An Algorithmic Balancing Act for Optimal Healthcare Office Scheduling

March 16, 2020

The creators of an algorithm account for all complexities behind scheduling in an atmosphere of daily unknowns.

By Cibeles Duran

In lobbies of doctor offices or outpatient clinics, patience may often be a virtue, not only for guests waiting their turn, but also for staff tasked with scheduling the day’s appointments. These schedulers must contend with several incongruous factors, mainly daily uncertainties including patient no-shows, non-punctuality, and emergency walk-ins, which conflict with performance goals. Endeavors to achieve short waiting times, minimized idle times of doctors or equipment, and less extended workdays become challenged by unmet, late, or unplanned appointments. Trying to solve one element can exacerbate another. To shorten waiting times, for example, management may hire more doctors, but then faces the likelihood of increased idle times when not enough patients fill the slots.

Under an environment of daily unknowns, how should health centers best approach scheduling to maximize resources and avoid operational disruptions?

Operations management experts Christos Zacharias and Tallys Yunes delved into integer vectors, discrete convexity properties, and multimodular functions to propose a solution. Their mathematical model and scholarly analysis, published in Management Science, yielded an algorithm that grapples with all variables for an optimal scheduling strategy based on each office’s needs.

“The idea for the model is to serve as a tool to help different clinics according to their own priorities,” Yunes says. Miami Herbert Business School researchers geared their computational procedure to resolve for the factors that matter most to each practice, be it shortening waiting times, reducing overtime, or taking full advantage of equipment use or doctor times. Once defining priority, tailoring entails inputting certain historical estimates, such as the length of time that the doctor spends with each patient, the frequency of walk-ins, and the number of appointments that go unmet. The algorithm then reveals the specific timeslots of the day to best schedule patients to attain the prioritized goal.

The tool allows for up to 96 slots a day, which signifies a full workday at five-minute slots, or an around the clock timeframe under 15- or 30-minute intervals. While the more customary timeslot per patient is a half hour, testing for the effect of shorter slots uncovered that longer service times tend to cause longer waiting times, as well as workload into overtime. “Clinics should consider going to shorter slots,” Yunes says. He also highlights that the program should be run periodically to optimally adjust scheduling for changes in data or circumstances. Seasonality, for example, could mean higher demand in certain months and a temporary need for more doctors.

Previous research had only focused on parts of the problem. Studies generally set assumptions, such as overall punctuality, or no emergency walk-ins, producing unrealistic and incomplete solutions. “Nobody had considered all of the details together,” Yunes says. “We realized that the more realistic approach looks at every aspect together because that’s what happens in real life.”

Yunes’ and Zacharias’ model is the first to undertake scheduling in its full complexity, considering the random nature of service times and the inevitable instances of no-shows, non-punctuality, and unscheduled walk-ins, along with impacts on performance goals. Their creation allows for computations of all variables to arrive at the best global solution, or the highest hilltop, as Yunes describes it: “The multimodular property of the model assures that, on a surface of all possible solutions, there is one highest hill, and once climbing it, you’ll be at the highest peak, the guaranteed best answer.”

Already, a urology clinic in the University of Miami’s Lennar Medical Center has implemented suggested changes. More healthcare offices may follow when the innovation progresses into interface format, a possibility that Yunes is open to exploring. “It’s doable,” he says. “We could take the extra step if there is enough interest.” With an algorithm that steers users to the “highest peak” amidst a mesh of scheduling possibilities, offering a higher degree of operational balance and staff peace of mind, a future as a concrete digital interface may be likely.

Zacharias, Christos and Yunes, Tallys (2020). Multimodularity in the Stochastic Appointment Scheduling Problem with Discrete Arrival Epochs. Management Science, 66 (2), 744-763.

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