Balancing a Four-Station Cell Against Takt with Scrap in the Picture
A single-piece-flow cell runs one 8-hour shift. Of the 480 minutes, 15 go to a startup meeting and two 10-minute breaks come out, leaving 445 minutes of planned run time. The customer requires 400 good units per shift. Current station cycle times are: Station 1 = 52 s, Station 2 = 61 s, Station 3 = 71 s, Station 4 = 58 s. The cell currently produces 372 units per shift and final test scraps 1.5%. Overtime is available at 1.5x labor cost but has been used every Saturday for six weeks. The line supervisor proposes buying a second fixture for Station 3.
1. Calculate takt time, the cell's current capacity, and the real gap. How many units must the cell start to ship 400 good?
Read the worked answer
- Takt time = available time / customer demand = 445 x 60 / 400 = 66.75 s per unit.
- Bottleneck is Station 3 at 71 s. Capacity = 445 x 60 / 71 = 376 units per shift - which matches the observed 372 plus normal losses.
- Gap at the bottleneck: 71 - 66.75 = 4.25 s per unit too slow when scrap is ignored.
- Scrap changes the target: to ship 400 good at 1.5% scrap you must start 400 / 0.985 = 406 units. That pushes the required cycle to 445 x 60 / 406 = 65.8 s, so the real gap at Station 3 is 71 - 65.8 = 5.2 s.
Ignoring the scrap term is a common exam trap: it makes the gap look smaller than it is and it guarantees the cell comes up short again next month as scrap drifts.
2. Recommend and justify a specific rebalance. Where should the work go?
Read the worked answer
The cell is out of balance, not short of stations - Stations 2 and 4 both have slack against the 65.8 s target:
- Station 2: 65.8 - 61 = 4.8 s slack
- Station 4: 65.8 - 58 = 7.8 s slack
Move roughly 5.2 s of work from Station 3 to Station 4 (the station with the most slack):
- Station 3: 71 - 5.2 = 65.8 s
- Station 4: 58 + 5.2 = 63.2 s
- New capacity = 445 x 60 / 65.8 = 406 starts, which at 98.5% first-pass yield is about 400 good units.
Notes that make the answer credible:
- Moving the element to Station 2 would leave Station 2 at 66.2 s and re-create a bottleneck - feasible on paper, but with no buffer for variation.
- Prefer a self-contained work element (a loading, gauging, or labeling step) that can be relocated without adding handling.
- Re-check after the move: if Station 3 work cannot be split below 65.8 s, the balancing is not the whole answer and the process content must be reduced.
3. Evaluate the supervisor's second-fixture proposal and the six-week overtime pattern.
Read the worked answer
On the fixture: a second fixture at Station 3 only adds capacity if it lets two units be processed in parallel on the same operation, or if it removes load/unload time from the 71 s. If it duplicates the same single-piece work, it buys floor space and capital cost with no throughput. The arithmetic question to ask the supervisor is: 'Which 5.2 s of the 71 does the fixture remove, and can you show the element breakdown?' If the answer is 'it should make it faster,' the purchase is premature - rebalancing costs almost nothing and closes the gap today.
On six weeks of Saturday overtime: that is a symptom, and it says the capacity problem is structural, not a one-week spike. Overtime at 1.5x is buying the missing 24-30 units at a premium every week while the 5.2 s imbalance stays in the line. It also hides the scrap rate, which will get worse as people rush.
Sequence the response: (1) rebalance 5.2 s off Station 3 into Station 4 now; (2) attack the 1.5% scrap - every point of scrap is 4 units of starts; (3) recover break coverage or run overlapping breaks to protect the 445 minutes; (4) only then consider capital at Station 3, with element-level data in hand.