 # Little’s Law and controlling WIP inventory

Optimizing work in-process  inventory levels is a prime focus in the manufacturing organizations across globe and there are myriad of methodology /algorithms  available to approach it .

One of the interesting approach is introduced by John Little.  It  is applicable to queuing systems i.e a  system  in which discrete objects is produced/arrives at some rate.

As per Little’s Law

The  work in-process inventory  in a stable system is equal to the average flow  rate, multiplied by the  average processing time .

Mathematically it can be expressed as

L = λW

where L = Work in process inventory

λ = Average output from process /Throughput:

W= Average Processing  time

WIP Inventory = Average output from process /Throughput  X Average Processing Time

Let us correlate Little’s law to real life scenario . Consider the below assembly line where raw materials is processed through series of work centers  and turned into a finished product after operation at work center 5. Production  rate of the assembly line is 4 pieces per hour and average  processing/cycle time to transform the raw material to finished product  is  60 minutes or 1hour.

If we use this information in Little’s law then this implies that the  work in process inventory at any time will be 4 Pieces ( Average output from process /Throughput  X Average Processing Time i.e . 4 X1).

One way to bring down this WIP inventory is to improve the cycle time .  30 % decrease in cycle time i.e  bringing the cycle time from 60 minutes to 42 minutes will result into 25 % decrease in WIP inventory.

Improved WIP inventory  =  4X 0.7  = 2.8 ~ 3 Pieces.

% Decrease in WIP   = (4-3)/4 *100 = 25 %

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