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Posts Tagged ‘Work In Progress’

Little’s Law: a fundamental principle used in performance measurement and Lean Six Sigma

Thursday, April 15th, 2010

Developed in 1961 by a former Massachusetts Institute of Technology (MIT) professor, John D. C. Little, the law that carries his name (Little’s Law) has emerged from being a queue theory at its origins to being applied currently in a variety of other aspects of every-day life, such as: Project Management, Manufacturing, Supply Chain etc.

Originally, Little’s Law was explained in the queuing theory as it follows (McDonough, 2009):

L = λ x W

Where:

L = # Long-term customers in the system

λ = # Long-term average arrival rate

W = # Long-term average time a customer spends in the system

Nowadays, the principle has become one of the fundamentals of Lean Six Sigma, a method that aims at increasing overall business performance (increased speed and reduced waste) and customer satisfaction.

Source: McDonough, 2009

Lean Six Sigma is based on five fundamental laws (Aveta Solutions, 2009), one of them being the Law of Velocity that relies on the equation embedded in Little’s Law:

# Work in process = # Throughput x # Average flow time

This can be applied in performance measurement in practically any kind of industry. Several examples could be the following:

In airlines, you know that you have an average queue size of 20 passengers and a throughput of 300 passengers embarking per hour, meaning 5 passengers per minute. To calculate the average time a passenger waits in the checkpoint queue, you will have to divide the work in process or the average inventory (of 20 passengers) to the throughput (5 passengers/minute) and you obtain an average wait time of 4 minutes.

In a restaurant, you serve an average of 50 customers per day (considering you are open for 10 hours from 12.00 to 22.00, that would mean a throughput of 5 customers/hour). At any time, there is an average of 10 customers, meaning an average inventory, inside the restaurant. If you wish to know the time a customer spends on average inside the restaurant, you divide the average inventory (of 10 customers) to the throughput (of 5 customers/hour) and obtain a 2 hours average flow time.

This has several implications for managers in their performance measurement and management initiatives, the most important being that, for a given throughput, the only way to reduce flow time is to reduce the inventory or the work in process.