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.
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.
