In the 1950’s, the design and implementation of the Toyota Production System (TPS) within Toyota had begun. In the 1960’s, Group Technology (GT) and Cellular Manufacturing (CM) were used by Serck Audco Valves, a high-mix low-volume (HMLV) manufacturer in the United Kingdom, to guide enterprise-wide transformation. In 1996, the publication of the book Lean Thinking introduced the entire world to Lean. Job Shop Lean integrates Lean with GT and CM by using the five Principles of Lean to guide its implementation: (1) identify value, (2) map the value stream, (3) create flow, (4) establish pull, and (5) seek perfection. Unfortunately, the tools typically used to implement the Principles of Lean are incapable of solving the three Industrial Engineering problems that HMLV manufacturers face when implementing Lean: (1) finding the product families in a product mix with hundreds of different products, (2) designing a flexible factory layout that "fits" hundreds of different product routings, and (3) scheduling a multi-product multi-machine production system subject to finite capacity constraints.