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John Little - MIT Professor |

Well how does this relate to manufacturing and value streams? If
we break down the statements in the definition and relate them to lean terms,
then this relationship can be easily understood.

“Average # of customers in a stable system L”: In a service
organization, Average # of customers in a stable system is essentially system
WIP. In a value stream map that would be the parts in the system. A stable
system in service would describe any time there isn’t a built in ramp up and
ramp down like opening time and closing time perhaps. A stable system in value
stream mapping would be similar – any time you are in normal production and not
new production introduction. In our new formula we’ll define L = WIP

“Average arrival rate λ”: How often a customer walks into a
service process is your arrival rate – well what would that be in lean? How
often should parts arrive into a value stream – theoretically at the customer
demand rate. The customer demand rate we will call throughput which will be a
measure of units over time (e.g 2 parts per day, 1 part per week, etc). For our
new formula, λ = T (throughput).

“Average time a customer spends in the system W”: For a service
organization this is exactly what it sounds like – basically how long he/she
waits for a response. If its McDonalds it’s the time from when the customer
walks in to when they order food and leave the queue. Relating this back to
manufacturing, if our customers are our WIP, then we can think about how long
the WIP is in our system. This is of course leadtime! So for our new formula W
= LT (leadtime)

So after breaking down Little’s Law we now have a modified formula
for manufacturing and value streams: WIP = T x LT. So the inventory in your value stream is a function of throughput times the leadtime. This is a very powerful relationship to understand and can prove useful in many situations. My boss recently told me that my inventory needed to be no more than $1.2m on a critical value stream. By knowing the average value of a part in the value stream, I could tell that this represented approximately 30 pieces of WIP. I knew based on required customer demand that throughput was 2 per day. So:

Target WIP = 30 pieces

Throughput = 2 per day

Lead Time = ?

30 = 2 * LT

LT = 15 days

So based on this, I know my target leadtime is now 15 days. I know based on system actuals that my current leadtime is 18.5 days. Based on this knowledge I know how much of a leadtime improvement I need to make in order to achieve my bosse's targets. Little's Law is also useful in doing sanity checks while doing value stream mapping.

Any thoughts about Little's Law and experience applying it to manufacturing situations?

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