The Goal Read online

  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 num- ber 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 manufac- turing 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."

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  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 mini- mum 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 num- bers.

  "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 aver- ages 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.

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  They're all excited now. They're practicing rolling the die. Meanwhile, I set up a grid on a sheet of paper. What I plan to do is record the amount that each of them deviates from the average. They all start at zero. If the roll of the die is a 4, 5, or 6 then I'll record-respectively-a gain of.5, 1.5, or 2.5. And if the roll is a 1, 2, or 3 then I'll record a loss of-2.5, -1.5, or -.5 respectively. The deviations, of course, have to be cumulative; if someone is 2.5 above, for example, his starting point on the next turn is 2.5, not zero. That's the way it would happen in the plant.

  "Okay, everybody ready?" I ask.

  "All set."

  I give the die to Andy.

  He rolls a two. So he takes two matches from the box and puts them in Ben's bowl. By rolling a two, Andy is down 1.5 from his quota of 3.5 and I note the deviation on the chart.

  Ben rolls next and the die comes up as a four.

  "Hey, Andy," he says. "I need a couple more matches."

  "No, no, no, no," I say. "The game does not work that way. You can only pass the matches that are in your bowl."

  "But I've only got two," says Ben.

  "Then you can only pass two."

  "Oh," says Ben.

  And he passes his two matches to Chuck. I record a deviation of-1.5 for him too.

  Chuck rolls next. He gets a five. But, again, there are only two matches he can move.

  "Hey, this isn't fair!" says Chuck.

  "Sure it is," I tell him. "The name of the game is to move matches. If both Andy and Ben had rolled five's, you'd have five matches to pass. But they didn't. So you don't." Chuck gives a dirty look to Andy.

  "Next time, roll a bigger number," Chuck says.

  "Hey, what could I do!" says Andy.

  "Don't worry," Ben says confidently. "We'll catch up."

  Chuck passes his measly two matches down to Dave, and I record a deviation of-1.5 for Chuck as well. We watch as Dave rolls the die. His roll is only a one. So he passes one match down to Evan. Then Evan also rolls a one. He takes the one match out of his bowl and puts it on the end of the table. For both Dave and Evan, I write a deviation of-2.5.

  "Okay, let's see if we can do better next time," I say.

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  Andy shakes the die in his hand for what seems like an hour. Everyone is yelling at him to roll. The die goes spinning onto the table. We all look. It's a six.

  "All right!"

  "Way to go, Andy!"

  He takes six match sticks out of the box and hands them to Ben. I record a gain of+2.5 for him, which puts his score at 1.0 on the grid.

  Ben takes the die and he too rolls a six. More cheers. He passes all six matches to Chuck. I record the same score for Ben as for Andy.

  But Chuck rolls a three. So after he passes three matches to Dave, he still has three left in his bowl. And I note a loss of-0.5 on the chart.

  Now Dave rolls the die; it comes up as a six. But he only has four matches to pass-the three that Chuck just passed to him and one from the last round. So he passes four to Evan. I write down a gain of +0.5 for him.

  Evan gets a three on the die. So the lone match on the end of the table is joined by three more. Evan still has one left in his bowl. And I record a loss of-0.5 for Evan.

  At the end of two rounds, this is what the chart looks like.

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  We keep going. The die spins on the table and passes from hand to hand. Matches come out of the box and move from bowl to bowl. Andy's rolls are-what else?-very average, no steady run of high or low numbers. He is able to meet the quota and then some. At the other end of the table, it's a different story.

  "Hey, let's keep those matches coming."

  "Yeah, we need more down here."

  "Keep rolling sixes, Andy."

  "It isn't Andy, it's Chuck. Look at him, he's got five."

  After four turns, I have to add more numbers-negative numbers-to the bottom of the chart. Not for Andy or for Ben or for Chuck, but for Dave and Evan. For them, it looks like there is no bottom deep enough.

  After five rounds, the chart looks like this:

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  "How am I doing, Mr. Rogo?" Evan asks me.

  "Well, Evan... ever hear the story of the Titanic?"

  He looks depressed.

  "You've got five rounds left," I.tell him. "Maybe you can pull through."

  "Yeah, remember the law of averages," says Chuck.

  "If I have to wash dishes because you guys didn't give me enough matches..." says Evan, letting vague implications of threat hang in the air.

  "I'm doing my job up here," says Andy.

  "Yeah, what's wrong with you guys down there?" asks Ben.

