How many operators does this line need? Takt, work content, balance and relief

The example line: 17 work elements, 252 seconds

Every number on this page comes from one line, so you can follow each sum. The line is illustrative: a manual line assembling a small electric water pump, five stations in a row, two shifts. Each time is the operator's lowest repeatable time over ten timed cycles, the lowest time that came up at least twice, as on the time study sheet. Only operator time counts: the leak tester runs for 45 seconds on its own, so element 14 is the operator's 14 seconds to load, start and unload it.

Step 2: the theoretical minimum is work content divided by takt

Total work content is the operator time for every element of one unit added up: 252 seconds here. Divide it by takt and round up, because you cannot staff 0.2 of a person. Groover calls the result the theoretical minimum number of workers: the smallest whole number at or above work content divided by cycle time.

It is a floor, not a plan. It assumes the work splits into equal slices, nobody waits for anybody, and the line never stops. Steps 3 and 4 test those assumptions, and they are where most staffing plans go wrong.

Step 4: split the work into stations and check the longest one

Five operators is the number. Whether five works depends on how the 252 seconds split into stations, in the order the pump is built. The line can only run as fast as its longest station, so check that station against the 57 seconds per pump, not the average.

Two measures say how good the split is. Balance efficiency is the total work content divided by the number of operators times the longest station time. Balance delay, also called balance loss, is 1 minus balance efficiency: the share of paid operator time spent waiting for the slowest station. Groover and Freivalds both define it this way, with every station allowed the slowest station's time.

The rebalance moved three elements and no work was removed. The walk for cover screws (element 4) went to station 1, unpacking the motor (element 8) went to station 3 next to the motor fitting it feeds, and the cable gland (element 11) went from station 4 to station 3. Station 2 fell from 66 to 50 seconds.

The two efficiencies answer different questions. Balance efficiency (96.9%) says the work is spread evenly. The line balancing calculator measures against takt when the longest station is under it (84.0%), because a line paced to demand still waits out the gap between its longest station and takt. Enter 57 as the takt to see the result with the stoppage factor in.

Move an element only if the build order still works, the parts and tools are in reach at the new station, and the operators who will do it agree it can be done. Try it at the line for a few cycles before you change the standard work.

Step 6: from operators per shift to people on the roster

Operators per shift is how many people the line needs at any moment. The roster also has to cover absence: holidays, sickness, training and anything else that takes trained people away. Divide by the share of people present on an average day, and round up for each crew, because someone on the day crew cannot cover nights.

If the line runs through breaks instead of stopping, available time goes up and takt gets longer, but every break needs a relief operator trained on that station. Count the minutes to cover each shift: 5 operators × 20 minutes of breaks is 100 minutes of relief a shift, and decide who does it.

The absence rate covers an average day. On a bad day it will not, and that is where cross-training matters. For each station, count the people on each crew who are qualified to work it alone. A job cover matrix is built for this, and two qualified people per job is a common starting point. With 6 people for 5 stations, a crew where everyone is qualified on at least two stations has 12 qualifications for the 10 it needs. Plan the training in the training matrix template or the cross-training plan, and keep the absence rate in the absenteeism tracker.

Where the formulas come from

The arithmetic on this page is standard industrial engineering. These are the sources it was checked against. The example line and its numbers are ours and illustrative.

• Takt time, operator balance chart, labor linearity and the standardized work combination table: Lean Enterprise Institute, Lean Lexicon, the entry for each term.
• Theoretical minimum number of workers, balance efficiency and balance delay: Mikell P. Groover, Automation, Production Systems, and Computer-Integrated Manufacturing, 3rd edition (Prentice Hall, 2008), chapter 15, Manual Assembly Lines.
• Line efficiency as total standard minutes over total allowed minutes, and dividing by an expected efficiency before rounding up: Andris Freivalds, Niebel's Methods, Standards, and Work Design, 12th edition (McGraw-Hill, 2009), chapter 2, line balancing.
• Standard time, relaxation allowances for personal needs and fatigue, and contingency allowances: International Labour Office, Introduction to Work Study, 4th revised edition, edited by George Kanawaty (ILO, 1992), chapter 23.
• The workbook on designing cells and lines this way: Mike Rother and Rick Harris, Creating Continuous Flow (Lean Enterprise Institute, 2001), especially the chapters What Is the Work and Distributing the Work.