# Accounting For Non-Productive Time on an Assembly Line

A common question from production managers when discussing the implementation of line balancing is how much time is lost at the beginning and end of a production run due to empty stations.  When materials first flow into the initial station of the line, all of the following stations are empty.  Once the first station fulfills its share of the last order, it then becomes non-productive.  The following illustration shows a single product moving through a 4 station assembly line: The red stations are idle.  Once the first station is finished, it passes the first product to the second station.  Because we are only building a single product, station 1 is now idle along with 3 and 4 while station 2 is now working. In this particular case with 4 stations and only 1 product moving through the line at a time, we can see that there will always be 3 empty stations. To understand what is happening here, we need some definitions.

Process Time – The total time required to build a single product

Cycle Time – The rate at which finished products flow off of the line.  In a perfect world, all stations are spending the same amount of time working on the product, so the cycle time is equal to the process time divided by the number of stations. Let’s say that the workers on our assembly line are building computers.  Each computer has a process time of 20 minutes.  Using the formula above, we can calculate a cycle time of 5 minutes.  So, how long does it take to build a single computer?  If you guessed 20 minutes, you’re incorrect.  To understand why, we need one more definition:

Man Minutes – The total time contributed to a particular task by all workers.  For example, if 2 people are fixing a car together for 30 minutes, 60 man minutes have been used.

Each row in the illustration represents a 5 minute block of real time.  There are 4 workers in each row.  This means that in that 5 minute block of real time, 20 man minutes have been used.  So while one person spends 5 minutes at his or her station working on the product, three people wait.  This non-productive time is referred to as Idle Time.  And the question that we are trying to answer is:

## How do we calculate idle time on an assembly line?

An easy way to do this with the example above is to count the number of empty (red) stations and then multiply that by the cycle time.  There are 12 empty stations, so the idle time is 60 minutes.  The time actually spent working on the computer, the productive time is the number of full stations multiplied by the cycle time.  There are 4 full stations so 20 minutes were spent building the computer.  This is easy when we only have a single fixture on the line, but how do we calculate the number of idle stations and idle time when there are more stations and more products?  It’ actually quite simple. Or in this case, 4*(4-1), or 12 idle stations

We then simply multiply the number of idle stations by the cycle time and we see that there are 60 minutes of idle time.  You may have noticed that this formula does not take into account how many products we are putting on the line.  This is because the idle time is the same in a production run whether we are building 1 product or 100 products.  The example below illustrates this point.  Here we see 4 products moving through a 4 station line.  Notice that there are still only 12 empty stations in the entire run. Because idle time is constant, with each additional product we add to the line we are only adding productive time.  We calculate the Total Productive Time in a production run with the following formula: Our total productive time in building a single fixture is 20 minutes.  It is 100 minutes if we are building 5 fixtures.  To calculate the total man minutes used on a production run, we simply add the Total Productive Time and Idle Time together: If we then divide the total man minutes by the # of products built, we get the Average Man Minutes per Fixture: To build just 1 product takes 80 man minutes.  A second product only takes an additional 20 minutes, so the average is 50.  This is still much greater than the process time.  The more fixtures we build though, the shorter the average time gets.  This is illustrated in the following spreadsheet: We can see how quickly the average time drops as we add products to the run.  If we were to build 100 computers, the average time per unit would be 20.6 man minutes.  This information can be used by production and operations managers to assess the point at which it makes sense to implement production lines.

Let’s suppose that when an individual builds a computer from start to finish on his or her own (without a team on an assembly line), the process time becomes 25 minutes. The point at which it becomes economically viable to institute a line is at the quantity when the average man minutes per product are less than 25 minutes.  So in this case, we would not want to use an assembly line for any quantity less than 13 computers.

It should also be noted that the idle time at the beginning and end of each production run does not need to be completely non-productive.  Workers can be cleaning stations, making sure they have all necessary tools and parts, etc.

I hope this answers some of your questions about idle time and maybe even inspires a few more.  Feel free to comment.