  "Hey, I just now got enough of them to pass," says Dave. "I've hardly had any before."

  Indeed, some of the inventory which had been stuck in the first three bowls had finally moved to Dave. But now it gets stuck in Dave's bowl. The couple of higher rolls he had in the first five rounds are averaging out. Now he's getti
ng low rolls just when he has inventory to move.

  "C'mon, Dave, gimme some matches," says Evan.

  Dave rolls a one.

  "Aw, Dave! One match!"

  "Andy, you hear what we're having for dinner tonight?" asks Ben.

  "I think it's spaghetti," says Andy.

  "Ah, man, that'll be a mess to dean up."

  "Yeah, glad I won't have to do it," says Andy.

  "You just wait," says Evan. "You just wait 'til Dave gets some good numbers for a change."

  But it doesn't get any better.

  "How are we doing now, Mr. Rogo?" asks Evan.

  "I think there's a Brillo pad with your name on it."

  "All right! No dishes tonight!" shouts Andy.

  After ten rounds, this is how the chart looks...

  I look at the chart. I still can hardly believe it. It was a bal- anced system. And yet throughput went down. Inventory went up. And operational expense? If there had been carrying costs on the matches, operational expense would have gone up too.

  What if this had been a real plant-with real customers? How many units did we manage to ship? We expected to ship thirty-five. But what was our actual throughput? It was only twenty. About half of what we needed. And it was nowhere near

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  the maximum potential of each station. If this had been an actual plant, half of our orders-or more-would have been late. We'd never be able to promise specific delivery dates. And if we did, our credibility with customers would drop through the floor.

  All of that sounds familiar, doesn't it?

  "Hey, we can't stop now!" Evan is clamoring.

  "Yea, let's keep playing," says Dave.

  "Okay," says Andy. "What do you want to bet this time? I'll take you on."

  "Let's play for who cooks dinner," says Ben.

  "Great," says Dave.

  "You're on," says Evan.

  They roll the die for another twenty rounds, but I run out of paper at the bottom of the page while tracking Dave and Evan. What was I expecting? My initial chart ranged from +6 to -6. I guess I was expecting some fairly regular highs and lows, a nor- mal sine curve. But I didn't get that. Instead, the chart looks like I'm tracing a cross-section of the Grand Canyon. Inventory moves through the system not in manageable flow, but in waves. The mound of matches in Dave's bowl passes to Evan's and onto the table finally-only to be replaced by another accumulating wave. And the system gets further and further behind schedule.

  "Want to play again?" asks Andy.

  "Yeah, only this time I get your seat," says Evan.

  "No way!" says Andy.

  Chuck is in the middle shaking his head, already resigned to defeat. Anyway, it's time to head on up the trail again.

  "Some game that turned out to be," says Evan.

  "Right, some game," I mumble.

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  15

  For a while, I watch the line ahead of me. As usual, the gaps are widening. I shake my head. If I can't even deal with this in a simple hike, how am I going to deal with it in the plant?

  What went wrong back there? Why didn't the balanced model work? For about an hour or so, I keep thinking about what happened. Twice I have to stop the troop to let us catch up. Sometime after the second stop, I've fairly well sorted out what happened.

  There was no reserve. When the kids downstream in the balanced model got behind, they had no extra capacity to make up for the loss. And as the negative deviations accumulated, they got deeper and deeper in the hole.

  Then a long-lost memory from way back in some math class in school comes to mind. It has to do with something called a covariance, the impact of one variable upon others in the same group. A mathematical principle says that in a linear dependency of two or more variables, the fluctuations of the variables down the line will fluctuate around the maximum deviation established by any preceding variables. That explains what happened in the balanced model.

  Fine, but what do I do about it?

  On the trail, when I see how far behind we are, I can tell everyone to hurry up. Or I can tell Ron to slow down or stop. And we close ranks. Inside a plant, when the departments get behind and work-in-process inventory starts building up, people are shifted around, they're put on overtime, managers start to crack the whip, product moves out the door, and inventories slowly go down again. Yeah, that's it: we run to catch up. (We always run, never stop; the other option, having some workers idle, is taboo.) So why can't we catch up at my plant? It feels like we're always running. We're running so hard we're out of breath.

  I look up the trail. Not only are the gaps still occurring, but they're expanding faster than ever! Then I notice something weird. Nobody in the column is stuck on the heels of anybody else. Except me. I'm stuck behind Herbie.

  Herbie? What's he doing back here?

