Maintenance Mindset: Little’s Law and lean manufacturing — A formula for operational excellence
Welcome to Maintenance Mindset, our editors’ takes on things going on in the worlds of manufacturing and asset management that deserve some extra attention. This will appear regularly in the Member’s Only section of the site.
John D.C. Little, professor emeritus at the Massachusetts Institute of Technology (MIT Sloan School of Management), who had been part of the institution for nearly 80 years, died on September 27. This week’s column is dedicated to remembering his life and work. If you’re familiar with him, you probably know his namesake theorem Little’s Law. He also innovated fields like operations research and marketing science, particularly by using computing methods to measure and make business decisions.
I want to focus on how his work in data and decision sciences applies to manufacturing. Little’s Law, proven in 1961, is an operations research concept for understanding the dynamics of queuing, and it’s widely used in manufacturing and many other industries too.
It’s a simple formula to describe the relationship between how many things are waiting in line, how often new ones arrive, and how long each thing takes to reach completion. Little’s Law is a fundamental concept of lean manufacturing, based on the relationship between inventory, throughput, and lead time. If a manufacturer can understand how these main factors interact, it will have a better basic understanding of its system. Just like the line at the drive-thru, some production lines move faster than others, and Little’s Law can mathematically tell you why.
Broadly, the theorem describes how the long-term average number of items (L) in a stationary system is equal to the long-term throughput (λ) multiplied by the average time (W) that an item spends waiting in the system. It applies to many sectors, from manufacturing to health care to customer service.
In the manufacturing world this means:
Inventory = throughput rate x cycle time
or
Work in progress (WIP) = exit rate x lead time
The equation can be used to estimate the lead time, WIP or throughput rate of a process. For example, the more items in line (L/inventory/WIP), the longer lead time (W/cycle time) it will take to complete the items, if the throughput rate (λ/exit time) stays the same. To reduce lead time, you can either increase the throughput, reduce the number of items in line, or restrict WIP.
It’s probably much harder (or more expensive) to double the production rate or throughput and easier to decrease inventory, and Little’s Law has become a mathematical justification for the push in lean manufacturing to reduce inventory, or to have a clearly defined limit on WIP.
A key principle of lean manufacturing is also eliminating waste. In an established production line, where you do have variability in the system, Little’s Law can be used to quantify and eliminate bottlenecks. For example, an automotive assembly plant can identify which particular workstation is the bottleneck, and increasing capacity there could reduce WIP and improve throughput.
Little’s Law can be used in things like capacity planning, long-term planning for production changes, and supply chain analysis to evaluate inventory across distribution networks. Little’s Law is also part of continuous improvement culture, using science to identify bottlenecks, suggest production improvements and embrace change on a continuum.
The simplicity of Little’s Law can also scale from a single- to a multi-queue system. So, it works for one line or multiple production lines in a manufacturing system, given you have a relatively stable system and consistent measurement among variables. Like any analysis, you need good data.
John Little will be remembered long after his death for the simple equation, widely used in manufacturing and across many other industries for customer service phone calls, software coding projects, network traffic loads, emergency room management, and patient flow. It’s a foundational theorem for lean manufacturing and basic efficiency analysis for production lines. Remember next time you’re standing in line at the grocery store, Little’s Law is at work, and it knows how long you’ll be waiting there.
