Little’s Law at the Hospital

This post is partly in tribute to Peter and his Little’s Law blogging at shmula.com (it’s not all Little’s Law all the time, however). More on Little’s Law at wikipedia. Or check out the excellent textbook Factory Physics for even more.

Today, I saw what appeared to be an illustration of Little’s Law in a hospital unit. Little’s Law is the relationship between “Work in Process” (WIP), Throughput, and Cycle Time. One way to think of it, in manufacturing terms:

Throughput (Pieces/Day) = WIP (Pieces) / CT (Days)

In a hospital unit with 48 beds, those full beds, those 48 patients are “WIP”. Their average length of stay (LOS), the average time a patient in a bed is about 6 days.

You might ask, how many beds do they turn over per day? Use Little’s Law:

Bed Turns = # of Beds / LOS = 48/6 = 8

Asking the clinical director their average # of discharges and new patients per day… of course the answer was 8.

The hospital wants to reduce the average length of stay. Doing so will mean an increase in resources required to discharge patients and to clean rooms for the next patient. If they want to reduce average LOS to 5 days, you can calculate the expected # of bed turns = 48 / 5 = 9.6 bed turns per day.

Is this incredibly helpful as a lean lesson? Probably not. But, the Industrial Engineering geek in me thought it was interesting.

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