The Goal: A Process of Ongoing Improvement, page 14
I’ve got to put an end to this.
The first one I check is Ron. But Ron, indeed, is setting a steady, "average’’ pace for the troop—a pace nobody should have any trouble with. I look back down the line, and all of the boys are walking at about the same rate as Ron. And Herbie? He’s not the problem anymore. Maybe he felt responsible for the last delay, because now he seems to be making a special effort to keep up. He’s right on the ass of the kid in front of him.
If we’re all walking at about the same pace, why is the distance between Ron, at the front of the line, and me, at the end of the line, increasing?
Statistical fluctuations?
Nah, couldn’t be. The fluctuations should be averaging out. We’re all moving at about the same speed, so that should mean the distance between any of us will vary somewhat, but will even out over a period of time. The distance between Ron and me should also expand and contract within a certain range, but should average about the same throughout the hike.
But it isn’t. As long as each of us is maintaining a normal, moderate pace like Ron, the length of the column is increasing. The gaps between us are expanding.
Except between Herbie and the kid in front of him.
So how is he doing it? I watch him. Every time Herbie gets a step behind, he runs for an extra step. Which means he’s actually expending more energy than Ron or the others at the front of the line in order to maintain the same relative speed. I’m wondering how long he’ll be able to keep up his walk-run routine.
Yet... why can’t we all just walk at the same pace as Ron and stay together?
I’m watching the line when something up ahead catches my eye. I see Davey slow down for a few seconds. He’s adjusting his packstraps. In front of him, Ron continues onward, oblivious. A gap of ten... fifteen... twenty feet opens up. Which means the entire line has grown by 20 feet.
That’s when I begin to understand what’s happening.
Ron is setting the pace. Every time someone moves slower than Ron, the line lengthens. It wouldn’t even have to be as obvious as when Dave slowed down. If one of the boys takes a step that’s half an inch shorter than the one Ron took, the length of the whole line could be affected.
But what happens when someone moves faster than Ron? Aren’t the longer or faster steps supposed to make up for the spreading? Don’t the differences average out?
Suppose I walk faster. Can I shorten the length of the line? Well, between me and the kid ahead of me is a gap of about five feet. If he continues walking at the same rate, and if I speed up, I can reduce the gap—and maybe reduce the total length of the column, depending upon what’s happening up ahead. But I can only do that until I’m bumping the kid’s rucksack (and if I did that he’d sure as hell tell his mother). So I have to slow down to his rate.
Once I’ve closed the gap between us, I can’t go any faster than the rate at which the kid in front of me is going. And he ultimately can’t go any faster than the kid in front of him. And so on up the line to Ron. Which means that, except for Ron, each of our speeds depends upon the speeds of those in front of us in the line.
It’s starting to make sense. Our hike is a set of dependent events...in combination with statistical fluctuations. Each of us is fluctuating in speed, faster and slower. But the ability to go faster than average is restricted. It depends upon all the others ahead of me in the line. So even if I could walk five miles per hour, I couldn’t do it if the boy in front of me could only walk two miles per hour. And even if the kid directly in front of me could walk that fast, neither of us could do it unless all the boys in the line were moving at five miles per hour at the same time.
So I’ve got limits on how fast I can go—both my own (I can only go so fast for so long before I fall over and pant to death) and those of the others on the hike. However, there is no limit on my ability to slow down. Or on anyone else’s ability to slow down. Or stop. And if any of us did, the line would extend indefinitely.
What’s happening isn’t an averaging out of the fluctuations in our various speeds, but an accumulation of the fluctuations. And mostly it’s an accumulation of slowness—because dependency limits the opportunities for higher fluctuations. And that’s why the line is spreading. We can make the line shrink only by having everyone in the back of the line move much faster than Ron’s average over some distance.
Looking ahead, I can see that how much distance each of us has to make up tends to be a matter of where we are in the line. Davey only has to make up for his own slower than average fluctuations relative to Ron—that twenty feet or so which is the gap in front of him. But for Herbie to keep the length of the line from growing, he would have to make up for his own fluctuations plus those of all the kids in front of him. And here I am at the end of the line. To make the total length of the line contract, I have to move faster than average for a distance equal to all the excess space between all the boys. I have to make up for the accumulation of all their slowness.
Then I start to wonder what this could mean to me on the job. In the plant, we’ve definitely got both dependent events and statistical fluctuations. And here on the trail we’ve got both of them. What if I were to say that this troop of boys is analogous to a manufacturing system . . . sort of a model. In fact, the troop does produce a product; we produce "walk trail.’’ Ron begins production by consuming the unwalked trail before him, which is the equivalent of raw materials. So Ron processes the trail first by walking over it, then Davey has to process it next, followed by the boy behind him, and so on back to Herbie and the others and on to me.
