“…As a lean thinker, I can start by asking myself, *what are the adjacent processes to my work to which I need to connect and what is the math of the flow between us?* That is, *who are my allies, whose outputs are my inputs, and who’s using my outputs as their inputs?* And how can I formally collaborate to connect these series of adjacent processes to create flow?…”

Sourced through the LeanCor blog

**Michel Baudin**‘s comments:

“Adjacent” is a good word for all the processes that directly exchange materials or data with one operation and, if adjacency is locally well managed at every operation, you have a smooth flow from start to finish. I will henceforth use this. At the start of his post, Robert confesses to having studied math as an undergrad, which is another thing we have in common besides having both written books about Lean Logistics.

Math was a passion ignited in me by a High School teacher when I was 17, and it didn’t subside until my manufacturing epiphany in Japan 10 years later. I had switched to engineering as a graduate student to understand what the math was good for but kept learning more, eventually publishing research papers, and the first one was about what I called “adjacency functions,” which made Robert’s post catch my attention.

I was working on methods to establish whether point processes have any clustering mechanism. Point processes are phenomena that manifest themselves as points in space or time, like series of events or stars in the night sky. A cloud of points may look clustered in the absence of any clustering mechanism, and the point was to tell when the points were *so* clustered that it could not be explained without an actual cause.

The idea I pursued was to focus on the space containing no points. My *adjacency function* was the probability of having no points within a ball of radius *r* and my *conditional adjacency function* was the probability of having no point within a distance *r* of a point.

I had been struggling with this problem for months when an insight struck me while on a spelunking trip with friends in 1979: if the adjacency functions are straight lines in a log-log plot, then the process is such that “seeds” occurring without clustering each spawned a cluster of points around it whose positions relative to the seed follow a Gaussian distribution. It took me two more years to work out the details, but the proof checked out and the paper was published in 1981 in the Journal of Applied Probability. It was of interest to, perhaps, 10 people worldwide.

This achievement, however, won me no points among manufacturing professionals in the US. My *engineering* background was OK but they had no use for any math beyond basic arithmetic. As J. Michael Harrison put it, “they have a low tolerance for abstraction.” It meant you couldn’t say “Assume you have *L* in inventory for a given item…” Instead, it needed to come out as “say you have 100 tons of pellets in stock…” It took some getting used to but you could eventually communicate. Instead of variables, you can always talk about column headers in spreadsheets. I found Europe to be no different until I landed in Russia, where I encountered consulting clients who demanded reports with mathematical formulas. There, suddenly, integral signs were no turnoffs; instead, they were a guarantee that the work was serious.

After I started working in manufacturing, I continued my math research as a hobby for several years, publishing three more papers. The last one, in 1986, had three coauthors and has, so far, 687 citations on Research Gate, which is ten times more than all my previous papers combined. It is on a different subject.

While this part of my background has been in the closet for 36 years, it has covertly influenced the way I work and write all along. After I finished writing Working With Machines, my editor at Productivity Press told me that the book felt like a mathematical construction with a logical progression from issues of individual operators and machines to the arrangement of these building blocks into cells or lines, and finally whole plants. I took it as a compliment and confessedto him about my math background. He had been working with me on two other books before but was not aware of it. I had seen to that.