Line capacity, takt time and an overtime request on a 12-operator shirt line
A shirt unit runs one line of 12 operators on a 480-minute shift. The shift includes a 30-minute lunch break and a 10-minute start-up meeting, leaving 440 productive minutes (26,400 seconds). The plan target is 800 pieces per shift. Time study gives these operation times in seconds: collar join 32, collar topstitch 18, placket attach 30, placket topstitch 16, sleeve attach 30, sleeve hem 16, side seam overlock 26, yoke join 24, cuff attach 22, cuff topstitch 10, body hem 18, buttonhole 16, button attach 12, bartack 8, trim and press 10, label and tag 10. Because machines of the same type sit together, the supervisor currently gives one operator two operations - collar join plus collar topstitch, side seam plus yoke - while three other operators spend much of the shift waiting or reworking. Actual output is 512 pieces per shift with about 150 pieces of work in progress queued before the collar operation. The supervisor wants to authorise about four hours of overtime every day to close the gap.
1. Calculate the takt time, the total work content, the minimum number of operators and the current capacity of the line. Use the numbers to explain why 12 operators are producing only 512 pieces.
Read the worked answer
Takt time = productive seconds divided by customer requirement = 26,400 / 800 = 33 seconds per piece.
Total work content = 32+18+30+16+30+16+26+24+22+10+18+16+12+8+10+10 = 298 seconds per piece.
Minimum operators = work content / takt = 298 / 33 = 9.03, so 10 operators. (You cannot have 9: 9 x 33 = 297 seconds, less than the 298 seconds of work.)
Current capacity is set by the bottleneck, not by the number of people. With collar join plus collar topstitch on one operator, that station is 32 + 18 = 50 seconds; side seam plus yoke is 26 + 24 = 50 seconds. Capacity = 26,400 / 50 = 528 pieces per shift.
Why only 512 pieces: 512 is about 97% of 528 - the line is running close to its own bottleneck capacity, so the shortfall against 800 is structural, not effort. Twelve operators are present, but the line is unbalanced: two stations are at 50 seconds against a 33-second takt, work piles up in front of them (150 pieces of work in progress), and downstream operators wait because flow is capped upstream. Adding people to an unbalanced line cannot lift output beyond the bottleneck.
2. Propose a rebalancing plan. State how many operators the balanced line needs, what you would do with the surplus, and calculate the expected output and balance efficiency.
Read the worked answer
Design rule: every station must be at or below the 33-second takt, and the 50-second combinations must be split.
Splitting: give collar join (32 s) and collar topstitch (18 s) back to separate stations, and split side seam (26 s) from yoke join (24 s). Now combine the short elements so that every station uses the operator fully:
- collar join 32 alone (32 s)
- placket attach 30 alone (30 s)
- sleeve attach 30 alone (30 s)
- side seam 26 alone (26 s)
- yoke join 24 + bartack 8 = 32 s
- cuff attach 22 + cuff topstitch 10 = 32 s
- collar topstitch 18 + button attach 12 = 30 s
- placket topstitch 16 + buttonhole 16 = 32 s
- sleeve hem 16 + label and tag 10 = 26 s
- body hem 18 + trim and press 10 = 28 s
Ten stations, all at or under 32 seconds, which meets the 33-second takt. Expected output = 26,400 / 32 = 825 pieces, so 800 is achievable with a small buffer. Balance efficiency = work content / (stations x takt) = 298 / (10 x 33) = 298 / 330 = 90.3%.
Surplus: 12 - 10 = 2 operators. Do not simply cut them. Redeploy one to a second line or to a relieving role (breaks, absenteeism, cutting-room support for bundles) and one to in-line inspection, which currently sits inside the trim operation and is the source of the rework seen in the waiting time. Cutting heads without fixing the balance just moves the problem to the next shift.
3. The supervisor still wants four hours of overtime a day. Evaluate that proposal with numbers and describe the work-study actions you would use to hold the gain after rebalancing.
Read the worked answer
The overtime arithmetic. At the current 528-piece capacity, reaching 800 pieces needs 800 x 50 = 40,000 seconds of bottleneck time. That is 40,000 / 60 = 667 minutes, against 440 productive minutes - about 227 extra minutes, or roughly 3.8 hours a day, which matches the supervisor's request. So the proposal is arithmetically consistent but economically and physically wrong: it buys 4 hours of overtime to protect an unbalanced layout, adds fatigue and defect risk exactly at the collar station, and does not fix the 150 pieces of work in progress.
Comparison: the rebalance costs nothing, frees two operators, and produces 800-825 pieces in the normal shift, so overtime is not needed at all. Any overtime should be reserved for genuine demand peaks.
Work-study actions to hold the gain
- Standard method sheet and time standard per operation, displayed at the station, revised whenever the method changes.
- Hourly output boarding by station so a station drifting above 33 seconds is visible within an hour, not at end of shift.
- Front-of-line feeding discipline and a cap on work in progress (say 20 pieces between stations) so the bottleneck cannot hide behind a queue.
- Balance review at every style change, re-using the same work content and takt calculation.
- Operator training for the split collar operation, since the person who did both halves now needs a defined single task and a defined cycle.
- Weekly check of balance efficiency (target 85% or better) and of the rework rate that was visible in the idle time.