The last session we've seen no desire to produce in large batches. Large batches are good for capacity. Now let's go back to our earlier example of the restaurant that is producing cheeseburgers and veggie sandwiches. Imagine we are 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 in the store from one to two will they just order cheeseburgers and from two to three 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. [inaudible]. 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 the restaurant making cheeseburgers and hamburgers. Look at what's happening in the kitchen. See, during this time here, we're making cheeseburgers, followed 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 when we are making veggie sandwiches, and thus we have to accumulate cheeseburger inventory. In contrast, veggie inventory is declining because I'm serving customers. Who wants a veggie sandwich, we'll I'm not producing any veggie sandwiches right now so that inventory is going down. Once I switch production and I move from producing cheeseburger to veggie sandwiches the reverse happens. My 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. Doesn't necessarily have to be a batch set of less than one but you notice that the batches are smaller here in the restaurant on the right. Notice how the smaller batches are leading to less inventory here in the process. Is extreme case, we would be switching between cheeseburger, veggie cheeseburger, veggie, one by one. This is what's called mixed model production, all in the Toyota production system, and we'll discuss later on in this course. We refer to this strategy as hai junka. Now, this example does not consider the impact that the larger batches have on lowering capacity because of the setup times. As we'll discuss later on, on this module, reducing the setup times is a very important enabler, of a mixed model production strategy. Now in the previous example I defined a batch as a collection of [inaudible] 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 formulas relating to 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 product and so our processing time, P, is simply one over 300 hours per unit. It takes 30 minutes to switch production from A to B, and so we have a setup time of half an hour. Now, earlier on, when we defined a batch, we were looking at a collection of product A, Cheeseburgers. We called that a batch. In the setting where you're producing multiple products, potentially with different demand traits, 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 gonna run a setup from A to B. We're gonna produce a bunch of product B's. 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 recede before repeating the pattern of production. With that definition in mind, you notice that we're gonna have two setups that are happening in this batch or another term for this is, is a production run. Both of them now in half an hour long, so that means really the total is one hour of setup. Now, how are we gonna choose the batch size here? Well, we know that we're gonna have. 170 units per hour to stay on top of demand. This is simply our target flows. Now, the capacity formula that we introduced early on in this modulus says its a floor, the capacity, that we can get out of this system was set up is driven by the batch size, divided by the set up time plus the batch size times the processing time p. In our example here, that is batch size, divided by one hour, plus said batch size times one over 300. This gives me a sample equation. 175 has to be equal to, the batch size divided by one plus the batch size. One over 300 which is a linear equation in B, I can simply cross multiply with one plus B divided by 300. And I can solve for B, to get B equals to 420. Now that means that this, the batch size, it is the total number of parts that are produced before repeating the pattern again. So those 420 they are bunch of A's in a bunch of B. Now, we notice that I have to make more A's than B's. And so, for that reason I can take 420 and simply make sure that the ratio from A to total is reflecting this so I multiplied it simply with 100 of A divided by 175 which is a total and that gives me 240 of product A. And then I know that since I have 420 in the veg total, 240, That means that there's 180 for B. That would simply be 420 times 75 divided by 175. And so we would now refer to a [inaudible] as 240 of type A followed by set up followed by 180 of type B followed by a set up, And that completes the production run. 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 50 units. 50 units of A2, this is our old demand of a 100 units per hour of A. And then B, 75 units per hour. And that's all old, 175 units per hour. The setup times are still as before, takes a half hour to switch from any one product to another. And it is taking us P = 1/300, and that would be, again, hours per unit. Now the production run that we're looking for is going to look something like this. We're gonna make some a1. So we're gonna change over, make some A2's. We change over, we make some B's. We change over, and then we start again. So the production run would look like this, and the batch is really a collection of A1's, A2's and B's. 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 set-ups in a, production run. And for that reason, S is now no longer one but 1.5, everything else really stays the same and just as we did before we can solve for B and I'll leave that to you as a homework assignment. You'll find that B = 630 units. So 630 units is set up before the whole pattern repeats itself. From the 630 units. 630 times 50, divided by 175, equals to 180 . Are gonna be produced on A1. The same, 630, 50 to 175. 180 will be a2. And b's will be 630 75 / 175 = to 270, will be of product B. Now the words of production run will look something like, like the following. 180 A1's set up, 180 of A2 set up. And then, 270 of product b. What you see here, is its productions runs got longer compared to the previous example. The total amount stays the same, but by adding a third product to the mix, I have increased the length of the production run and I'm now I am 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 part B, I'm making 270. So what we're seeing 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 notice how variety leads to more setups, which leads to more inventory. This is one of the biggest cost of offering variety. Did I just squeeze it to mismatch between supply and demand. But I just have that's a root cause for inventory. In this session we will see how a firm that increases its variety by, for example adding a third product to it's 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 set-ups 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 [inaudible]. Mixed model production. As we will 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 SMET.
