Many interesting operations are somewhat more complicated then what we can analyze presently with our tool box. One reason for this complexity is that many processes need to serve multiple types of flow units. Think of an emergency department. They have trauma cases. The 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 might just want one 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 in 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 four 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 three cases per hours. Now you notice here in the process flow diagram that while we still have the same symbols of boxes and triangles kept showing activities and inventory that these three different types of accounts are taking different paths through the process flow diagram. This is illustrated here by use of color. With the green arrows capturing the flow from the filing account, 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. The reason that the definition no longer works is that one particular resource might have little capacity, but the flow of the flow units might be such that very few flow units actually require service at the resource. Let me illustrate how you find a 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. It could be, in this case, the first step, filing. So foreign department, department one, department two, or the printing department. Now each of these resources has a capacity, which we just compute as always. A number of resources, divided by the activity time. For the first set, that is one over three. This is expressed in applications per minute, which we can transform to 20 units per hour. In this same way, we find that the capacity at the foreign department is six units per hour; 12 at department one; 15 and department two; and 30 per printing. This is expressed an 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 three types of demand here. There are the foreign accounts, there are the regular accounts, and then there are the easy accounts. Each of these three flow units is contributing to demand and to various resources. If you look at the filing department, we have three units of the foreign accounts, 11 units of the regular accounts, and four units of the easy accounts, contributing to demand. This is equal to a total demand, what's three plus 11 plus four equals 18 units per hour. In the foreign step the situation is different because only the foreign units, three units per hour are going to arrive at this department, there is no demand from the regular units and the easy units. In department one, we have the three 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 four units per hour. Finally everybody shows up at printing and the total amount there is three plus 11 plus four equals to 18. So you notice here that a nice process flow 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 a ratio between the demand and the capacity as a sense of business. We will call this measure the implied utilization. Notice that this measure is different from our utilization, which we define as a floor ray divided by capacity. Flow rate by capacity by definition has to be less than a hundred percent, less or equal to a hundred percent. 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 implied utilization for filing. Three divided by six at the foreign department. 14 divided by 12 at the department one, 4 divided by15 at department two, and 18 divided by 30 at department three. We see that the highest applied utilization, 14 divided by 12, which is roughly 116.6%. This highest implied utilization makes 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 had 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. At the foreign department we have two persons working there and together they're able to provide 120 minutes of work. At department number one, we have three people creating a total amount of time available of 180 minutes. 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 three flow unit types. The foreign one, the regular ones, and the easy ones. Now, we know It's a filing department. We have three units per hour arriving. Each of them will take three minutes of work, regular units. We have 11 units arriving. Each of them requiring three minutes of work. And the easy ones, we have four units arriving every hour. Requiring three 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 following department we have three units arriving. Just as before, three units arriving, each of them first went into 20 minutes of work. This creates a total workload of 60 minutes. There is no workload created in the foreign department by regular units and the easy units. Department one, we have three times15 minutes caused by the foreign cases. 11 times 15 minutes, caused by the regular cases, and no work cost by the easy cases. In department two, we have only the work from the easy cases, of which there are four units an hour times eight minutes per unit. Finally everybody shows up at printing, creating a workload of three times two minutes for the foreign cases, 11 times two minutes for the regular cases and four times two 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 a score of 54 divided by 60, 60 divided by 120, 210 divided by180, 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. What is this reason? We can still call this the implied utilization. So the numbers here are exactly the same as they were before as far as the implied utilization is concerned and you also see that these numbers here, in each of these columns, indeed 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 easiest cases take two minutes here at printing, while the foreign account cases might take five minutes per case. And now the worse 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 is conceptually a little bit more difficult because you have to think about the generic flow unit being one unit of work. The very useful application or new way of finding the bottleneck. This was processes that have an attrition loss. Consider the following example of a 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 the script development. The scripts then are reviewed, and the best 20 scripts are then moved into pilot production. Out of these 20 pilots, six are turned into new shows and then the very best two are coming out as new series. The computation of finding the bottom line 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 end of the process. For this reason, it is misleading to look at the capacity at each of these five steps and pick the lowest one as the bottleneck. Instead, we should do a similar calculation as we did before. This starts by first calculating the flow of ideas to each of the five units. Only two of these 500 will makes it all the way to the new series production. Second we're going to look at the capacity. At each of these 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 floor units. What do you 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 of the 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 bottle neck in such a system. Both methods are what we have based on the concept of an implied utilization, which looks at the ratio between the work load of that resource relatively to its capacity. Now I have to acknowledge that an interesting extension that we didn't cover in this module is the case where you can adjust the product mix. You can adjust the products mix to optimize some measure such as profits by changing the mix, the percentages of the flow units. This is something the requires some tools that are a little bit beyond what we can do in this first course.