So why are some operations more productive than others? Why are some operations more responsive than others? To answer these questions we have to go inside the business processes that make up for the operations. This is the purpose of this module, process analysis. In this module, we're going to introduce the three most important performance measures of an operation, which are called flow rate, also known as the throughput, inventory, and flow time. To motivate these three performance measures and get some intuition on how process analysis works, I would like you to join me once again over to our local subway restaurant, and just see what's going on. We'll make ourselves outside, comfortable outside the restaurant and we'll just spend a couple of hours observing how people come in and out of the restaurant. Now we're here to learn not to eat, and so I will not let you get inside the restaurant, instead I will give you an assignment. Keep track at what times the various customers arrive. Then try to draw the following graph. On the x-axis in this graph you're going to plot the time. On the vertical dimension you're going to draw the cumulative number of the customers that have arrived. That means if the first customer arrived after two minutes and 30 seconds, you're going to draw the first point here. If the next customer came in a minute later, at three minutes 30, the second person has arrived and you're going to plot another data point over here. So, step-by-step, you're going to draw the times of which customers arrive and then the number of the customer that just have arrived. This will create a graph that we can call the cumulative inflow of customers to the restroom. I will do a similar exercise. I will draw a graph, but my time points are not based on the arrival of the customers but based on their departure. So whenever there is a customer leaving I'm going to draw a step up and keep track of the departure times. When we do this, we're going to get a graph that looks like the following. Now 25 minutes later, you and I will have collected the following data. I will show your graph and my graph on the same piece of paper. The information here looks like this. Remember, you were in charge of keeping track of the cumulative inflow of the customers here while I was computing the cumulative outflow. You'll notice that our first customer came at roughly 30 seconds into it. And then stayed in the system for about a minute and a half. At which time, the customer left again. That's when I grab the customer and make this person an outflow. If you look at our two graphs, you can see a couple of interesting things. The vertical distance between our graphs is a number of customers currently in the restaurant. These are customers that went in, that have not yet come out of the restaurant. The horizontal difference between our lines is the amount of time the customer spent in the restroom. We saw this was the first customer who arrived after roughly 30 seconds of observation time and then left after two minutes. And then we see later on that some customers have a little longer wait. So for example if you look here at the seventh customer, this person came in around here and it took until here, until this person was leaving. This suggests that there was beyond the activity times in the process potentially a fair bit of waiting going on. Now before we can do any process analysis we first have to define what we want to analyze. We defined the flow unit of the process as the atomic unit of analysis. In this case we want to analyze the flow of customers. Note that we could also analyze other things in the process, for example, the flow of cheese, the flow of money, the flow of sandwiches, or other things. For this computation here, our flow unit is, indeed, the customer. We define the flow rate of the process or also known as the throughput. That's the number of flow units going through the process per unit of time. This is expressed in customers per unit of time. For example, customers per hour. It's simply correspondent to the slope of the two lines that we've just been drawing as a cumulative influence or cumulative outflow. Second, we define the flow time as the time it takes the flow unit to go through the process. This was, as you recall, the horizontal difference between the inflow line and the outflow line. And third, we define the inventory as a number of flow units in the process at any given moment of time. This was the vertical distance between your line and my line. Given how important these three definitions are, let's practice them with four examples. Consider first an immigration process. In this case the flow unit would be the Visa application. The flow rate would be the total number of Visa applications that are either approved or rejected in a given period of time. So flow time would be the processing time, how long our Visa applicant had to wait for his or her Visa. And finally, the inventory would be the number of pending cases. Next consider the production of champagne. The flow unit would be a bottle of champagne. The flow rate would be the bottles sold every year. The flow time would be the time that the champagne would sit in the cellar before it is sold. And the inventory would simply be the content of the wine cellar. Consider an MBA program as a production process. So flow unit here is the student. The flow rate is the incoming and, or the graduating class, so simply the number of students going through the process per year. The processing time at least here at Wharton, it's a two year program, so that's the time that the student spends at school. The inventory time is the total number of students on campus in the first year and in the second year. And finally consider a car company. The flow unit here is a car. And the flow rate is the amount of cars sold every year. So flow time is the time from the beginning of the production to the time that the vehicle is finally sold, and the inventory of the cars and the system. Notice that only in the second and fourth case here, my definition of inventory will be similar to the world of financial accounting. In this case here, and in this case here or the service settings, these are flow units that I would never show up on the balance sheet of an organization. So inventory, the number of flow units in the system. Flow rate, the number of flow units going through the system per unit of time. And flow time, the amount of time it takes a flow unit to go from the beginning of the process to the end. I said at the beginning of this session that those are the most important performance measures in any operations. But why? Who cares about inventory? Now let me give you some reasons to care about inventory. In the US economy alone, in a typical year, we have about $1 trillion of inventory. And that is just the manufacturing sector, because this is accounting inventory. Now we'll notice that I, as an operations professor, define inventory somewhat carefully and somewhat differently from an accountant. For me a customer waiting for service in the hospital is inventory. You will not look at a balance sheet of a hospital and see the patients there are listed as an asset. For me, these people are inventory. Inventory happens whenever you have mismatches between supply and demand. Now my colleagues in Economics Department, they kind of like to ignore the supply-demand mismatches. They take comfort in the notion of markets and that prices will adjust once we have a mismatch between supply and demand. However, if you are sick, and you're sitting in an emergency department prices were not source of problem. If you're hungry waiting for your lunch, this is not a matter of prices. For this reason I argue that understanding inventory, flow rate, and flow time are indeed the most important issues, not just what we do in operations, what we do in management in general. So, keep those three measures in mind when, next time, you go through a process, be it as a tourist, as a person going for lunch or when you have a chance to tour a factory. And always look for the three things, flow rate, inventory, and flow time.