by E M Goldratt
There: if I'd been measuring my stride, I would have re- corded statistical fluctuations. But, again, what's the big deal?
If I say that I'm walking at the rate of "two miles per hour," I don't mean I'm walking exactly at a constant rate of two miles per hour every instant. Sometimes I'll be going 2.5 miles per hour; sometimes maybe I'll be walking at only 1.2 miles per hour. The rate is going to fluctuate according to the length and speed of each step. But over time and distance, I should be averaging about two miles per hour, more or less.
The same thing happens in the plant. How long does it take to solder the wire leads on a transformer? Well, if you get out your stopwatch and time the operation over and over again, you might find that it takes, let's say, 4.3 minutes on the average. But the actual time on any given instance may range between 2.1 minutes up to 6.4 minutes. And nobody in advance can say, "This one will take 2.1 minutes... this one will take 5.8 minutes." Nobody can predict that information.
So what's wrong with that? Nothing as far as I can see. Any- way, we don't have any choice. What else are we going to use in place of an "average" or an "estimate"?
I find I'm almost stepping on the boy in front of me. We've slowed down somewhat. It's because we're climbing a long, fairly steep hill. All of us are backed up behind Herbie.
"Come on, Herpes!" says one of the kids.
Herpes?
"Yeah, Herpes, let's move it," says another.
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"Okay, enough of that," I say to the persecutors.
Then Herbie reaches the top. He turns around. His face is red from the climb.
"Atta boy, Herbie!" I say to encourage him. "Let's keep it moving!"
Herbie disappears over the crest. The others continue the climb, and I trudge behind them until I get to the top. Pausing there, I look down the trail.
Holy cow! Where's Ron? He must be half a mile ahead of us. I can see a couple of boys in front of Herbie, and everyone else is lost in the distance. I cup my hands over my mouth.
"HEY! LET'S GO UP THERE! LET'S CLOSE RANKS!" I yell. "DOUBLE TIME! DOUBLE TIME!"
Herbie eases into a trot. The kids behind him start to run. I jog after them. Rucksacks and canteens and sleeping bags are bouncing and shaking with every step. And Herbie-I don't know what this kid is carrying, but it sounds like he's got a junk- yard on his back with all the clattering and clanking he makes when he runs. After a couple hundred yards, we still haven't caught up. Herbie is slowing down. The kids are yelling at him to hurry up. I'm huffing and puffing along. Finally I can see Ron off in the distance.
"HEY RON!" I shout. "HOLD UP!"
The call is relayed up the trail by the other boys. Ron, who probably heard the call the first time, turns and looks back. Herbie, seeing relief in sight, slows to a fast walk. And so do the rest of us. As we approach, all heads are turned our way.
"Ron, I thought I told you to set a moderate pace," I say.
"But I did!" he protests.
"Well, let's just all try to stay together next time," I tell them.
"Hey, Mr. Rogo, whadd'ya say we take five?" asks Herbie.
"Okay, let's take a break," I tell them.
Herbie falls over beside the trail, his tongue hanging out. Everyone reaches for canteens. I find the most comfortable log in sight and sit down. After a few minutes, Davey comes over and sits down next to me.
"You're doing great, Dad," he says.
"Thanks. How far do you think we've come?"
"About two miles," he says.
"Is that all?" I ask. "It feels like we ought to be there by now. We must have covered more distance than two miles."
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"Not according to the map Ron has," he says.
"Oh," I say. "Well, I guess we'd better get a move on."
The boys are already lining up.
"All right, let's go," I say.
We start out again. The trail is straight here, so I can see everyone. We haven't gone thirty yards before I notice it starting all over again. The line is spreading out; gaps between the boys are widening. Dammit, we're going to be running and stopping all day long if this keeps up. Half the troop is liable to get lost if we can't stay together.
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 de- lay, 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 dis- tance 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
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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 obvi- ous 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. H
owever, 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
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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 fluc- tuations 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 accumula- tion 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.
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And what is operational expense? It's whatever lets us turn inventory into throughput, which in our case would be the en- ergy 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 oth- ers. Hmmm. So as the slower than average fluctuations accumu- late, 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, when- ever 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, opera- tional expense is increasing any time we hurry to catch up, be- cause we expend more energy than we otherwise would.
Inventory is going up. Throughput is going down. And op- erational 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 some- thing 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 two- mile-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."
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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 ne- cessities. (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 over- come the effects. I mean, obviously, we'd all go out of business if inventory was always increasing, and throughput was always de- creasing.
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 mar- ket? 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 every- body 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
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me off. I mean, sure, it shows me the effect of statistical fluctua- tions 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 ev- erything 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 capac- ity. 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 practic- ing for his next trip to Vegas or something. I don't mind-al- though 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?" -
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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 de- cide 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 mini- mum of one to a maximum of six.