Beyond Deming
Conversations on transformational leadership and management, inspired by the work of Dr W. Edwards Deming and brought to you by the Deming Alliance.
Beyond Deming
Kingman's Equation – John Bicheno
In this episode of Beyond Deming, host James Lawther sits down with Professor John Bicheno of the Lean Enterprise Research Centre (LERC) to unravel the mysteries of Kingman’s Equation and its relevance to management thinking. Together, they debunk the common myth that maximum efficiency comes from running operations at full utilisation, revealing how this approach can actually drive up costs and create massive queues.
John explains the non-linear relationship between utilisation and queue length, drawing on real-world examples from manufacturing, service industries, and even motorway traffic. The discussion covers the critical roles of arrival and process variation, the dangers of batching, and the infamous bullwhip effect in supply chains. Listeners will also hear about a simple dice game that brings these concepts to life, and get practical tips for reducing variation and improving flow.
Whether you’re a manager, process improvement enthusiast, or just curious about the science behind queues, this episode offers valuable insights and actionable advice. Plus, John shares his favourite resources for learning more about lean thinking and systems improvement.
Tune in to discover why understanding Kingman’s Equation is essential for anyone looking to optimise performance and reduce waste in any organisation.
Hello and welcome to the Demi conversation. I'm joined today by John Bino, but before I start, I'll let John introduce himself and then we'll take the conversation from there.
John Bicheno:Well, thank you, James. I'm, of course, I'm John Bino, and, I'm actually, uh, retired although I'm still interested in lean one of my claims to fame, if you like, was that, I used to run, an MSC in, uh, in lean at Cardiff business school for about 16 years, which then moved to the University of Buckham. As I say, I'm still learning about Lean and there's lots to learn about all the time.
James Lawther:Good. And I have to say, John, a friend of mine went on that MSC and he raves about it all the time. So, I suppose the joy of these, Deming conversations and I get to talk to interesting people about, A whole host of interesting topics. And what we're gonna talk today, I suppose, is we're gonna try and debunk a great management myth. And that management myth is that really, if you want to keep your costs as low as possible, you have to have everything working at full utilisation. So a hundred percent, efficiency is the goal. So that's the management myth. John, tell me why is, um, cost efficiency in that way? A bit of a fool. Errands.
John Bicheno:Well, you know, uh, James, what we are gonna be looking at here is essentially queuing and, uh, and queuing actually happens in both manufacturing and service. So it's a sort of a universal phenomena and, there are many queue queuing formula and, uh, and, and queuing analysis. But the one that I think is most useful is so-called kingman's equation, which is the equation for, for the average queue length. So this, uh, this, so Kingman's equation has Variables. Uh, arrival, variation, process variation and utilisation, plus the time, the service time. So maybe three or four variables. And, why, why we concerned with this is because queues happen, as we said everywhere, uh, in both manufacturing and, uh, and service and queues, They're, uh, they annoy people. They lead to cost, maybe cost, uh, and any, and of course queues can also be in terms of people waiting for service, but they can also be in terms of, of, of inventory. So queues also take up space. And quite interestingly enough queues also lead to deterioration in quality because, if you've got a long cue, your chance of, of. Picking up a problem, uh, is decreased with a, with a longer queue. So for all those reasons, uh, I think queue is queuing is a, is a very important topic in this, area of lean, and should be. I I, and I'm sure should be something that many managers should be aware of. Yeah.
James Lawther:How does utilisation affect queuing then?
John Bicheno:Okay. utilisation is essentially, demand divided by capacity or if you like, low divided by capacity. So what we are concerned with here is. Pretty well main mainly on bottleneck processes or, or heavily loaded processes. In, in many factory or or office situation, you'll have, various stages that are not very highly utilized, but there'll be, be a number of, of stages that are, are heavily, uh, utilized. The point about this is that there's,, there's a nonlinear effect between utilisation and queue length. So I think a lot of managers, well, at least some managers, think that there's a linear effect. In other words, if you double the utilisation, you double the queue length. In fact, that's absolutely not true, particularly at higher, uh, higher levels of utilisation. So there's a, there's a, a, an exponential kind of shape of this. So the difference between, say, 80, 80% utilisation and 90% utilisation, just 10% difference could lead to a doubling in queue length, for example. Uh, so.
