The Math of Block Time Optimization


In a previous post, I suggested that applying math-based solutions might help you make convenient OR time available to providers who need it, subsequently improving patient access and providing a measurable return on investment. There are a number of areas in which math-based analysis can help. I've chosen to focus on four that I consider particularly impactful:

  1. Locating - in advance - block time likely to go unused
  2. Allocating block time appropriately in a template to optimize for strategic imperatives
  3. Booking the right amount of time for each case
  4. Changing provider behavior with data

If you have access to data science resources in your health system, they may be looking into some of these challenges already. If not, consultants focusing on statistics and data science may be able to help.  Solving these challenges is why Copient Health exists.

1. Locating Block Time Likely to go Unused

How can you know in advance whether a provider or service line's block time on a certain day will be appropriately utilized?  This is definitely a job for machine learning.  Machine learning (ML) is a broad category but the type of ML we're talking about is focused on predictive modeling.  Assuming a reasonable data set, you should be able to predict, well in advance of any mandatory release deadline already in place, whether a particular block on a particular day will get filled up.  

What would you do with that knowledge if you had it?  You could start by reclaiming that time on that day from the block holder.  This is sometimes easier said than done, but that's a topic for another post.  Once the time was reclaimed, under normal circumstances you'd get it into the hands of providers who could use it and for whom it matched their preferences and availability.  However, considering the prevalent staffing issues we are all facing, you may instead decide to close the room.  Either way, the ability to predict the future is always helpful.

2. Allocating Block Time Appropriately

The term "right-sizing" blocks is often used to refer to the periodic shuffling of block time based predominantly on the last quarter's utilization statistics.  However, considering utilization alone can lead to bad decisions for several reasons:

  • OR Utilization for individual surgeons varies widely over time.  As reported by Dexter et. al. in Anesthesiology 2003, during a 3-month period for a surgeon with measured adjusted utilization of 65%, there is a 95% chance that the surgeon's average adjusted utilization is as low as 38% or as high as 83%.  That's quite a wide range - one you might not want to base block allocation decisions on in a vacuum.
  • Surgical specialties with shorter case durations often report higher utilization than specialties with longer durations.  This makes intuitive sense. The game of Tetris taught us that it's easier to fit a small piece into a slot than a big piece.
  • OR Utilization frequently doesn't correlate with your strategic objectives.  Those objectives might include a desire to grow a particular service line or to simply maximize contribution margin per operating room hour.  A specialty, particularly one with short procedure durations, might have high utilization but low contribution margin per hour.
  • You have to consider resource constraints. If you allocate all of the time to a high contribution margin specialty that also sends a lot of patients to the ICU, you may run into a downstream resource issue

Instead of optimizing your block schedule solely around utilization, utilization can just be one of several inputs into an optimization model.  The mathematical method often used in situations like this is called Linear Programming, or in this case Linear Integer Programming.  Again, if you have a data science resource, they’ll probably be familiar with this technique. Essentially it takes a linear equation that describes your maximization function, along with all of the constraints you need to address, expressed in mathematical formulas. Based on these definitions you put together, it can assemble an optimized block schedule for you. A handful of journal articles describe this technique or variations of it for allocating block time.

3. Booking the right amount of time for each case

We hear a very common complaint from nearly every hospital we meet. It’s around how much time gets scheduled for a particular case, and the inaccuracy of the amount of time recommended by the scheduling system or requested by the provider. Just like the previous two challenges, we can solve this problem with data science.  Any number of ML tools, even linear regression in an excel spreadsheet, can meaningfully improve predictions of case length.  The harder part may be to arrange for convenient access to this data when you need it - when scheduling a case.

4. Changing Provider Behavior with Data

A near-universal complaint we constantly hear about the analysis and reporting tools available in the scheduling modules of most EMRs is that they are woefully inadequate. We often hear that they are inaccurate as well, but we have only anecdotal data to support this.  It appears that many utilization reporting solutions tie utilization specifically to a room ID.  When the room changes last-minute as it often does, the provider is not credited for the utilization. No wonder they doubt the data. 

In a previous post, I mentioned leveraging the availability heuristic to manage providers' assumptions about their block performance, so they are never surprised.  Making sure providers see accurate data regularly that summarizes their block performance accomplishes two tasks:  it eliminates the scenario where a provider believes they're being taken by surprise with potentially inaccurate data out of the blue, and it gradually nudges them toward the block management behavior you want; that is, to release time they won't use. 

An entity that focuses exclusively on helping you use data science to optimize your operating room is in a far better position to make actionable real-time reporting available to you, your staff, and your providers. 

If you are interested in optimizing block usage and growing surgical volume at your facility, reach out to us – it’s our favorite subject!


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