Little’s Law and Manufacturing WIP

What do manufacturing facilities share in common with supermarkets, post offices and wireless networks? They all involve waiting in queues, whether it’s a computer waiting to connect to public Wi-Fi, customers in a queue to check out at the grocery store or work in progress (WIP) sitting until a machine is open at a shop – and regardless of the business or activity involved, no one likes having to wait. As a result, a great deal of research has gone into what is known as “queueing theory,” the study of these types of systems, and one key theorem in this field of study is known as “Little’s Law,” a simple formula that can make a big impact in your shop’s productivity.

Introduced by John Little in 1961, Little’s Law is summed up with the equation L=lW. The average arrival rate of items in the system, l, is multiplied by the average amount of time an item spends in the system, W. The result is the average number of items in the system, L. Much like Einstein’s famed E=MC2, however, the simplicity of the formula belies its importance to the world of queuing – as well as profitability in manufacturing.

In a supermarket, the “items” in the queuing system are people, but in a machine shop, it’s parts. Manufacturers can think of Little’s Law as a way to understand the relationship of lead time (W), throughput (l) and WIP (L). Perhaps the most important takeaway comes from turning the formula around: W=L/l. In other words, as the amount of WIP in a system increases and throughput decreases, lead times go up dramatically.

This result can seem counterintuitive to many manufacturers, but it is a key component to succeeding in high-mix/low-volume (HMLV) production environments. A good way to envision this is to compare a supermarket with a rollercoaster. At a supermarket, customers arrive whenever they want and enter the store as soon as they arrive; if it becomes more crowded, with more people getting in each other’s way, it takes longer to get through the store and checked out. A rollercoaster never has this problem, as only a certain number of people are allowed on the ride at any given time, so while the amount of time it takes to get on the ride varies, the length of the ride itself is never affected.

Most shops operate like supermarkets; as soon as a customer orders the part, the job order goes directly into production. Like shoppers crowding a grocery store’s aisles, WIP piles up at various machines, and in HMLV shops, each part may require a completely different setup. As a result, any error at any stage of the manufacturing process and any confusion created by operators choosing to do jobs in an unexpected order, will impact the lead times of everything behind that point in the queue. And when your lead times are uncertain, you lose the ability to make and keep promises to customers.

Instead, manufacturers should make their processes into rollercoasters. Limiting WIP creates very predictable lead times by eliminating mid-process bottlenecks, which, in turn, contributes to much higher throughput. However, this can’t be accomplished with winding, maze-like corridors used for rollercoaster queues. And whatever advertisements may say, there is no software solution to do all this hard work for you.

While the first step is limiting WIP in the front office by putting new jobs into production only when there’s room in the queue, every operator in a shop has to be dedicated to this practice. Visual planning that gives real-time feedback about key performance indicators to machinists is a great way to accomplish this; instead of simply measuring the number of parts, for example, shops can show operators how long a part has been waiting in their queue and require them to keep parts for no more than two days.

The profitability of many businesses, including manufacturing, depends on keeping promises to customers. Clients will go to another shop if they think a lead time is too long; they’ll never come back for another part if a shop promises a quick turnaround and delivers the part late. Maximizing profits requires minimizing and standardizing lead times as much as possible – and thanks to the work of John Little, we have mathematical proof that the best way to do this in manufacturing is by limiting WIP.