James Lawther:so can you gimme an example of that, A real world example?
John Bicheno:We often know about the effects in driving on a motorway so that, you're driving along quite happily. And, maybe the motorway is, is relatively, uh. Full, but it's going along quite happily. And then just, uh, uh, there's some sort of relatively minor disturbance and suddenly the queue explodes or, or more dramatically. Sometimes there's roadworks. And so what was previously quite, uh, a happy driving experience turns out to be quite a, a nightmare. So this is what we pick up on. This is the, is the nonlinear effect, uh, which I think we've all. Which we've all experienced, I think. Yeah.
James Lawther:Yeah. And presumably the reverse is true then as well. So when you're on the motorway, all of a sudden the cue can just seem to vanish for no reason whatsoever,
John Bicheno:Yeah. So with the, uh, yeah, absolutely.
James Lawther:right? Yeah. Okay, I got that. And, um, there is a, there is actually a game which I've seen you play, which demonstrates these really, really beautifully.
John Bicheno:Yes. So we, we have a very simple little dice game to, uh, to show this. In fact, it does appear in, uh, I have a book, uh, the, the, the Lean Games and Simulation book, which, Uh, but, uh, but actually, uh, I'm happy to distribute this free of charge if you like it's a simple game.
James Lawther:Oh, that's great. So I'll make sure that it goes in the show notes and people can get it.
John Bicheno:yeah. Fine..
James Lawther:So the Kingman equation, so you say there were sort of three or four elements to this.
John Bicheno:Yes. So, just to repeat a little bit, uh, it's, it's arrival variation. Um, so it's, for example, the, the distribution of customers arriving at a service point in, in a service, uh, operation. Uh, the process variation that is how long the process takes. Maybe the how long the server takes, to actually serve a customer. And the third thing, and the third aspect is, is utilisation. In other words, how busy the server is. And the, the fourth, aspect is just the, the average service time. How long it takes to, to service the, the average customer whilst actually serving is taking place. Those are the critical things. Now, the, point is that, uh, quite a lot of pe uh, people are, are concerned with process variation. So. For example, in, in, in the area called Six Sigma, uh, there's a lot of attention towards process, the, the variation of the process, but there's hardly anything about arrival variation. So, uh, one of the messages that I'm trying to often put across is that, in kingman's equation, these factors are equally weighted. So process variation and arrival variation count the same., If you only go to look at the process variation, you're only of course looking at half the problem. And, uh, moreover, sometimes, uh, in some respects, uh, arrival variation can be manipulated or changed relatively, easily or, cost effectively, I should say.
James Lawther:Uh, okay. So coming back to your example of the motorway,
John Bicheno:I.
James Lawther:then, um, if you whiz around the M 20, you quickly get caught in sort of, uh, mandatory speed limits, but above fact that they are slowing people down. Effectively changes, arrival variation. Is that, have I got that right?
John Bicheno:Uh, yes, that, that's right. So, uh, yeah, that, that's an interesting one. So, uh, um, o often there's speed limits and it, it's just a little bit counterintuitive. So why is it that, highway engineers or, or traffic police, try to slow down the, the average speed at busy times in a, in a way it's counterintuitive because you might think, well, if, if the motorways busy, they should go faster. But what they're actually trying to do is to, to reduce the average, the, the average speed. Because of course, if, let's say the speed limit is 70 miles an hour. Certainly there'll be a few people that are doing 90 miles an hour, but there'll still be some one or two people, uh, doing 30 miles an hour, so that, that has a larger variation. So by reducing the, the speed limit, they're trying to reduce the variation. So that's, that's one. Uh. Spec one, one way in which, uh, traffic, uh, police try to do things. Uh, another way is on access control. Now there's a few, examples of this, uh, on various, British motorways is that they have a traffic light, which, uh, only allows cars onto a motorway. At, at. If you like, non-busy times, or at least gaps in the, in the distribution. Those are two sort of simple ways in which, uh, uh, arrival variation can be influenced.
