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Why medical scheduling algorithms are a bit like reserving a tennis court

The parallel between making tennis court reservations and scheduling medical appointments is very clear to me.

When it comes to tennis, I’m definitely at the “weekend warrior” level of play. With more practice, I’m sure I could improve, but without a reliably available tennis court, getting in a few sets every day seems unlikely. In fact, the simple act of reserving a tennis court at a convenient time — early mornings or evenings during the weekend so as not to spoil the entire day or early mornings on weekdays before heading off to the office — conspires against me. It’s the same constraint that impedes the progress of most other tennis players. The parallel between making tennis court reservations and scheduling medical appointments is very clear to me.

Most health system scheduling operates under the scheduling framework provided by their EHR or scheduling application and has a resource-based view of their world. For example, if the diagnostic imaging department has four CT scanners, there will be a template that lays out all of the operating hours of each day down the page and the four machines across the top, and each “slot” gets assigned to a specific patient as their appointment is made. This template could either be electronic or on paper, and the assignment to the specific machine could either be real or virtual — but the logic still applies. This approach is also applied to virtually every other “countable asset” in the health system — radiation oncology machines, infusion chairs, MRI machines and so on.

This is essentially the same process used by the racquet club: It has a dozen tennis courts, and as each reservation is made, the specific time slot is marked as “taken” and the process continues.

The reason that it works for the racquet club is exactly the same reason that it does not work for the health system.

Tennis court reservations are precisely one-hour long, i.e. — they are predictable or deterministic. The expected duration of a medical appointment is, at best, an estimate (albeit accurate in many cases), i.e. — it is random or stochastic.

Imagine if the racquet club were to suddenly decide to become “player centric” and to adopt the following reservation policies:

  1. We understand that traffic sometimes causes players to arrive late; we will therefore guarantee that they can still use their assigned court if they are late (up to a maximum of 30 minutes beyond the designated start time).
  2. We want our players to fully enjoy their experience and will therefore not restrict our players to 60 minutes of court time but will instead allow them to “play until they are tired” (up to a maximum of 120 minutes of playing time).

These “simple” policies will throw the entire system into chaos. When you arrive at your designated court at your designated time, you have no idea if the current occupants on the court started on time or were 15-20 minutes late. Looking at them running energetically around the court, you wonder if they may also decide to play up to their full 120 minutes. You quickly realize that you may have to wait 60-90 minutes past your “scheduled time.” At this stage, your best approach would be to go to the pro shop and to figure out if there are any open courts.

While trying to accommodate your request, the magic game of Tetris will automatically commence as they attempt to meet the needs of all of the waiting players while honoring their commitment to the players who are already on the court. The only recourse left for the racquet club (unless they are willing to reverse their new policy) is to create one of two possible buffers:

A time-based buffer (blocking out 2.5 hours for each reservation to allow for the 30-minute delay in the start time and the extended play for 120 minutes instead of 60 minutes) or

An asset-based buffer (keeping one court free out of every cluster of four courts to allow for the variability in start and end times).

This is exactly what happens in health systems. Time-based buffers are created by “sandbagging” appointment lengths beyond the accurate prediction of the expected duration, while asset-based buffers are created by approving capital budgets that demand more machines even while the actual utilization of the existing machines is only ~50 percent (if measured in a “strict” manner by counting the minutes in which a patient is actually in the machine as a percent of the number of minutes in the operational hours for that machine).

Using a reservation approach that was designed for a deterministic (predictable) system in order to manage a stochastic (random) system is guaranteed to result in an underutilization of assets as well as long and unpredictable wait times. It is a bit like using the travel time for the light rail system to cover 10 miles as a way of estimating the commute time for driving the same 10 miles at different times of the day, based on the logic that they both travel at 60 miles per hour and in the same direction from the same point A to point B. All of that might be true — but the light rail system has a predictable speed of travel from station to station without the randomness of the widely variable number of cars on the road at each hour of the day that has a dramatic impact on the average speed of traffic.

Health systems need to use advanced algorithms to accurately forecast the volume of patients by hour for each day. They also need to be able to accurately estimate the duration of each type of appointment and then optimize the allocation of appointments across the relevant set of assets in a manner that accommodates the expected (and unexpected) variability in order to create as flat a utilization profile as possible. A flatter utilization profile enables a more intelligent allocation of staff in addition to minimizing the wait time experienced by patients since peak volumes create “rush hour conditions” which lead to extended wait times. Finally, they need to adopt a “control system” mindset of feedback loops to monitor, learn and adjust the forecasts in an ongoing manner.

Data scientists, engineers, and product managers have spent the last 5-6 years building these algorithms and embedding them into scalable software solutions that can be deployed within a matter of weeks and can co-exist with any EHR or scheduling system. The algorithms continue to “learn” at an astonishing clip, providing a way to break through the log jam that exists in the U.S. healthcare system.

Image: cosmin4000, Getty Images 


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Mohan Giridharadas

Mohan Giridharadas is an accomplished expert in lean methodologies. During his 18-year career at McKinsey & Company (where he was a Senior Partner/Director for six years), he co-created the lean service operations practice and ran the North American lean manufacturing and service operations practices and the Asia-Pacific operations practice. He has helped numerous Fortune 500 companies drive operational efficiency with lean practices. As Founder and CEO of LeanTaaS -- a Silicon Valley-based innovator of cloud-based solutions to healthcare's biggest challenges -- Mohan has worked closely with dozens of leading healthcare institutions including Stanford Health Care, UCHealth, UCSF, Wake Forest and more. Mohan holds a B.Tech from IIT Bombay, MS in Computer Science from Georgia Institute of Technology and an MBA from Stanford GSB. He is on the faculty of Continuing Education at Stanford University and UC Berkeley Haas School of Business and has been named by Becker’s Hospital Review as one of the top entrepreneurs innovating in healthcare. For more information on LeanTaaS, please visit http://www.leantaas.com

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