Many interesting operations are somewhat more complicated than what we can analyse presently with our toolbox. One reason for this complexity is that many processes need to serve multiple types of flow units. Think of an Emergency Department. For example, there are trauma cases, there are severely sick patients, and then there are patients that are just mildly sick. Also, think about our Subway restaurant example. Some people might just want to have a cookie, others want a coffee and a sandwich, and yet others want just want to order for the entire family. The consequence of that is that the processing times that the customers require when they go through the process, they might differ for each and every particular customer. Secondly, even the path that these customers take through the process flow diagram might differ by customer. In this session, we will introduce a more general way of finding the bottleneck and determining flow rate, assuming that there's going to be a mix of flow units that's going to journey through the process. Consider the situation of a tax accounting firm. The firm gets three types of cases come to their office. Easy cases, of which they are arriving roughly 4 cases per hour. Regular cases at a rate arriving at 11 per hour, and cases with foreign accounts, they're arriving at a rate of 3 cases per hours. Now, you notice here in the process flow diagram that while we still have the same symbols of boxes and triangles capturing activities and inventory, that these three different types of accounts are taking different paths through the process flow diagrams. This is illustrated to you by use of color with the GREEN arrows, capturing the flow for the foreign accounts, which is different from the RED flow and from the BLACK flow. How do we find the bottleneck in a process like this? This is arguably somewhat more complicated. We no longer can use our definition that the step with the lowest capacity is the bottleneck. So, the reason that the condition no longer works is that one particular resource might have little capacity, but the flow solution might be such that very few flow units actually require service at the resource. Let me illustrate how you find the bottleneck in a situation like this. You take a look at each of the resources in the process. Each and every one of them is a candidate for being the bottleneck, which could be in this case, the first at Filing, the Foreign Department, Department 1, Department 2, or the Printing Department. Now, each of these resources has a capacity which we just compute as always, the number of resources divided by the activity time. For the first step, that is one over three. This is expressed in applications per minute which we can transform to 20 units per hour. In the same way, we find that the capacity of the Foreign Department is 6 units per hour, 12 at Department one, 15 at Department two, and 30 for Printing. This is expressed in applications per hour. Next, we ask ourselves, what's the demand for service at each and every one of the five resources? Well, there are 3 types of demand here. We have the foreign accounts, there are the regular accounts, and then there are the easy accounts. Each of these 3 flow units is contributing to demand into various resources. If you look at the Filing Department, we have 3 units of the foreign accounts, 11 units of the regular accounts, and 4 units of the easy accounts contributing to demand. This is equal to a total demand of 3 plus 11 plus 4 equals 18 units per hour. At the Foreign step, this situation is different, because only the foreign units, 3 units per hour are going to arrive at this department. There's no demand from the regular units and the easy units. In Department one, we have the 3 units arriving from the Foreign Department, the foreign units. We have the 11 regular ones, but we don't have any ones from the easy. In Department two, however, we have no foreign, no regular, just easy ones at a rate of 4 units per hour. Finally, everybody shows up at printing, and the total demand there is 3 plus 11 plus 4 equals to eighteen. So, you notice here that a nice process for diagram ideally using different colors to illustrate the different flows is going to be very helpful as you do these calculations. Finally, we can compute the ratio between the demand and the capacity as a sense of busy-ness. We will call this measure the implied utilization. Notice that this measure is different from our utilization, which we defined as a flow rate divided by capacity. Flow rate, by capacity, by definition, has to be less than 100%, less or equal to 100%. In contrast, implied utilization can well exceed 100 % if there's more demand for a service than we have capacity. In this case, we notice that 18 divided by 20 is the implied utilization for filing. 3 divided by 6, it's a Foreign Department. 