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  I lean to the side so I can see the line better. Ron i's no longer leading the troop; he's a third of the way back now. And Davey is ahead of him. I don't know who's leading. I can't see that far. Well, son of a gun. The little bastards changed their marching order on me.

  "Herbie, how come you're all the way back here?" I ask.

  "Oh, hi, Mr. Rogo," says Herbie as he turns around. "I just thought I'd stay back here with you. This way I won't hold any- body up."

  He's walking backwards as he says this.

  "Hu- huh, well, that's thoughtful of you. Watch out!"

  Herbie trips on a tree root and goes flying onto his backside. I help him up.

  "Are you okay?" I ask.

  "Yeah, but I guess I'd better walk forwards, huh?" he says. "Kind of hard to talk that way though."

  "That's okay, Herbie," I tell him as we start walking again. "You just enjoy the hike. I've got lots to think about."

  And that's no lie. Because I think Herbie may have just put me onto something. My guess is that Herbie, unless he's trying very hard, as he was before lunch, is the slowest one in the troop. I mean, he seems like a good kid and everything. He's clearly very conscientious-but he's slower than all the others. (Some- body's got to be, right?) So when Herbie is walking at what I'll loosely call his "optimal" pace-a pace that's comfortable to him -he's going to be moving slower than anybody who happens to be behind him. Like me.

  At the moment, Herbie isn't limiting the progress of anyone except me. In fact, all the boys have arranged themselves (delib- erately or accidentally, I'm not sure which) in an order that allows every one of them to walk without restriction. As I look up the line, I can't see anybody who is being held back by anybody else. The order in which they've put themselves has placed the fastest kid at the front of the line, and the slowest at the back of the line. In effect, each of them, like Herbie, has found an optimal pace for himself. If this were my plant, it would be as if there were a never-ending supply of work-no idle time.

  But look at what's happening: the length of the line is spreading farther and faster than ever before. The gaps between the boys are widening. The closer to the front of the line, the wider the gaps become and the faster they expand.

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  You can look at it this way, too: Herbie is advancing at his own speed, which happens to be slower than my potential speed. But because of dependency, my maximum speed is the rate at which Herbie is walking. My rate is throughput. Herbie's rate governs mine. So Herbie really is determining the maximum throughput.

  My head feels as though it's going to take off.

  Because, see, it really doesn't matter how fast any o ne of us can go, or does go. Somebody up there, whoever is leading right now, is walking faster than average, say, three miles per hour. So what! Is his speed helping the troop as a whole to move faster, to gain more throughput? No way. Each of the other boys down the line is walking a little bit faster than the kid directly behind him. Are any of them helping to move the troop faster? Absolutely not. Herbie is walking at his own slower speed. He is the one who is governing throughput for the troop as a whole.

  In
fact, whoever is moving the slowest in the troop is the one who will govern throughput. And that person may not always be Herbie. Before lunch, Herbie was walking faster. It really wasn't obvious who was the slowest in the troop. So the role of Herbie- the greatest limit on throughput-was actually floating through the troop; it depended upon who was moving the slowest at a particular time. But overall, Herbie has the least capacity for walking. His rate ultimately determines the troop's rate. Which means-

  "Hey, look at this, Mr. Rogo," says Herbie.

  He's pointing at a marker made of concrete next to the trail. I take a look. Well, I'll be... it's a milestone! A genuine, hon- est-to-god milestone! How many speeches have I heard where somebody talks about these damn things? And this is the first one I've ever come across. This is what it says:

  "- 5-" miles

  Hmmm. It must mean there are five miles to walk in both directions. So this must be the mid-point of the hike. Five miles to

  go.

  What time is it?

  I check my watch. Gee, it's 2:30 P.M. already. And we left at

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  8:30 A.M. So subtracting the hour we took for lunch, that means we've covered five miles... in five hours?

  We aren't moving at two miles per hour. We are moving at the rate of one mile per hour. So with five hours to go...

  It's going to be DARK by the time we get there.

  And Herbie is standing here next to me delaying the throughput of the entire troop.

  "Okay, let's go! Let's go!" I tell him.

  "All right! All right!" says Herbie, jumping.

  What am I going to do?

  Rogo, (I'm telling myself in my head), you loser! You can't even manage a troop of Boy Scouts! Up front, you've got some kid who wants to set a speed record, and here you are stuck behind Fat Herbie, the slowest kid in the woods. After an hour, the kid in front-if he's really moving at three miles per hour-is going to be two miles ahead. Which means you're going to have to run two miles to catch up with him.