Except between Herbie and the kid in front of him.
So how is he doing it? I watch him. Every time Herbie gets a step behind, he runs for an extra step. Which means he's actually expending more energy than Ron or the others at the front of the line in order to maintain the same relative speed. I'm wondering how long he'll be able to keep up his walk-run routine.
Yet... why can't we all just walk at the same pace as Ron and stay together?
I'm watching the line when something up ahead catches my eye. I see Davey slow down for a few seconds. He's adjusting his
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packstraps. In front of him, Ron continues onward, oblivious. A gap of ten... fifteen... twenty feet opens up. Which means the entire line has grown by 20 feet.
That's when I begin to understand what's happening.
Ron is setting the pace. Every time someone moves slower than Ron, the line lengthens. It wouldn't even have to be as obvi- ous as when Dave slowed down. If one of the boys takes a step that's half an inch shorter than the one Ron took, the length of the whole line could be affected.
But what happens when someone moves faster than Ron? Aren't the longer or faster steps supposed to make up for the spreading? Don't the differences average out?
Suppose I walk faster. Can I shorten the length of the line? 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
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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.
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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."
"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. There are tables, a water pump, garbage cans, barbecue grills-all the ne- cessities. (This is my kind of wilderness I'll have you know.)