James Lawther:And what about, manufacturing processes or the service industry? Can you think of or give us some examples how you can reduce arrival variation there
John Bicheno:Well, uh, yes. Generally speaking, you can think about that there are two, uh, two forms in this, that, that is externally generated and internally generated. So externally generated. Is where, the variation is, uh, occurs by, by some factor that's outside the, the control or influence of the, uh, the process itself. So of course, uh, in many service operations, uh, and, and manufacturing operations, there obviously is variation, but, uh, just ways in which it can be influenced is, uh, by simply. Giving information, saying, you know, we are, we are, the bank or whatever is busy at certain times of the day, and you find this in, in, uh. Yeah, in call centers as well. And another way is via pricing, of course. So, uh, which is very common in, in many kinds of service, uh, uh, operations to try and influence, uh, demand. Um, so that's ex external, um, internal, variation. I mean, a, a classic case of internal variation is, amplification. And the big one here is, uh, something called the Bull whipp effect. So, uh, so the bull whipp effect is, uh, if you've got a supply chain, as orders move through the supply chain, what happens is that the, the, uh, orders become amplified because. People along the supply chain, the, the decision makers along the supply chain aren't trying to protect themselves. They don't want to be outta stock, so they just allow for to, uh, for a few, uh, for extra orders if you like. But then that, that happens at one stage and has passed on to the next stage. And which also, uh. Orders a few extras. So by the time it gets to the actual manufacturer or supplier, uh, there's quite a lot of amplification. That's a classic, occurrence. Of course, uh, it requires quite a lot of, of coordination to, to do something about it. So it's, uh, uh, but, but essentially it's, uh, it is a well-known phenomena.
James Lawther:Yeah, I can actually, now you said that I can think of an example myself. I used to work for a. A bank, and this is going back to the early two thousands email wasn't really a thing. So we were, I think we were probably the biggest junk mail poster in the uk. Maybe it's not something to brag about, but I think we probably were. But, um, of course the marketing guys were held bent on, um, reducing their costs. And the way they did that was they, released everything into the, mail all on the same day because then they'd, get the biggest postal discount. But of course when we were sitting in the call center, oh, we just got walloped, you know, calls coming out of our ears. But we were our own worst enemy because it really was feast or famine, but we were creating that variation within the business.
John Bicheno:Yes. So, you know, uh, so batching in fact is a, is a classic, uh, phenomena. So, uh, let's say you, you have one order per hour, uh, coming in, which would be nice, smooth demand. And then what happens is that you have some sort of. Procedure, which, uh, says that we are not gonna produce one power. We're going to produce, let's say, uh, uh, one per day. So, um, a ba a batch of eight. Uh, and, but in, in so doing, uh, you actually increase, uh, the, the variation. So this is done supposedly on the, uh, on the basis of e of economics. Now, there, there might be something on this. Something to this, but, a way to address this would be of course via the, the good old lean concept of setup reduction or change over reduction. So, yeah.
James Lawther:Yeah. Okay. So are there any other examples you can think of where, um, organisations have reduced demand variation and that's had a positive effect.
John Bicheno:Well, basically every, every organisation has, what we call Pareto demand. So in other words, if a, a cross a period, there'll be a number of, of popular products and a, and a large number of less popular products. So just by understanding that variation and,, maybe changing the price or, or,. Or scheduling them so that you get the, you produce the regular orders more regularly and the, and the irregulars, you, you, you move to the side that has an a, a smoothing effect, which is in fact, uh, is this is sort of classic lean stuff or classic lean scheduling, uh, procedure that, uh, is, is adopted. Yeah.
James Lawther:Yeah. Okay. So then you've got, I suppose you've got, how do you reduce arrival variation? Your next stage is the whole question of how do you reduce process variation. But of course, those two things are then affect, uh, links to your point about the bull width, bull width effect, because in any supply chain Process variation can create arrival variation in the next stage.
John Bicheno:Yes. So, uh, of course, in in any manufacturing and or service operation, there will o obviously be, variation. Um, but, but there, there are things that one can do about it. So that, uh, first of all is, is really appreciating the, the kinds of process variation so that, uh, in, for example, a service, You will know that, uh, some customers take a, lot of time and other customers, maybe your more experie experienced customers take, less time because they're familiar with the process. So what, uh, what, for example, car hire companies do, they may have a separate lane for, for experienced customers. So, which they don't then have to explain the whole process. So this reduces the. Process variation. Um, yeah.
