Unit content
Assembly-line balancing under precedence constraints
An assembly line divides required work among stations. A good balance keeps station workloads compatible with the required cycle time while respecting task precedence.
If task times are $t_j$ and target station cycle time is $C$, the total work content gives a lower bound on the number of stations:
$$N_{min}\ge \left\lceil\frac{\sum_j t_j}{C}\right\rceil,$$
where $\lceil x\rceil$ means rounding $x$ upward to the next integer.
Suppose tasks require 30, 40, 50 and 20 seconds, for total work content 140 s, and the required cycle is 60 s/unit. Then
$$N_{min}\ge\left\lceil\frac{140}{60}\right\rceil=3.$$
Three stations may still be impossible if precedence or task indivisibility prevents feasible grouping.
For example, if the 50 s task must be followed by the 40 s task and neither can be split, they cannot occupy one 60 s station. Tasks must be assigned while ensuring each station load is no greater than $C$ and all predecessors are completed before their dependent tasks.
Balance loss appears when stations have idle time because work cannot be distributed perfectly.
Line balancing therefore combines demand pace, task times and an assembly precedence graph. It is not simply dividing total time by the number of workers.