Physician scheduling can be synonymous with headaches and major time consumption, and if you’re the one responsible for building your group’s schedule, you know such pain firsthand. If you’re the one responsible for building your group’s schedule, you’re also probably juggling a lot more than you even realize.

Every scheduling period, the number of assignments and providers as well as the length of the scheduling period are all generally set variables, so why does it take so long to turn these variables into a workable schedule? The answer lies in the number of possible schedule outcomes that exist when set scheduling variables are combined.

To gain further insight, let’s find the total number of schedule possibilities in a few example scheduling scenarios. We’ll use the equation N=2D*P*A, where

N is the number of possible schedules;

D is the number of days in the scheduling period;

P is the number of providers being scheduled; and

A is the number of assignments being scheduled for.

In the equation, 2 is constant because it accounts for the two scheduling options for each day, provider, and assignment: (1) scheduled or (2) not scheduled. It also does not restrict demand to 1, meaning the equation accounts for scheduling no providers, one provider, or more than one provider to the same assignment or on the same day.

Starting Simple

Let’s take a closer look at the equation above with simple scheduling variables: 1 assignment, 2 providers, and 2 days.

Applying the logic behind the equation, we get a total of 16 possible schedules: We find the same result when we plug these variables into our equation:

### N=22*2*1=24=16

Increasing the Complexity

To add a little more complexity to the variables above, let’s increase the scheduling period to a month. If we schedule the same 2 providers and 1 assignment but this time for a monthlong schedule, the number of possible schedules dramatically increases to 1.2×1018. That’s more than 1 quintillion possibilities!

### N=230*2*1=260=1.2×1018

For perspective, it would take today’s state-of-the-art MacBook Pro 401 years to find all 1.2×1018 possible outcomes. Over 400 years for just 1 assignment, 2 providers, and a one month schedule!

Scheduling a Small Physician Group

To apply our equation to a more realistic scheduling scenario, let’s use variables more reflective of an actual schedule for a small physician group with 3 providers and 4 assignments. For a one month schedule, the number of possible schedules is approximately 2.3×10108.

### N=230*3*4=2360=2.3×10108

That’s 2 followed by 108 zeros:

#### 2,300,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

With an estimated 4×1081 atoms in the known universe, that’s more schedule possibilities than the number of atoms in the universe!

Scheduling a Medium-to-Large Physician Group

Even though we know it will be significantly more than the number of atoms in the universe, let’s see just how many more possibilities exist for a medium-to-large physician group with 40 providers and 6 assignments. Factoring in these variables for a one month schedule, the number of possible schedules is literally infinite.

### N=230*40*6=27,200=∞

That’s a convenient fact for schedulers to have in their back pocket next time someone comments that the schedule isn’t done yet!

Administrators or physicians who create physician schedules by hand or rely on their own memory to account for each scheduling need and preference every scheduling period are faced with narrowing down an infinite number of schedule possibilities to find that one optimal solution. But it’s not humanly possible, so the result is unbalanced, inefficient schedules that can lack equity and fail to meet providers’ work-life balance preferences. If it’s not humanly possible to find an optimal schedule from an infinite number of possibilities, is it possible at all?

Yes — thanks to something called optimization software, which uses complex algorithms, which uses complex algorithms to reach the solutions in fractions of the time it would take to do the computations outright. In 2007, Lightning Bolt became the first physician scheduling platform to utilize this technology for physician scheduling. Lightning Bolt’s web-based application allows physician groups to define scheduling rules according to their specific needs and preferences, which act as constraints and limit the number of possible schedules within the software. Lightning Bolt’s sophisticated algorithms are able to find that one optimal schedule that best meets your requirements from an infinite number of possible schedules.