Now in the last session we've seen our desire to produce in large batches. Large batches are good for capacity. Now let's go back to our early example of the restaurant that is producing cheeseburgers and veggie sandwiches. Imagine we're producing 100 cheeseburgers, followed by 100 veggie sandwiches. That is, however, just the supply side of the business. From the demand side, it's very unlikely that customers walk into the store, from 1:00 to 2:00, they just order cheeseburgers, and from 2:00 to 3:00, when we're making veggie sandwiches, they just all order veggie sandwiches. More realistically, you have a veggie customer come in, a cheeseburger customer, a veggie, a cheeseburger. The demand is just more realistically mixed. So when you're producing in these large batches, what you're doing, is you're creating a mismatch between supply and demand. And that leads to what? Exactly, it leads to inventory. Either we will have customers waiting for their sandwiches while we're making cheeseburgers, the veggie customers are lining up waiting for their veggie sandwich and their production run to start, or we have sandwiches waiting for customers. Long batches leads to inventory. Now let's formalize the example of that restaurant making cheeseburgers and hamburgers. Look at what's happening in the kitchen. See, during this time here we're making cheeseburgers. Follows by a long batch of veggie sandwiches. Now, what's happening to inventory as we produce? While we are producing cheeseburger, we are serving the cheeseburger demand. But we also have to prepare for those days where we're making veggie sandwiches, and thus, we have to accumulate cheeseburger inventory. In contrast, veggie inventory is declining because I'm serving customers who want a veggie sandwich, but I'm not producing any veggie sandwiches right now, so that inventory is going down. Once I switch production, and then move from producing cheeseburger to veggie sandwiches, the reverse happens. The veggie inventory is start to build up, and the cheeseburger inventory will be, in the very meaning of the word, will be eaten up. You see that the average inventory level, on the left side here, is relatively high. That's what I meant when I said long production runs and big batches lead to lots of inventory. Now consider an alternative. Consider a frequent change over from making the cheeseburgers to making the veggies, to the cheeseburgers, to the veggies. It doesn't necessarily have to be a batch size of one, but you notice the batches are much smaller here in the restaurant on the right. Notice how this smaller batches are leaning to less inventory here in the process. In the extreme case, we would be switching between cheeseburger, veggie, cheeseburger, veggie, one by one. This is what's called mixed model production, or in the Toyota production system that we'll discuss later on in this course, we refer to this strategy as heijunka. Now, this example does not consider the impact that the larger batches have a lowered capacity because of the setup times. As we discuss later on in this module, reducing the setup time is a very important enabler of a mixed model production strategy. Now in the previous example, I defined a batch as a collection of floor units that were produced between two setups. This is a definition that is quite common in practice. However, I will now argue that this definition needs some generalization to be really useful for more interesting cases. Consider a firm that is making two products, A and B. Cheeseburgers and veggie sandwiches. Demand for A is 100 units per hour, and demand for B is 75 units per hour. The production line can make 300 units per hour of either of the products, and so our processing time, P, is simply 1 over 300 hours per unit. It takes thirty minutes to switch production from A to B, and so we have a set up time of half an hour. Now, earlier on when we defined the batch, we were looking at a collection of product A, cheeseburgers. We call that a batch. In a setting where you're producing multiple products, potentially with different demand rates, I found it useful to take a different approach of what we think of a batch. In this case here, we're producing product A. We're then going to run a set up from A to B. We're going to produce a bunch of product Bs. We change over again from B to A. And then we go back to producing A. Instead of the previously somewhat more narrow view of the batch, I now want you to think of a batch as all of these units, of A and of B that we see before repeating the pattern of production. With that definition in mind, you notice that we're going to have two set ups that are happening in this batch, or another term for this is a production run, both of them now a half hour long, so that means, really, the total is one hour of setup. Now, how are we going to choose the batch size here? Well, we know that we're going to have 170 units per hour to stay on top of demand. This is simply our target flow. Now, the capacity formula we introduced early on in this module set is a flow of the capacity that we can get out of a system with setup, is driven by the batch size, divided by the setup time plus the batch size times the processing time, P. In our example here, that is batch size divided by one hour, plus the batch size times 1 over 300. This gives me a simple equation, 175 has to be equal to the batch size divided by 1 plus the batch size, times 1 over 300, which is a linear equation in B. I can simply cross multiply with 1 plus B divided by 300. And I can solve for B to get B equals to 420. Now, that means that the batch size, that is a total number of parts that are produced before repeating the pattern again. So those 420, they're a bunch of As, and a bunch of B. Now we notice that I have to make more As than Bs, and so, for that reason, I can take those 420 and simply make sure that the ratio from A to total is reflecting this. So I multiply this simply with 100 of A, divided by 175, which is the total. And that gives me 240 of product A, and then I know that since I have 420 in the batch total, 240 that means that leaves 180 for B, that would simply be 420 times 75 divided by 175. And so, we will now refer to as a batch as 240 of type A, followed by setup, followed by 180 of type B, followed by setup, and that completes the production line. Now let's continue the example of the previous slide and imagine the case that our marketing folks are adding a third product to the mix. This might be a situation where our old product A is simply offered in two versions, A1 and A2. Total demand, we assume for now, is staying the same. So product A1 is offering fifty units. Fifty units of A2, this is our old demand of 100 units per hour of A. And then B, 75 units per hour. And that's our old 175 units per hour. So set up times are still as before. Takes a half hour to switch from any one product to another, and it is taking us P equals to 1 over 300. And there would be, again, hours per unit. Now, the production run that we're looking for is going to look something like this. We're going to to make some A1s, then we're going to to change over and make some A2s. We change over, we make some Bs. We change over, and then we start again. So the production run would look like this, and the batch is really a collection of A1s, A2s, and Bs. The question here is, of course, how do we choose the batch size? Well, again we have to produce at 175 units per hour. We know that this is equal to the batch size divided by the set up time plus the batch size times P. You notice now, however, that there are three setups in a production run. And for that reason, S is now no longer 1, but 1.5. Everything else really stays the same. And just as we did before, we can solve for B, and I leave that to you as a homework assignment. You will find that B is equal to 630 units. So 600 units are set up before the whole pattern repeats itself. From the 630 units 630 times 50 divided by 175 equals to 180, are going to be produced on A1. The same, 630, 50 to 175. 180 will be A2, and Bs will be 630 times 75 divided by 175, equals to 270 will be of product B. In other words, the production run will look something like the following, 180 A1s, setup, 180 of A2, setup, and then 270 of product B. What you see here is that the production runs got longer compared to the previous example. The total demand has stayed the same, but by adding a third product to the mix I have increased the length of the production run, and I'm now working in larger batches. Note further that product B, which really has not been affected in terms of its demand, is also produced now in larger batches than before. Instead of making 180 of product B, I'm making 207. So what we've seen here is that more setups force us to spend more capacity on setup. That means we have to do bigger production runs to keep up with the total demand rate, and that will lead to more inventory. So, once again, you noticed how variety leads to more setups, which leads to more inventory. This is one of the biggest costs of offering variety. Batches create a mismatch between supply and demand. Batches are thus a route cause for inventory. In this session, we have seen that a firm that increase its variety by, for example, adding a third product to its product line, is going to be forced to add more inventory. The reason for this was holding the overall flow constant. The extra product required extra setups which we can only afford if we run longer batches. The dream of every plant manager is to produce at exactly the rate and the mix of demand. This is what is called heijunka, mix model production. And so we'll see later on in this module, this, however, requires that we get these setup times reduced further and further. This is done by a technique that we will refer to as ZMET.