James Lawther:Yeah. Yeah, that makes perfect sense.
John Bicheno:Yes.
James Lawther:Yeah.
John Bicheno:Again, it's, uh, understanding the, the sources of variation I think is the key to do this.
James Lawther:yeah. And so then this, there is a, there is a lean term for this then, isn't it? Overburdened? Well, I can't remember what the Japanese word for it is.
John Bicheno:Okay. Yes. so a big thing in Lean is about the reduction of waste, or, or muda as it's called. So in fact, Womack and Jones's famous book, lean Thinking, the first sentence of Womack and Jones' book was"Muda, it's the one Japanese word you've gotta understand." So, the, the Toyota production system is. Very much focused on the re reduction of, of waste or mouda. But actually, in the, in, in the Toyota system, they don't only talk about mouda, they also talk about muri and mura. Mura is amplification or variation and, uh, muri is overload or utilisation. So, in fact, uh, I often talk about Kingman's equation. This is, I'm pushing my luck a little bit on this one, saying that it's the equation of lean because, uh, it incorporates, uh, muda, the, the, the queue with mura, uh, the, uh. Um, amplification or variation and muri the overload or, or utilisation. So hence, Kingman's equation ties all these, these three nicely to, uh, together.
James Lawther:Yeah. Okay. So if I just. Go back over what you told me so I understand it. One of the basic problems is people believe that what they should be doing is running at maximum utilisation. The minute you start running at maximum utilisation though, because of this, um, uh, non-linear effect, you just generate huge queues. And, um, speaking, the man who's worked in several call centers in my life, I've experienced some pretty huge queues. And they're not pretty. And you're right, they are, they're hugely expensive things. Yeah. So rather than, um, focusing on utilisation, people will be far better off focusing on reducing variation, both in process and in arrival, and that would reduce those queues substantially and therefore reduce the cost.
John Bicheno:Well, um, it's not, it's, you really need to, no, you, you really need to focus on all three. So what can you do about arrival? Variation, what can you do about process variation? And what can you do about utilisation? Now utilisation, is about, uh, demand Now there's various categories of demand. So again, we, um, as with, uh, variation talk about internal and external. But, the, the same thing happens with, demand. So, an example of internally generated extra demand is a classic. One, of course is rework. So if you have to rework a a product, or that means that you, it has to go through a a process more than once. So of course, it adds to the load or it adds to the demand. So by tackling rework actually can reduce the, the, the demand. And that has an, in fact, a non-linear effect on, on queues. Okay. An example of, uh, of externally generated, uh, demand would be what, uh, what John Seddon in famously is called, uh, failure demand. Failure demand is, is not getting it right the first time. But, uh, essentially that's the same sort of thing is that, uh, if you can reduce failure, demand, or try to make sure that cus customers are dealt with right first time, then that reduces the, the load. So, um. So you now you need to focus on both these things or both these, the, all these causes. Again, there are relatively sim simple things that you can do here. Uh, but a very simple sort, a simple thing to reduce, uh, demand is simply overproduction. Like if in manufacturing. So we, where this machine is set up and, uh, we're supposed to make a batch of a hundred, but we are, while the machine is set up, we'll just make an extra 50. So, or whatever the case might be. Well, this is overproduction or, so it's one of the, one of Ohno's classic wastes is overproduction. Now the, the, the consequences of that is. It can be seen directly through Kingman's equation because it loads up, demand and reduces, um, the queue. So actually it's, it's kind of interesting if you can reduce demand, uh, then you reduce utilisation. If you reduce utilisation, you reduce the queues, you reduce the queue exponentially, not linearly. Uh, The denominator of the equation, load divided by capacity or demand, divided capacity. Capacity. If you can free up some capacity you increase your capacity, uh, you reduce your utilisation, you reduce your utilisation, it reduces your queue, not linearly, but exponentially. So this is the power of this thing, uh, that, uh, uh, by getting after these relatively simple, straightforward things, uh, you can have a dramatic non-linear effect, uh, which is I think something that's not. Not every manager appreciates
James Lawther:yeah. And so I remember once I, um, I was working with, a lean consultant actually. He said to me, the problem is, James, when you start to chase the costs, they run away from you. But people chasing costs will screw down their efficiency to make it as highly utilized as possible. They will start to batch things up. But as you've explained, all of these things actually. Increase queue lengths, which then in turn just drives cost into your organisation. So it is counterintuitive, but the way to do look at it is to understand the system and then start to pull out the levers that will reduce those costs.
