Let me formalize the concept of line balancing.

Before we do this, though, let's review some basic definitions.

We define the capacity of a resource as a ratio between M, the number of people or

machines at this resource, divided by the processing time.

We define the process capacity as the minimum of the capacities of the various

resources in the process. And then, the flow rate is the minimum

between the amount and capacity. Value with the previously defined

utilization, as the ratio between flow rate and capacity.

Now, consider the following process. Imagine I have four stations, each staffed

with one worker. The processing times are shown in this

picture here in green. You see that station one has a shorter

processing time than station four. Consequently, given that there's one

worker at each of these stations, we're going to see that station four is our

bottleneck. Given that station four is slower than

stations one, two and three. Stations one, two and three have some

slight time relative to our bottleneck. We refer to this slight time as idle time.

To formally figure out how much red time, how much idle time these three steps have,

let me introduce the concept of the cycle time.

The cycle time is simply one over the flow rate.

The cycle time is like measuring at the end of the process how much time passes

between the completion of two subsequent units.

For example, I might say that this process is operating on a 115 second cycle.

That means, that there is a process unit leaving every 115 seconds.

Next, we define the direct labor content as the sum of the processing times.

This is simply in the previous picture, the sum of the green bars.

Next, we define for each resource the idle time as the difference between the cycle

time and the processing time. So, that's idle time for the first

resource is exactly this difference here. We can add that idle time up across all

resources to get the total red, in this picture, the total amount of idle time.

We can then define the average labor utilization in the process as a ratio

between the labor content, remember the sum of the processing time, and the labor

content plus all the direct idle time. The labor content ruling measures how much

green there is in the process, versus the labor content plus the direct idle time,

the denominator here in this definition, captures how much time I have to be paying

for in total, which is the labor content plus the idle time.

Finally, we define the cost of direct labor as a ratio between the total wages

per unit of time. For example, four workers times the hourly

wage rate, divided by the flow rate per a unit of time.

To practice our new definitions consider the following example.

This year is a machine paced line consisting of six workers working in

sequence. It does a machine base line because you

notice, there are no buffers between the stations.

Meaning, that these six workers have to work exactly at the same pace.

Though the first station has a shorter activity time thus x as capacity, that

station cannot run ahead. The entire process will be paced by the

slowest step that we will see in a moment is the station number five.

Now, let's practice our definitions. We have the processing times over here in

this first row. Next, we can compute the capacity as

simply as one over the processing times. For the first one, let me put the units

along here, so this is units per minute. One over five, one over two, one over

three, one over six, one over two. We can apply our definition of the

bottleneck and say that the step with the lowest capacity is the bottleneck.

That makes station five indeed the bottleneck.

Assuming there is enough demand for this process we're going to have a flow rate

that is going to be one unit every six minutes, which corresponds two a six unit

per minute. Or, alternatively, we could say that this

process is producing ten units per hour. We can then define the cycle time of the

process as six minutes between units, which I hope is intuitive because that is

exactly the activity time that we have here at the bottom.

Next, we can compute the idle time at each of the resources, as a difference between

the cycle time and the processing time. That would be three minutes here, one

minute here, four minutes here, three minutes here, zero minutes here, and four

minutes here. We'll then define the labor content as the

sum of the processing times, which is three plus five plus two plus three plus

six plus two, which makes an eight, a total of 21 minutes per unit.

The total idle time across all units is three plus one plus four plus three plus

four, which is fifteen minutes. We can then define the average labor

utilization as 21 minutes labor content divided by 21 plus fifteen, which is the

average utilization in this process. We can also compute the cost of direct

labor in this process as the ratio between the wages and the flow rate.

Say, for sake of arguments, each of my workers here is making $twenty per hours.

So, my wages are six workers times $twenty per hour, divided by the flow rate, which

we said was ten units per hour. This gives me a, direct cost of labor of

$twelve per unit. Let me take these calculations that are

arguably somewhat messy right now, and pluck them over to my excess spreadsheet

where you can read them more clearly. Alright, let's review these calculations

in Excel. So, first thing we are going to do is we

compute the capacity of each of the resources as one divided by the

corresponding processing times. This is now expressed in units per minute.

Next, we're going to compute the process capacity as a minimum of the individual

capacity levels which determines that indeed station five is, as we expected,

the bottleneck. We can then compute the flow rate as the

minimum between the margin capacity. We assumed here that there was

sufficiently margin so the flow rate is given by the process capacity.

