You need to read a book called "The Goal". Forgot who wrote it but it is a cheap paperback book. Lean Manufacturing came from Toyota. The head honcho there was grocery shopping one day and marveled at the way inventory was restocked on the shelves. Thus Lean Mfg was born. Basically you have just enough inventory to keep your lines running "Eliminating storage and warehousing". Lean MFG will uncover your process problems because excess inventory hides them. That is the core of lean. Also lean manufacturing means " taking a job that requires 5 people and making due with four" gotta go problem just came up.
The author of the "The Goal" is Eliyahu M. Goldratt.
I would argue that "Lean Manufacturing" is a bastardized version of what Toyota did/does. "Lean Manufacturing" makes for a good catch-phrase.
Lean Manufacturing wasn't born out of the grocery store, it makes for a good story, but that is incomplete. The supermarket provided the spark for the concept of JIT (Just-in-Time). JIT is just one of the two pillars that the The Toyota Production System is built upon.
Ohno is largely credited with the material flow/JIT aspect of the Toyota system, but Shigeo Shingo was really the thought leader behind the rest. Keep in mind that Ohno himself believed calling it a production system was incorrect. He believed it should have been called the Toyota Management System.
Kanban isn't about quantity, it is about time. It is about the time necessary to replenish the kanban, and the length of time that the kanban will last based on the production levels. The inventory levels are what is necessary to satisfy the customer, and satisfying the customer is the ultimate goal. Eliminating inventory and warehousing is a great concept, like zero-defects, but the purpose is to minimize the amount required. The entire system really is about methods to minimize time, quantities are not the first priority.
The core of Lean is about waste, in any shape or form, not about inventory or headcount reduction. Where Lean most often fails is that it doesn't look at the long term strategic view, which Toyota did in their development of TPS over the decades. More often than not, Lean is trained as a bunch of discrete tools that one can hammer into place when needed. It doesn't work that way, which is probably the biggest reason so few companies have come close to being able to operate like Toyota.
Wayne