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:
"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 getting 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.
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.