We can compute that the cycle time is one divided by the flow rate, which is telling

us that we are making a unit every six minutes.

This allows me then to compute the idle time at each of the resources.

For that, I'm going to take the cycle time, and I'm going to subtract the

processing time at each of the resources. With this in mind, I can compute the total

idle time, which we confirm to be fifteen minutes.

Now, is fifteen minutes a lot of idle time or not?

This is really hard to judge. And so, we compare this number to the

total labor content in the process which we had previously defined as the sum of

the activity times. I can then, compute my labor utilization,

and it's the ratio between the labor content and the labor content plus the

idle time. 58 percent is my average language

utilization in the process. Note the following, let's quickly compute

the utilization of each of the six steps in the process.

Utilization, remember, is the flow rate divided by the capacity.

You notice 100 percent utilization at the bottleneck, which I hope is intuitive.

We can then go ahead and we can average delivery, the utilization of the six

resources and, voila, we also see a 58.3%. At the risk of repeating myself, let's go

back to the Subway example and revisit the previous calculations that we did.

Now, extend these calculations as the following.

So, the cycle time is computed as follows. We said that there were 60 customers per

hour. That means, every 60 seconds, let's say,

there are 3,600 seconds in the hour, every 60 seconds we have a unit of demand.

The cycle time thus is 60 seconds. We then can compute the idle time of the

various resources. As the difference between the cycle time

and the processing times. We can sum up the total idle time and find

it to be 60 seconds. This is really 60 seconds per sandwich.

The next thing that we can do is we can compute the labor content, which is also

expressed per sandwich as the sum of the processing times.

With those two pieces of information, I can compute the labor utilization then as

the ratio between the labor content, and the labor content plus the idle time.

This is 66.6%. Notice, by the way, that as before, this

is also exactly the average of the individually computed utilizations.

I often get asked, why we make such a big deal out of labor costs.

If you analyze the P and L, from big corporations and manufacturing these days,

we actually see relatively little labor costs on their P and L's.

My colleague from MIT, Dan Whitman, has done a very interesting analysis in the

automotive industry that addresses this matter.

If you analyze the Profit and Loss statements of an automotive company, you

indeed see that the vast majority of the money is spent on purchasing.

About 70 percent of the total cost incurred at Daimler Chrysler, at that

point, was spent on purchasing. This is very similar, if you look at

electronics makers, who are also going to spend 70 to 80 percent of the total cost

on procuring costs for items like disk drives and microprocessors.

Now, the labor costs here, if you look at things related to assembly labor, and

maybe inventory cost, is just a tiny fraction.

However, this is misleading. This is hiding the fact that your

purchasing costs are the total costs of your supplier, and that includes their

labor cost. So, you see, that if you look at your

labor cost plus what the supplier's spending, actually labor is becoming a

bigger component. If you're rolling this up throughout the

value chain, you actually notice that a very significant part of the item in a

vehicle is spent on assembly labor. With the recent trend stores relying more

on suppliers and emphasising purchasing more has done to the P and L statements,

it has been hiding labor costs from our books shifting the labor costs to our

suppliers. However, they haven't disappeared.

They're still in the value chain. At what top notch manufacturing companies

do is working closely with suppliers to further reduce and reduce these labor

costs independent of which books they are listed.

In this session, we introduced two measures of labor productivity.

We talked about labor utilization and we talked about the cost of direct labor.

Either of these two measures is good or bad by itself.

Labor utilization is more a measure of line belts.

However, we might have a perfectly balanced line of very expensive workers,

so a process could be very unproductive but have a perfect labor utilization.

The cost of direct labor is capturing another angle of that productivity.

This captures the wages that we have, as well, as the productivity of the employees

in terms of how many units of output that they can create relative to their wages.

We've also seen how firms can hide labor from their box, and relying more on their

suppliers by outsourcing ultimately that labor.

If you think about Apple and Foxcom, Apple might have only 60 or 70,000 employees,

but Foxcom, as their main supplier, has over a million.

So, just saying that based on the financials of Apple, we don't see a lot of

manufacturing labor there, thus manufacturing labor is not important for

Apple computers, is really misleading. Labor productivity on your books, on your

supplier's books is absolutely critical in operations.

For this reason, we will visit many aspects of labor productivity as we talk

about the productivity module in a week from now.