The simple way, in theory, to resolve a constraint is to throw inventory ahead of it, right? After all, with enough material coming into the bottleneck, you never have to worry about it being in a wait state, with its consequent waste. That inventory is directly related to lead time, and thus, the ability to deliver to customers on time (i.e., “make the schedule”). Of course, we know intuitively that there is a cost associated with this too, potentially greater than the cost associated with waiting at the bottleneck.
Which brings us to Little’s Law. It’s named for John Little, who in the 1960’s, working out of a university in Cleveland, Ohio (my home town) defined something called queueing theory. It states that the Length of a queue is equal to the Average Arrival Rate times the Average Waiting Time. It’s pretty simple when you think about it. It relates three performance measures in a production system, and states them as a basic manufacturing principle. Little expressed this as:
L= λ W
(Thus, Length of the queue equals lambda (a mathematical expression here used for, basically, Throughput) times Wait)
You can Google this stuff ad nauseum, but suffice it to say it’s useful in identifying a lot of different process flows and bottlenecks, including your own. It’s used in business to calculate wait times, planned inventory times, desired warehouse inventory turns, ways to reduce WIP (Work in Process), process flows, etc.
In production it can be simply applied: A machine that can process a part a minute (i.e., 60 per hour) and that has 500 pieces in front of it has about 8 hours of WIP. (All examples assume a ‘static’ environment, i.e., all other things being equal and unvaried.) By itself, this figure holds less value than it does in context: if throughput is indeed 60 pieces per hour, then 500 pieces can be pushed through in a day. But if the process in question can utilize just 6 pieces per hour, then you have an 80 hour (i.e., two week) WIP backlog, and that’s probably not good. Too much inventory makes for good on-time delivery perhaps, but costs a fortune in excess inventory.
But from this calculation, a trained observer can roughly determine whether the flow into a work center is too much (thus wasting too much inventory), or is a good fit. The 500 parts seem ‘reasonable’ with a 60 piece per hour flow rate, but much less so with a 6 piece rate. Plant managers can begin using that knowledge to determine rough cut estimates of just how much inventory needs to flow into a bottleneck to keep it from becoming a major constraint of the system.
Simple. Intuitive. But a useful tool for getting at core calculations about your own throughput, bottleneck identification, and what to do about them. This is the Buffer component of Drum-Buffer-Rope. Find your biggest constraint, and calculate the rough level of inventory (or Buffer) – no more or less – that is required ahead of it to keep that constraint from going into serious waste mode.
In our next article, we’ll look at flow time in assembly, and the effects of WIP.