Each of us is like an operation which has to be performed to produce a product in the plant; each of us is one of a set of dependent events. Does it matter what order we’re in? Well, somebody has to be first and somebody else has to be last. So we have dependent events no matter if we switch the order of the boys.
I’m the last operation. Only after I have walked the trail is the product "sold,’’ so to speak. And that would have to be our throughput—not the rate at which Ron walks the trail, but the rate at which I do.
What about the amount of trail between Ron and me? It has to be inventory. Ron is consuming raw materials, so the trail the rest of us are walking is inventory until it passes behind me.
And what is operational expense? It’s whatever lets us turn inventory into throughput, which in our case would be the energy the boys need to walk. I can’t really quantify that for the model, except that I know when I’m getting tired.
If the distance between Ron and me is expanding, it can only mean that inventory is increasing. Throughput is my rate of walking. Which is influenced by the fluctuating rates of the others. Hmmm. So as the slower than average fluctuations accumulate, they work their way back to me. Which means I have to slow down. Which means that, relative to the growth of inventory, throughput for the entire system goes down.
And operational expense? I’m not sure. For UniCo, whenever inventory goes up, carrying costs on the inventory go up as well. Carrying costs are a part of operational expense, so that measurement also must be going up. In terms of the hike, operational expense is increasing any time we hurry to catch up, because we expend more energy than we otherwise would.
Inventory is going up. Throughput is going down. And operational expense is probably increasing.
Is that what’s happening in my plant?
Yes, I think it is.
Just then, I look up and see that I’m nearly running into the kid in front of me.
Ah ha! Okay! Here’s proof I must have overlooked something in the analogy. The line in front of me is contracting rather than expanding. Everything must be averaging out after all. I’m going to lean to the side and see Ron walking his average twomile-an-hour pace.
But Ron is not walking the average pace. He’s standing still at the edge of the trail.
"How come we’re stopping?’’
He says, "Time for lunch, Mr. Rogo.’’
14
"But we’re not supposed to be having lunch here,’’ says one of the kids. "We’re not supposed to eat until we’re farther down the trail, when we reach the Rampage River.’’
"According to the schedule the troopmaster gave us, we’re supposed to eat lunch at 12:00 noon,’’ says Ron.
"And it is now 12:00 noon,’’ Herbie says, pointing to his watch. "So we have to eat lunch.’’
"But we’re supposed to be at Rampage River by now and we’re not.’’
"Who cares?’’ says Ron. "This is a great spot for lunch. Look around.’’
Ron has a point. The trail is taking us through a park, and it so happens that we’re passing through a picnic area. There are tables, a water pump, garbage cans, barbecue grills—all the necessities. (This is my kind of wilderness I’ll have you know.)
"Okay,’’ I say. "Let’s just take a vote to see who wants to eat now. Anyone who’s hungry, raise your hand.’’
Everyone raises his hand; it’s unanimous. We stop for lunch.
I sit down at one of the tables and ponder a few thoughts as I eat a sandwich. What’s bothering me now is that, first of all, there is no real way I could operate a manufacturing plant without having dependent events and statistical fluctuations. I can’t get away from that combination. But there must be a way to overcome the effects. I mean, obviously, we’d all go out of business if inventory was always increasing, and throughput was always decreasing.
What if I had a balanced plant, the kind that Jonah was saying managers are constantly trying to achieve, a plant with every resource exactly equal in capacity to demand from the market? In fact, couldn’t that be the answer to the problem? If I could get capacity perfectly balanced with demand, wouldn’t my excess inventory go away? Wouldn’t my shortages of certain parts disappear? And, anyway, how could Jonah be right and everybody else be wrong? Managers have always trimmed capacity to cut costs and increase profits; that’s the game.
I’m beginning to think maybe this hiking model has thrown me off. I mean, sure, it shows me the effect of statistical fluctuations and dependent events in combination. But is it a balanced system? Let’s say the demand on us is to walk two miles every hour—no more, no less. Could I adjust the capacity of each kid so he would be able to walk two miles per hour and no faster? If I could, I’d simply keep everyone moving constantly at the pace he should go—by yelling, whip-cracking, money, whatever—and everything would be perfectly balanced.
The problem is how can I realistically trim the capacity of fifteen kids? Maybe I could tie each one’s ankles with pieces of rope so that each would only take the same size step. But that’s a little kinky. Or maybe I could clone myself fifteen times so I have a troop of Alex Rogos with exactly the same trail-walking capacity. But that isn’t practical until we get some advancements in cloning technology. Or maybe I could set up some other kind of model, a more controllable one, to let me see beyond any doubt what goes on.