14 divided by 12, it's Department one. 4 divided by 15 at Department two, and 18 divided by 30 at Department three. We see that there's highest implied utilization, 14 divided by 12, which is roughly 116.6%. This highest implied utilization makes the Department one the bottleneck. The first approach was based on simply adding up the flows at the various resources, computing a total flow, and using that as our demand rate. The second approach I want to illustrate is slightly different. Think about work flowing through the system. At each of the resources, we have a certain amount of work that the various resources can provide. For example, at the Filing Department we are able to provide 60 minutes per hour of time. And so, Foreign Department, we have two persons working there and together their able to provide 120 minutes of work. At Department number one, we have 3 people, creating a total amount of time available of a 180 minutes, a 120 minutes for Department two, and then, a total of 60 minutes at the Printing Department. Now, ask yourself, how much work time will be required by each of the flow units? Similar to the previous calculations, we'll look at the 3 flow unit types. So, foreign ones, the regular ones, and the easy ones. Now, we know at the Filing Department, we have 3 units per hour arriving. Each of them will take 3 minutes of work. Regular units, we have 11 units arriving, each of them requiring 3 minutes of work. And easy ones, we have 4 units arriving every hour, requiring 3 minutes of work each. This creates a total workload of 54 minutes. So, the units here are really minutes of work per hour. In the same way, we can compute that in the Foreign Department, we have 3 units arriving, just as before, 3 units arriving. Each of them corresponding to 20 minutes of work. This creates is a total workload of 60 minutes. There's no workload created in the Foreign Department by regular units and the easy units. Department one, we have 3 times 15 minutes caused by the foreign cases, 11 times 15 minutes caused by the regular cases, and no work caused by the easy cases. In Department two, we have only the work from the easy cases of which there are 4 units an hour times 8 minutes per unit. Finally, everybody shows up at printing. Creating a workload of 3 times 2 minutes for the foreign cases, 11 times 2 minutes for the regular cases, and 4 times 2 units for the easy cases. So, if we total these various rows, we see that the workload in the Department one is 210 minutes. It is going to be 32 minutes in Department two, and 36 minutes in the Printing Department. Now, how do we find the bottleneck? We simply compare the time that is requested for work at each of the resources relative to the time available. This creates score of 54 divided by 60, 60 divided by 120, 210 divided by 180, 32 divided by 120, and 36 divided by 60. Note that, these are exactly the same numbers as we have computed in the first approach. For this reason, we can still call this, the implied utilization. So, the numbers here are exactly the same as they are before as far as the implied utilization is concerned. And, you also see that these numbers here, in each of these columns, and these correspond to what we had in the first approach. The benefit of the second approach is that you have more flexibility. For example, it might be that the easy cases take 2 minutes here at printing, while the foreign account cases might take 5 minutes per case. In other words, you can make the processing time contingent on the flow units which you can only analyze with the second approach. The second approach, however, comes at the expense that it is conceptually little bit more difficult because you have to think about the generic flow unit being 1 minute of work. The very useful application of our new way of finding the bottleneck, these were processes that have an attrition loss. Consider the following example of the television firm. The firm is looking for new series that they can air on television. For that, they consider 500 ideas every year. These ideas are pitched, 70 of these 500 are moved towards a script development. These script then are reviewed, and the best twenty scripts are then moved into pilot production. Out of these 20 pilots, 6 are turned into new shows, and then the very best 2 are coming out as new series. The computational finding the bottleneck in this process is very similar to what we have done. It hinges on the basic idea that not every one of these 500 ideas will all the way make it over to the end of the process. For this reason, it is misleading to look at the capacity at each of these 5 steps and pick the lowest one as the bottleneck. Instead, we should do a similar calculation as we did before. This starts by, first, calculation, calculating the flow of ideas to each of the five units. Only two of these 500 will make it all the way to the new series production. Second, we're going to look at the capacity of each of those five resources. And then, third, we will look at the implied utilization as a ratio between the flow and the available capacity. This will determine the location of the bottleneck. Other examples of processes with attrition loss include underwriting processes such as insurance and mortgage applications, as well as assembly processes or other production processes that have quality problems, and where you have to scrap a chunk of the flow units. What do you do if you have a mix of products of flow units going through the same process? One complication that we have seen is a flow unit might take different amounts of processing time than another flow unit at particular resources. Flow units might also differ in how they will journey through the process flow diagram, as we have seen in the example with the attrition loss. In this session, you've learned two methods of how to find the bottleneck in such a system. Both methods are typically are based on the concept of an implied utilization, which looks at the ration between the workload at the resource relative to its capacity. Now, I have to acknowledge that an interesting extension, that we didn't cover in this module, is the case when you can adjust the product mix. You can adjust the products mix to optimize some measures, such as profits, by changing the mix of the percentages of the flow units. This is something that requires some tools that are a little bit beyond what we can do in this first course.