Line Balancing Efficiency
Size a paced assembly line — cycle time, theoretical station count, and balance efficiency from total work content and demand.
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The engineering
Line balance efficiency measures how well work is spread across a paced assembly line. Twc is the sum of every task time on the product; Tc is the cycle time that sets the line's rhythm (usually derived from required output rate). With n stations, n·Tc is the total labor time available per unit — divide the useful work Twc by it and you get the fraction actually spent working. The rest is balance delay: idle time forced by the fact that tasks don't split into perfectly equal chunks.
The theoretical minimum station count is ⌈Twc/Tc⌉ — you can never do better. Real lines land above that because precedence constraints and indivisible tasks leave slack. Rule of thumb: efficiencies of 90–95% are excellent for hand assembly; if you're below ~75%, look for a large task hogging a station or a cycle time set too tight. Watch units — every task time and Tc must share the same time base (minutes here).
Where this math comes from
The assembly-line balancing problem was born the moment Henry Ford's moving line (1913) forced managers to chop the work into equal-time bites — but the math stayed informal for decades. The first formal statement came in 1955 when Merten Salveson published a linear-programming formulation of the assembly line balancing problem, turning shop-floor intuition into an optimization.
Mikell Groover's Automation, Production Systems, and Computer-Integrated Manufacturing codified the practical metrics engineers still use — line efficiency Eb, balance delay d, and repositioning losses — as a clean bench recipe. This card follows Groover's definitions directly.
- 1913Henry FordMoving assembly line makes equal-time task allocation an economic necessity.
- 1955Merten E. SalvesonFirst formal (linear-programming) statement of the assembly line balancing problem.
- 1961Fred M. TongePublishes heuristic methods for balancing large lines by computer.
- 1987Mikell P. GrooverStandardizes line efficiency and balance delay metrics in his production-systems text.
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