I’m puzzling over how to do this when I notice a kid sitting at one of the other tables, rolling a pair of dice. I guess he’s practicing for his next trip to Vegas or something. I don’t mind—although I’m sure he won’t get any merit badges for shooting craps —but the dice give me an idea. I get up and go over to him.
"Say, mind if I borrow those for a while?’’ I ask.
The kid shrugs, then hands them over.
I go back to the table again and roll the dice a couple of times. Yes, indeed: statistical fluctuations. Every time I roll the dice, I get a random number that is predictable only within a certain range, specifically numbers one to six on each die. Now what I need next for the model is a set of dependent events.
After scavenging around for a minute or two, I find a box of match sticks (the strike-anywhere kind), and some bowls from the aluminum mess kit. I set the bowls in a line along the length of the table and put the matches at one end. And this gives me a model of a perfectly balanced system.
While I’m setting this up and figuring out how to operate the model, Dave wanders over with a friend of his. They stand by the table and watch me roll the die and move matches around.
"What are you doing?’’ asks Dave.
"Well, I’m sort of inventing a game,’’ I say.
"A game? Really?’’ says his friend. "Can we play it, Mr. Rogo?’’
Why not?
"Sure you can,’’ I say.
All of a sudden Dave is interested.
"Hey, can I play too?’’ he asks.
"Yeah, I guess I’ll let you in,’’ I tell him. "In fact, why don’t you round up a couple more of the guys to help us do this.’’
While they go get the others, I figure out the details. The system I’ve set up is intended to "process’’ matches. It does this by moving a quantity of match sticks out of their box, and through each of the bowls in succession. The dice determine how many matches can be moved from one bowl to the next. The dice represent the capacity of each resource, each bowl; the set of bowls are my dependent events, my stages of production. Each has exactly the same capacity as the others, but its actual yield will fluctuate somewhat.
In order to keep those fluctuations minimal, however, I decide to use only one of the dice. This allows the fluctuations to range from one to six. So from the first bowl, I can move to the next bowls in line any quantity of matches ranging from a minimum of one to a maximum of six.
Throughput in this system is the speed at which matches come out of the last bowl. Inventory consists of the total number of matches in all of the bowls at any time. And I’m going to assume that market demand is exactly equal to the average number of matches that the system can process. Production capacity of each resource and market demand are perfectly in balance. So that means I now have a model of a perfectly balanced manufacturing plant.
Five of the boys decide to play. Besides Dave, there are Andy, Ben, Chuck, and Evan. Each of them sits behind one of the bowls. I find some paper and a pencil to record what happens. Then I explain what they’re supposed to do.
"The idea is to move as many matches as you can from your bowl to the bowl on your right. When it’s your turn, you roll the die, and the number that comes up is the number of matches you can move. Got it?’’
They all nod. "But you can only move as many matches as you’ve got in your bowl. So if you roll a five and you only have two matches in your bowl, then you can only move two matches. And if it comes to your turn and you don’t have any matches, then naturally you can’t move any.’’
They nod again.
"How many matches do you think we can move through the line each time we go through the cycle?’’ I ask them.
Perplexity descends over their faces.
"Well, if you’re able to move a maximum of six and a minimum of one when it’s your turn, what’s the average number you ought to be moving?’’ I ask them.
"Three,’’ says Andy.
"No, it won’t be three,’’ I tell them. "The mid-point between one and six isn’t three.’’
I draw some numbers on my paper.
"Here, look,’’ I say, and I show them this:
123456
And I explain that 3.5 is really the average of those six numbers.
"So how many matches do you think each of you should have moved on the average after we’ve gone through the cycle a number of times?’’ I ask.
"Three and a half per turn,’’ says Andy.
"And after ten cycles?’’
"Thirty-five,’’ says Chuck.
"And after twenty cycles?’’
"Seventy,’’ says Ben.
"Okay, let’s see if we can do it,’’ I say.
Then I hear a long sigh from the end of the table. Evan looks at me.
"Would you mind if I don’t play this game, Mr. Rogo?’’ he asks.
"How come?’’
"Cause I think it’s going to be kind of boring,’’ he says.
"Yeah,’’ says Chuck. "Just moving matches around. Like who cares, you know?’’
"I think I’d rather go tie some knots,’’ says Evan.
"Tell you what,’’ I say. "Just to make it more interesting, we’ll have a reward. Let’s say that everybody has a quota of 3.5 matches per turn. Anybody who does better than that, who averages more than 3.5 matches, doesn’t have to wash any dishes tonight. But anybody who averages less than 3.5 per turn, has to do extra dishes after dinner.’’
"Yeah, all right!’’ says Evan.
"You got it!’’ says Dave.
