallways. It’s harder to deliver comprehensive medical care that way, but the patients need to be treated somewhere.

It seems like the answer to overcrowding in the emergency department should be simple: Build more beds. And many hospitals are. Years ago, when one facility was considering a $10 million expansion of its emergency department, Eugene Litvak, president of the non-profit Institute for Healthcare Optimization, shook his head. “How about you give me $5 million and you do nothing and both of us will benefit,” he recalled telling the hospital’s president.

It was more than an idle challenge, coming from Litvak. He’s done it before.

Litvak specializes in operations management, a branch of applied mathematics that uses statistical techniques to efficiently match resources with variable demand. In the late 1990s, he began looking for ways to apply his professional training to American health care.

At the time, hospitals were struggling to figure out how to allocate enough nurses, operating rooms, and physicians to handle peak patient volumes without overstaffing during slower periods, which was exactly the kind of problem that operations management was designed to handle. Litvak assumed that the difficulty was primarily due to the unpredictable nature of patient demand — after all, most medical emergencies don’t happen according to a schedule.

What Litvak found, however, was that patients showed up to emergency departments in fairly predictable patterns; the problem was that hospitals were trying to meet that naturally varying demand with guesswork and intuition instead of statistics. Litvak also found a second, self-inflicted contribution to overcrowding: hospitals’ own scheduling and triage practices.

Take the operating room, where surgeons have historically been free to create their own operating schedules. Litvak found that there was nothing to prevent surgeons from deciding, for example, to schedule a full slate of surgeries for Monday and Tuesday, but none for Thursday. This uneven scheduling in the operating room can create spikes in the demand for inpatient beds, with sometimes deadly consequences.

Litvak calls these kinds of spikes artificial variability, and surgeons aren’t the only culprits. For instance, he also noticed a widespread tendency for emergency room doctors to send patients to intensive care units, even when moderate care would do, contributing to backups in those units and, in turn, in the ER.

Of course, some variability is inevitable — the number of patients in need of medical care will always be a moving target. But Litvak figured that if he could apply the methods of operations management to anticipate natural variability and work closely with hospital administrators to root out sources of artificial variability, he could more closely align a hospital’s resources with the ups and downs of patient demand. In the operating room, that meant telling surgeons when to operate; in the emergency room, it meant imposing standardized triage protocols to make admissions more predictable.

In the early 2000s, Litvak put his methods to the test at St. John’s Hospital in Springfield, Missouri and Boston Medical Center in Massachusetts. Most effective, he says, was his work a few years later with Cincinnati Children’s Hospital — an institution that, in the words of its former president and CEO, Jim Anderson, was riddled with inefficiencies at the time. “It mystified me why health care hadn’t adopted some of the management principles that industry has used for years,” says Anderson, who has a background in private industry.

Litvak collaborated with the hospital on ambitious measures to manage variation and “smooth out” patient demand. In just over a year, the operating room cut wait times by around 30 percent and overtime hours by 57 percent, despite a sharp increase in the number of surgeries performed. Yearly revenue increased by more than $130 million, and a $100 million hospital expansion was not needed.

Other hospitals have also experienced striking results. Boston Medical Center virtually eliminated delays and cancellations in elective surgeries, cut its ER waiting time by a third, and cut nursing costs by $130,000 in one unit. A hospital in South Carolina cut wait times for urgent or emergent surgery by 38 percent, saving an anticipated $8 million annually. And a consortium of hospitals in New Jersey improved hospital efficiency and flow to such a degree that ER capacity was projected to increase by 20,000 patients, and inpatient capacity by 17,000 patients, all without adding additional beds or resources. One hospital saved $18 million in just three months, while improving ER wait times and hospital length-of-stay.

Implemented on a national level, efficiency gains like these could yield truly staggering numbers. Writing in The New England Journal of Medicine in 2013, Litvak and his co-author predicted that if each American hospital achieved just one tenth of what Cincinnati Children’s and others had, the savings would approach $60 billion. If every hospital avoided adding just one extra bed through improved efficiency, the country could save between $6 billion and $12 billion.

So what’s holding us back?

For one thing, many health care professionals, patients, and legislators aren’t even aware that there exists such a promising method to reduce overcrowding, improve the quality of health care, and reduce total per capita spending. Even in the ER where I work — where we often have as many as 60 patients waiting for a hospital bed — none of my colleagues have heard of Litvak or his work.

An even bigger barrier may be the extraordinary difficulty of changing hospital culture. Most hospital executives who have implemented Litvak’s methods say that this challenge shouldn’t be underestimated. “It’s not easy to do,” Cincinnati’s Anderson told me. The culture of medicine has always been slow to change, and many institutions have become set in their ways. A case in point: The medical community has been debating work limits for residents for decades, and it still hasn’t reached consensus on whether residents should work more or less.

Litvak sums up the problem with the well-worn aphorism about defining insanity as doing the same thing over and over again, but expecting different results. Maybe now, with the health care debate again in the national headlines, people are finally ready for something different.

Clayton Dalton is a resident physician at Massachusetts General and Brigham & Women’s Hospitals, in Boston. He graduated from the Columbia University College of Physicians & Surgeons in 2016.

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8 comments / Join the Discussion

    Maybe use SAS medics tactic in time of distress . Mark patients by level of priority . Those with low priority can be delayed for days when hospital is not busy . Those whose life is in danger treat immediately . Those that can wait can wait if their life is not in danger …
    Just good doctor that will be able to show empathy and explain that their life is not in danger and that they can go home . Drink tea and relax as that is best way to prepare for operation that will be made in 1 week time . Everybody happy . But when Hospital is running for profit all mathematics will fall in water … How many lives will you save is the question and how

    Don’t look on it as business but saving lives …
    When you are saving lives you need to be efficient . It is hard to change old ways . Without trying to change them you already lost . Use mathematics and watch best medics in the special forces …


    I work for Optum, a division of UnitedHealth Group, and one of the things that we have invested heavily in is data to drive decisions. I found this essay to be very interesting.


    You shouldn’t expect nurses, doctors, and orderlies to behave like a robot.

    In these algorithms, build in time for people to have breaks.


    I’m pretty sure they build breaks into the algorithms. They are for “optimizing”, not “maximizing” :-)


    This article started out so promising but it never got to the actual beef of it. HOW EXACTLY did Litvak make changes so that these results where achieved; the article says he did but now how. It seems like an intro only but no meat on the bones.


    The technical details of this intervention could be found in the following Joint Commission books:

    1. “Managing Patient Flow in Hospitals: Strategies and Solutions” –

    2. “Optimizing Patient Flow: Advanced Strategies for Managing Variability to Enhance Access, Quality, and Safety” –

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