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Theoretical Minimum Number of Stations

Also known as minimum workstations · Nmin · theoretical minimum stations · how many stations does the line need · work content over cycle time

Nmin⁡=∑tiCN_{\min} = \frac{\sum t_i}{C}

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See also
Takt Time — The cycle time C in this formula is normally the takt time.Line Balancing Efficiency — Compare Nmin with the stations you actually used to see how much idle time you bought.

Learning zone

Add up every task time on the line and divide by the cycle time. That ratio is the fewest stations physically capable of doing the work: 1,500 seconds of content at a 200-second cycle needs at least 7.5 stations, so eight. The formula returns the raw 7.5 on purpose, because the fraction tells you something the rounded number hides.

A result of 7.5 means the eighth station will be half idle no matter how cleverly you assign tasks. A result of 7.05 means you are one small task away from needing only seven, and it is worth an hour looking for that task. Rounding before you look at the remainder throws away the only diagnostic in the calculation.

It is called theoretical because task precedence usually makes it unreachable. Tasks have to happen in order, some cannot be split, and some need a machine that exists once. Real lines commonly land one or two stations above the theoretical minimum, and the gap between the two is exactly the balance delay the efficiency formula reports.

Theoretical Minimum Number of Stations
Nmin⁡=∑tiCN_{\min} = \frac{\sum t_i}{C}
Where
  • Nmin⁡N_{\min}= Theoretical minimum stations (stations)
  • ∑ti\sum t_i= Total work content (s)
  • CC= Cycle time (s)
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