This Guest paper was submitted for publication and is copyright to Angelo Baratta, © 2013 published here February 2015. Much of the material in this paper was first published on line at: www.projecttimes.com/ articles/understanding- the-chemistry-and- physics-of-change-part- 1-the-physics.html

## Understanding Unsolvable Problems

Some problems can't be solved economically. They must be de‑escalated – reduced in size, scope, or intensity. Basically what we have is a subway with a single train running continuously. The train carried 1,000 people per trip mostly one way. It made one round trip along a five-kilometer corridor in 10 minutes. That means 6 trips per hour at 1,000 people per trip at \$1.00 per person giving a revenue of \$6,000 per hour. That was the breakeven point.

Then the city expanded the subway to a 10-kilometer corridor to accommodate an additional 6,000 new residents, all living along the new corridor. So now we needed to transport 12,000 residents per hour, i.e., double the initial load. The question is:

"By how much do we need to increase capacity, and how much do we need to charge the new residents if we don't want to change the fare along the original shorter corridor?"

A doubling of demand to 12,000 would seem to imply a doubling of capacity, and most people might come up with that answer. But let's look at that in more detail. The original single subway train could carry 1,000 passengers per trip. It still only carries 1,000 passengers per trip on the longer corridor. However, it used to make 6 round trips per hour. Since each round trip is now 20 minutes, it can only make 3 round trips. That means it can only carry 3,000 people per hour (1,000 x 3). But we now have 12,000 people per hour that need to be transported. Since a single train can only carry 3,000 per hour, that means we need 4 trains to the previous one (4 trains x 3 trips per hour x 1,000 per trip) to carry 12,000 people.

Yes, that's right. We have doubled demand but capacity has to go up by a factor of four (4) not 2. Since we need \$6,000 per train per hour to run the operation, we now need \$24,000 per hour to the previous \$6,000. Now, we want to leave the original fare the same for the previous users. That means that the first group of residents will be contributing \$6,000 per hour leaving a shortfall of \$18.000 per hour that must be paid by the new users.

So each new user has to pay a fare of \$3.00 (\$18,000 / 6,000). That means that the second 5 km corridor is three times more expensive than the first!

That's an exponential increase in cost to handle a linear (doubling) increase in demand. Imagine the impact of doubling the line to 20 kilometers and doubling the demand to 24,000. Each train would require 40 minutes to make a round trip. That's 1.5 trips per hour or 1,500 people per hour. That means we'd need to increase trips to 16 trains per hour to carry 24,000 people. So every time we double the demand the capacity goes up by a factor of four (two squared) – a linear increase resulting in an exponential response.

This problem can't be solved using Six Sigma or Lean or any other methodology. A problem that increases linearly while its solution increases exponentially can't be solved with linear thinking or linear methods. I call these Business Process 3.0 problems.

Can you recognize the Business Process 3.0 problems in your organization? Maybe you're working on one right now, but without knowing it. So, beware.