According to Littles law, which of the following can be used to estimate work-in-process inventory

Perhaps you’ve heard of process lead time, a common metric in manufacturing that gives you an idea of how long you’ll have to wait on a widget if you start working on it right now. But you might not know that it’s closely related to a queue theory concept called Little’s Law.

These are fundamental concepts that have paved the way for waves of improvement in many fields.

At Veryable, we champion the importance of operational improvements, no matter where you are in your journey. We help businesses every day to reach new levels of efficiency through the application of on-demand labor in their operations. We won’t talk about that solution here, because we’re going to focus on explaining the fundamental concept of process lead time.

In this article, you’ll learn about Little’s Law, how it can help you calculate process lead times quickly, and how you can use that information to make operational improvements.

What is Little’s Law?

Little’s Law was theorized by John Little, a professor at MIT and an awarded operations researcher, to determine how many people are in a given system (e.g. traffic light) at any time.

The equation is as follows:

L=ƛW

In this equation, L is the average number of people in line, ƛ is the average exit rate, and W is the average time spent in the queue.

Little’s Law example situation

A practical example of Little’s Law in action would be a checkout line. Imagine that a store owner only has one checkout line, and it’s creating a backup in the store because the line is getting too long. So he grabs a notepad, watches his checkout line in action, and does some quick math to figure out what’s causing the problem.

He notices that 16 people enter the store and check out every hour, and they spend an average of 15 minutes (0.25 hours) in line. Using Little’s Law, he calculates that this results in four people in line at any given time.

The store owner might seek to influence the length of the queue by speeding up checkouts from its current rate of four minutes per customer. Or, he might open more lines to serve more customers at once.

That leads us to the practical applications of little’s law as it relates to lead times and inventory.

Process lead time calculation using Little’s Law

The process lead time equation is analogous to Little’s Law, but uses manufacturing terminology. With a little algebra, you end up with the following equation:

PLT = WIP / ER

Process lead time (PLT) is equivalent to the work in process (WIP) divided by the exit rate (ER).

For example, if you have 20 widgets in process and they exit the line at 2 every minute, then you have a process lead time of 10 minutes.

What is process lead time used for?

The process lead time calculation using Little’s Law gives you a quick, back of the napkin way to see where you stand. When you know your process lead time, you have a baseline for making operational improvements.

Using this information, you can decide whether you need to speed up your process or run more lines in parallel to improve output. In other words, you could seek to speed up the exit rate for each line or reduce the work in process per line.

How to improve process lead time

Based on the equation above derived from Little’s Law, you can improve process lead time by reducing the work in process or by making process improvements to speed up the exit rate. That would mean either adding more lines running in parallel or reducing the time each worker spends on their step in the process.

There are other ways outside of this simplification to achieve process lead time improvements. Learn more ways to improve process lead time in our blog about using on-demand labor to improve lead time.

A theorem that determines the average number of items in queuing systems

What is Little’s Law?

Little’s Law is a theorem that determines the average number of items in a stationary queuing system, based on the average waiting time of an item within a system and the average number of items arriving at the system per unit of time.

The law provides a simple and intuitive approach for the assessment of the efficiency of queuing systems. The concept is hugely significant for business operations because it states that the number of items in the queuing system primarily depends on two key variables and is not affected by other factors, such as the distribution of the service or service order.

Almost any queuing system and even any sub-system (think about a single teller in a supermarket) can be assessed using the law. In addition, the theorem can be applied in different fields, from running a small coffee shop to the maintenance of the operations of a military airbase.

Our Math for Corporate Finance course demonstrates the foundational mathematics required for Financial Analysis and Corporate Finance.

Origin of Little’s Law

Massachusetts Institute of Technology (MIT) professor, John Little, developed Little’s Law in 1954. The initial publication of the law did not contain any proof of the theorem. However, in 1961, Little published proof that there is no queuing situation where the described relationship does not hold. Little later received recognition for his work in operations research.

Formula for Little’s Law

Mathematically, Little’s Law is expressed through the following equation:

Where:

L – the average number of items in a queuing system

λ – the average number of items arriving at the system per unit of time

W – the average waiting time an item spends in a queuing system

Example of Little’s Law

John owns a small coffee shop. He wants to know the average number of customers queuing in his coffee shop, to decide whether he needs to add more space to accommodate more customers. Currently, his queuing area can accommodate no more than eight people.

John measured that, on average, 40 customers arrive at his coffee shop every hour. He also determined that, on average, a customer spends around 6 minutes in his store (or 0.1 hours). Given these inputs, John can find the average number of customers queuing in his coffee shop by applying Little’s Law:

L  =  40 x 0.1  =  4 customers

Little’s Law shows that, on average, there are only four customers queuing in John’s coffee shop. Therefore, he does not need to create more space in the store to accommodate more queuing customers.

Related Readings

CFI is the official provider of the Financial Modeling and Valuation Analyst (FMVA)™ certification program, designed to transform anyone into a world-class financial analyst. To keep learning and developing your knowledge of financial analysis, we highly recommend the additional CFI resources below:

• First-in, First-out (FIFO)
• Inventory
• Last-in, First-out (LIFO)
• Lead Time

How does Littles law calculate work in progress?

What is Little's law used for?

What does Little's law show about inventory?

Which of the following is correct about Little's law?