In this session we're continuing analysis of the Subway restaurant. We're going to be zooming in on the labor productivity of the employees at Subway. Specifically we want to have some performance measures we can track telling us how much productivity is going on in the store. For this I will first introduce three new variables. The labor content, the cycle time and the idle time. Based on these three variables, I'll then introduce two new performance measures. They'll be called the average labor utilization and the cost of direct labor. 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 on 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 plot flow rate as the minimum between the amount and capacity. Finally we previously defined the utilization as a ratio between the floor rate and capacity. Now consider the following process, imagine I have four stations each staffed with one worker. The processing times are shown here in this picture in green, you see that station one has a shorter processing time than station four. Consequently, given that their'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, nd three have some slack time relative to our bottleneck. We refer to this slack time as idle time. To formally figure out how much red time, how much idle time these thre steps have, let me introduce a concept of cycle time. So 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 subsequence units. For example I might say that this program 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 a sum of the processing times. This is simply, in the previous pictures, the sum of the green box. Next we define for each resource the idle time as the difference between the cycle time and the processing time. So the idle time for the first resources is exactly this difference here. We can add that idle time up across all resources to get the total rec 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 direct idle time. The labor content really measure how much green there is in the process versus the labor content plus a 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, for workers times the hourly wage rate divided by the flow rate per unit of time. To practice our new definitions, consider the following example. This here is a machine pace line consisting of six workers working in sequence. It is a machine pace 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 and thus X is capacity that station cannot run ahead. The entire process will be paced by the slowest step that we will see in a moment. This to station number five. Now let's practice our definitions. We have some processing times over here in this first row. Next we can compute the capacity as simply as 1 over the processing times. For the first one let me put the units that's on here. So this is unit per minute. 1 over 5, 1 over 2, 1 over 3, 1 over 6, 1 over 2. 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 are going to have a flow rate. That is going to be one unit every six minutes which corresponds to six units 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 bottleneck. Next we can compute the idle time at each of the resources as the 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 samples and processing times which is 3+5+2+3+6+2, which makes a total of 21 minutes per unit. The total idle time, across all units is 3+1+4+3+4 which is 15 minutes. You can then define the average labor utilization as 21 minutes labor content divided by 21+15 which is the average utilization in this process. We can also compute the cost of direct labor in this process as a ratio between the wages and the flow rate. Say for sake of argument each of our workers is making $20 per hour. So my wages are 6 workers times $20 per hours, divided by the flow rate, which we said was 10 units per hour. This gives me a direct cost of labour of $12 per unit. Let me take this calculations that are arguably somewhat messy right now, and plot them over in my Excel spreadsheet where you can read them more clearly. Alright. Let's review this calculation in Excel. So first thing we're going to do is we compute the capacity of each of the resources as 1 divided by the corresponding processing times. This is now expressed in units per minute. Next, we're going to compute the process capacity as the minimum of the individual capacity levels which determines that station five is indeed as we expected the bottleneck. We can then compute the floor rate as the minimum between demand and capacity. We assumed here that there was sufficient demand and so the floor rate is given by the process capacity. We can then compute the cycle time. Is one divided by the flow rate which is telling us that we're 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 a total idle time which we confirm to be 15 minutes. Now is 15 minutes a lot of idle time, or not? This is really hard to judge. And so we compared this number to the total labor content in the process, which we previously defined as the sum of the activity times. I can then compute my labor utilization As the ratio between the labor content and the labor content plus the idle time. 58% is my average labor utilization in the process. Note the following. Let's quickly compute a utilization of each of the six steps in the process. Utilization remember is the flow rate divided by the capacity. You notice 100% utilization at the bottleneck which I hope is intuitive, we can then go ahead and we can average the utilization of the six recourses. And we also see a 58.3%. At a risk of repeating myself lets go back to the Subway example and revisit the previous calculations that we did. Now extend these calculations, as the following. So cycle time is computed as follows, we said since there were 60 customers per hour, that means every 60 seconds, since there are 3600 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, it's 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 a 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 0.66 +0.6%. 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&L from big corporations and manufacturing these days, you actually see relatively little labor costs on their P&L's. My colleague from NRT, Dan Whitney 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% 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, we're also going to spend 70 to 80% of the total cost. Of procuring costs or items such as disk drives and microprocessors. Now, the labor cost here, if you look at things related to assembly labor and maybe inventory costs, 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. That includes their labor cost. So, you see, that if you look at your labor costs, that's what the supplier is spelling, that your labor is becoming a bigger component. If you're rolling this up throughout the value chain, you will 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 emphasizing purchasing has done to the P&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. And what top notch manufacturing companies do is working closely with their suppliers to further reduce and reuse its' labor cost independent of which books they are listed. In this session we introduced two measure of labor productivity. We talked about labor utilization. Here we talked about the cost of direct labor. Neither of these two measures is good or bad by itself. Labor utilization is more a measure of line balance. However, we might have a perfectly balanced line of very expensive workers, so the process could be very unproductive but have a perfect labor utilization. Because of direct labor is capturing another angle of the productivity. It 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 books are relying more on their suppliers by outsourcing ultimately the labor. If you think about Apple and Foxconn, Apple might only have 60 or 70,000 employees. But Foxconn as their main supplier has over a million. So just saying that based on the financials at Apple, we don't see a lot of manufacturing labor there. Manufacturing labor is not important for Apple computers. It's really misleading. Labor productivity on your books, on your suppliers books is absolutely critical in operations. For this reason, we revisit many aspects of labor productivity as we talk about the productivity module in a week from now.