Little’s Law at the Hospital


This post is partly in tribute to Peter and his Little's Law blogging at (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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  1. Gretchen Davenport says

    As a nurse and a Lean Coach I’m actually suprised the manager didn’t say they had more than 8 admissions & discharges a day. From a patient care perspective you always feel like you are doing more than the numbers show.

    From a medical lean perspective I would be concerned that their average LOS is 6 days. Unless this is a very high acuity unit without a step down unit 6 days is a hefty LOS and a decreased LOS is very possible. With, of course, buy in from the physician and nursing staff.

    1. Mark Graban says

      Hi Gretchen-

      You’re right, 6 days would be very high… it’s somewhat an old example (from 2006) and lengths of stay have generally come down since then for a number of reasons, but I also chose numbers that made for easy math.

      If LOS was 4.0 days, then they would have 12 admits and discharges a day… and if LOS was 3.0 days, they’d have 18 admits and discharges.

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