A production line is only as fast as its SLOWEST station — the bottleneck. Speed up any other station and nothing changes; work just piles up in front of the slow one. To go faster you must fix the bottleneck itself, and the moment you do, a NEW station becomes the constraint. That’s the Theory of Constraints, and it’s true of factories, code, and agents alike. Slide which station you improve.
Throughput of a serial line equals the rate of its SLOWEST station: T = min(rates). This has a sharp consequence — improving a non-bottleneck station raises no output at all (it only builds inventory ahead of the constraint), while improving the bottleneck raises throughput until some OTHER station becomes the new bottleneck. Goldratt’s Theory of Constraints turns this into a method: find the constraint, exploit it, subordinate everything else, elevate it, repeat. A fail-loud self-check throws unless speeding a non-bottleneck leaves throughput unchanged while speeding the bottleneck raises it. ◆ real operations research, node-verified.
A deterministic serial line (the exact min-rate throughput and constraint logic); real systems add variability and buffers that blur the bottleneck — the improve-only-the-constraint rule is exact.