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.
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:
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.
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.
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."