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. However, 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
E.M. Goldratt
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107
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.
E.M. Goldratt
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108
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."
E.M. Goldratt
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Captured by Plamen T.
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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. The
re 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
E.M. Goldratt
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Captured by Plamen T.
110
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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The Goal: A Process of Ongoing Improvement
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111
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."
E.M. Goldratt
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Captured by Plamen T.
112
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.
E.M. Goldratt
The Goal: A Process of Ongoing Improvement
Captured by Plamen T.
113
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'l 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."
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