John Bicheno:Yes, uh, that's right. We like to say that, lean is really, requires a sort of a systems approach. So you've, you need to understand all the factors, the, the people factors, the, the non-people factors, but also some of the accounting factors I think are quite a, a corpus of, of these things that we are talking about. Like, increasing utilisation. Simply because the organisation is using some sort of accounting system, which, tracks vari variance. Which really has the effect of encouraging, uh. But greater utilisation. There's quite a number of examples of, of traditional accounting getting in the way of lean. So, and another example, uh, really relating to demand is that in some sort of traditional accounting inventories and asset, okay, so that means if you make more, That's good news, but in terms of lean inventory is not an asset. Inventory is something that you want to reduce to be just in line with demand. So there's quite a number of of examples of this, which result from using wrong measures, which drive you to maybe overproduce or,.
James Lawther:Yeah, no, absolutely. So rather than just,'cause we could be here for hours talking about that. There's my pet subjects, but very interesting stuff. Is there anything else we've missed talking about Kingman's equation, do you think?
John Bicheno:So I think, uh, one of the early stages, not necessarily the. First stage, but certainly an early stage in lean implementation is a much more thorough understanding of, of demand. The causes of demand and, and the drivers of demand. Yeah.
James Lawther:I suppose brings me to my last question then, which is, if people want to learn more, where would you point them? Where do you think they should, um, to go to understand how all these things work?
John Bicheno:I have a little bit of a prejudice opinion on this one, having, being, uh, written the, the, the lean toolbox and so on. Um, but, uh, these days there, there are such a, a, a, a lot of really great books on, on, on lean and so on. But I have some, some favorite, uh, if you like, websites, one of, one of which is called All, uh, all About Lean. That's by my friend, Christophe Rosser. Uh, all about Lean is a nice, uh, uh, website. There's also the, the, the classic, books by, by Lean Enterprise Institute, which is on like all sorts of things, value stream, mapping, uh, scheduling, uh, whatnot. And of course, a very fashionable one, possibly, but a big one is so-called a three problem solving. So a three, uh, is really relates to homing in on the particular problem. Uh, so, well, those would be a few things, uh, that, uh, I, I would focus on. Yeah.
James Lawther:Lovely. Thank you very much. Is there anything that you think we have missed or totally missed the point on.
John Bicheno:I would say that, uh, first of all, Kingman's equation is a nice, conceptual equation. So, it. Talks about these factors, the arrival, variation, process, variation, uh, and, and utilisation. And the point is that, a arrival variation, process variation are equally weighted. So you need to give equal attention to those. And then utilisation, uh, is, is the, the, the next factor. But o of course the equation is not something you'd plug numbers into. It's really a conceptual, equation and, uh, or a good explanation of, the, of the root causes of queue problems. So please don't try to plug a whole lot of numbers into it. I think you'll be in in lots of trouble if you try to do that.
James Lawther:Okay. Um, and I would recommend as well for anybody who's interested, uh, have a go at playing the game because if you intrinsically think when people are screaming at you, to have maximum utilisation. You're just thinking, this is nuts. The dice game beautifully explained why it doesn't quite that way.
John Bicheno:you know, uh, I'm a big fan of Kingman, so, uh, I've been after this for a long, long time and, uh, because I think that it's something that, uh, is not widely appreciated. So, uh, it's good to be able to speak to you about it.
James Lawther:Super. Thank you very much for your time.
John Bicheno:Well, uh, it's very nice to speak to you, James. So, uh, yeah, it's, uh,
James Lawther:Thank you very much.
