Takt time and line balancing: how do I find the minimum number of assembly workstations?

Takt time is available production time divided by customer demand. Available time is 480 - 30 = 450 minutes = 27,000 seconds, so takt = 27,000 / 300 = 90 seconds per unit. The line must release one unit every 90 seconds, so no station may be given more than 90 seconds of work.

The theoretical minimum number of stations is total work content divided by takt, rounded up: 400 / 90 = 4.44, so 5 stations. That is a lower bound; whether 5 is achievable depends on how the tasks can be grouped.

Grouping is constrained by the precedence diagram: a task can only be assigned once all its predecessors are assigned. A simple heuristic is the largest-candidate rule: list the tasks by duration, and for each station in turn keep adding the longest task that is eligible and still fits in the remaining time. Ranked positional weight is a refinement that ranks each task by its own time plus the time of all tasks that follow it.

Heuristics do not guarantee the minimum. If one gives 6 stations where the bound is 5, try another rule or break ties differently before accepting it.

Balance efficiency = total work content / (number of stations × cycle time). With 5 stations at 90 s: 400 / 450 = 88.9 percent; the remaining 11.1 percent is balance delay, which is idle time built into the line. With 6 stations it would be 400 / 540 = 74 percent.

Also look at how the idle time is distributed. A balance of 88, 88, 88, 88 and 48 seconds has the same efficiency as 80 seconds at every station, but the second is smoother, easier on the operators and more tolerant of variation.

On the terminology: takt time is a demand figure, set by the customer and the available hours. Cycle time is a process figure, how long a station or the line actually takes per unit. A line is designed so that its cycle time is at or a little below takt. If the largest station load in your balance is 88 s, the line could run a cycle of 88 s and make 27,000 / 88 = 306 units.

Many plants plan to a cycle time several percent below takt to absorb minor stops and quality losses, since a line loaded to exactly 90 s has no recovery capacity.

Two situations the basic method does not cover. If a single task is longer than takt, no grouping helps; that station has to be duplicated in parallel, or the task must be split or improved. With your 70 s maximum against a 90 s takt this does not arise, but it would if demand rose to 400 units (takt 67.5 s).

And task times on a manual line are averages. Operators vary from cycle to cycle, so stations loaded to nearly 100 percent of takt will overrun regularly. Small buffers between stations, or loading stations to around 90 percent, keep the line from stalling.