# Little’s Law and controlling WIP inventory

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 %*

How is your production rate 4 pieces per hour when your workstation #3 can only do 3 parts per hour?. Thanks!

Hey can you please tell me from which you have written this .A question has been framed from this in one of the exam.