After defining inventory as the number of flow units in the system. Flow rate, the number of flow units flowing through the system per unit of time. And flow time, the time it takes a flow unit from entering the system to leaving the system. The purpose of this session is to find out what are the drivers behind the three variables. In this session, we will introduce a concept of a bottleneck, which is probably the most important definition in this course. We'll also talk about process flow diagrams, which are really maps describing how the flow units goes from being an input into the process, just from leaving the process as a finished unit of output. To see these concepts in action, I would like you to join me, once again, and let's take a walk together over to our local Subway restaurant, and see how the operation now look inside the restaurant. No, time to go inside the restroom. From some training materials that somebody kindly shared with me I now know that there are a couple of tasks that need to be carried out in order to make a sandwich. In this picture, here you see how there are three workers three stations that are making subway sandwiches in this store at this hour. The work started. Station one was greeting the customers, that takes four seconds, followed by five seconds to take the order. If we add up the activities that are carried out by the first station, we get a total time of four + five + four + three + twelve +nine which is equal to 37 seconds per customer. We refer to this time as a processing time. Notice that processing times are always expressed in seconds per customer, so more generally, in units of time for flow unit. In the same way, I can compute that it is taking 46 seconds per customer at station two, and 37 seconds per customer at station three. Again, those numbers are called the activity times. Throughout this course, I will use the words activity time and processing times interchangeably, so pardon the ambiguity when I just said activity times. I really was thinking about processing times. So, be aware of that in the future. Activity times and processing times are one and the same thing. I want to be a little bit of a hand waving here about the toasting activity. Keeping in mind that toasting doesn't require the direct hands on work by a worker, but instead is automated through a touser. If there should be a limited amount of toasting capacity, that is indeed something that we would consider. But for now, I'll be head waving over this matter. Now, this is pretty useful, because now we know that there are three workers carrying out the work. We know all the things that need to be carried out to make a sandwich and we know that the total time it makes it takes to make a sandwich is 37 plus 46 seconds plus 37 seconds. Now, let me proposed a slightly different representation of the same data. This way, we can draw a little picture. It captures the flow of the flow unit through the process here at subway. This picture is called a process flow diagram. Our experience at subway starts with the waiting line, and in general, we will refer with triangles as the pictures capturing wherever there is waiting lines or inventory. Boxes will capture activities, and so we know that the processing time at the first box, is going to be 37 seconds per unit. The work is then handed off to the next worker, which might potentially include some delay, and that's why I draw this triangle here. Where there are another 46 seconds of work. From there, potentially another little waiting before you hit the checkout, there's a third station where again we going to have 37 seconds per unit. Finally, the customer is served and can happily leave the restaurant. Now, I have redrawn this process flow diagram here in PowerPoint to get rid of my ugly handwriting. Just to iterate the symbols, the triangle stands for floor units waiting. Arrows capture the floor unit and boxes capture the resources that are carrying out the activities and the process flow. Now, let me, at this point, refer you to an important difference between project management and process management. Process management, the topic of this course, is all about doing things repeatedly we want to serve hundreds and hundreds of customers over the day and at this point are primarily interested in computing the flow of customers through the process. It turns out that for the flow of customers through the process, it doesn't matter whether the work stations one, two, or three sequentially or in parallel. If all you have to do is make one sandwich, it would be lovely to, for example, bring out the customer, at station three, in parallel to actually making the sandwich at station one and two. But, at the end of the day, every customer here on the floor has to go through station one, two and three. And so, we are not going to serve any more customers by working in parallel. Now , we are ready for some definitions. We have already seen the concept of the processing time which captures how long a resource takes to serve a floor unit. For example, station two in our previous setting had a processing time of 46 seconds per customer. Next, we define the capacity of some resource as one over the processing time. In our case, one over 46. And now, careful with the units, that is customers per second. Now, in casual English, you will typically not say that a worker has a capacity of serving a 46th of a customer per second. If you want to make this something easier to imagine, just multiply this with the 3,600 seconds that there are in an hour. And you see that the worker here at station two is able to serve roughly some 78 customers per hour. Now, this is a case where we have just one person working as a resource. If there are a multiple persons or multiple machines carrying out the same work, we define the capacity as M, the number of parallel resources M divided by the processing time. Now, the chain is only as strong as it's weakest link and if we ask ourselves how much capacity the entire restaurant has, we're going to look for the capacity of each individual step and we will then pick the lowest capacity. This is the idea behind the concept of a bottleneck. The bottleneck is a step with the lowest capacity. Next, we want to figure out the flow rate. We already defined the flow rate as the number of customers going through the process per unit of time. Well, there can never, by definition, be more flow through the process than we have capacity at the bottleneck. However, there might be a situation, when even the bottleneck has some excess capacity. Those are situations where we have insufficient demand. In off hours, late at night, early morning, we might just not have the demand rate to keep the bottleneck busy, and so the flow rate is defined as the minimum between demand and process capacity. We can then compute the utilization of a resource as a ratio between the flow rate and the capacity. Now, remember, the flow rate captures the flow, meaning it captures how much work a resource is currently doing, versus a capacity, which really measures how much work the resource could be doing if it worked all out. Just to reiterate, we already have defined in a previous session , the flow time, the time it takes a flow unit to go through the process. And the inventory, the number of flow units in the system. Now, let's jump to Excel and practice our new definitions. Let's start with the processing times. Station one has a processing time of 37 seconds, Station two have 46, Station three have 37 seconds. And all of this is expressed in seconds per unit. We then saw that the capacity is defined as one over the processing time. And this is now expressed in units per second. If you want to get to the capacity per hour, we simply multiply he previous numbers with three, 600. And this is now expressed in units per hour. Next, we define the process capacity as the minimum of these capacities above, which in this case, is driven here by 78.26. Now, the flow rate is a minimum between demand and capacity. Let's say, for sake of argument, that we have a demand through the process of 50 units per hour. There's 50 customers per hour. We can then compute a utilization, off, remember the definition, we're dividing the flow rate, in this case, it would be demand, flow rate divided by the capacity, which gives us a utilization of 51 percent at the first station. You notice that the utilization is higher at the second station, the bottleneck, with 63 percent and then again, it's 51 percent at the last station. If there is more demand coming our way, so if we improve here the, the demand rate from 50 to 60, the utilization goes up. Notice that according to our definition though, the utilization can never exceed a 100%, because a flow rate is a minimum between demand and capacity. In this session, I threw a lot of vocabulary. We saw how resources and workers have processing times. How we can use the processing times to compute capacity levels. And how the resource with the lowest capacity in the process is called the bottleneck. We also introduced the measure of utilization. Together these calculations help us to determine the flow rate of the process without actually observing the process in action. In the last sessions, we just sat there at subway and counted customers to computer the customer serve for hours. Now, we're actually able to just predict the flow rate by simply knowing the processing times, the staffing level, and the demand rate.