The size of the batch is not written in stone. The size of the batch is under the control of management. Maybe by being smart about the batch size, we can try to improve the process. We could potentially increase capacity or we can reduce the inventory level. But how do you set a good batch size? What is a good batch size? This is the topic of this session. In the previous session we chose the batch size B, based on demand. We pretty much ignored the rest of what's going on in the process, we just looked at the one machine with this set up. Now consider again the process of the apparel making. We call the four steps of the process including the cutting department, section 1, section 2, and finally the finishing. We called it only the first step, the cutting department, actually had setups. Now, let's first consider an arbitrary batch size of B equals to five. With the B equals to five, our capacity at cutting is, remember the formula B / the setup time, + B x processing time, which turns in this case, to 5 / 20 + 4 x 5, and that is 5 / 40, which is 0.125. Then as a next step we have, 8 / 40. Notice there's not set up time here, so we can just use our good old formula, number of workers divided by the processing time so, 8 / 40, that is 0.2. Five by 30, which is 0.1666. And then one divided by three, which is 0.333. So, for batch size of B=5, we see that the bottleneck Is going to be as a cutting machine. Right you notice that the capacity here is at it's minimum. Now that was just an arbitrary batch size of B=5. Let's consider another one. Say B=50. Now at B=50, here's what's going to change. It's a cutting machine. We now have to look at 50 / 20 + 4 X 50 and that is simply 50 divided by 220 which is roughly 0.227. And the other capacities have not changed because there was really no setup involved. Their capacity is independent of the batch size and remains as 0.1666 for section 2, 0.333 for the finishing department. Now look what has happened. By increasing the bench size on B = 5 to B = 50, we have been able to shift the bottleneck. Now the bottleneck is at section 2. Now this is interesting in the sense that, by choosing the batch size, we determine the bottleneck. For B = 5, it looks like our batch size currently is too small. Why that? Because every time we shut down the machine, every time we shut down the cutting machine, we shut down the entire plant. Because cutting is the bottleneck. However, for B = 50, the batch size seems to be too big. Why is it too big? Well, we are optimizing the capacity, we are increasing the capacity at the cutting machine, but it's really of no value. We are ultimately constrained by section 2, and so what's the point of operating in higher batches, hence higher inventory at the cutting machine, only to notice that the constraint is then at section 2? To choose a good batch size, what you want to do, is you want to balance the line. You know that you can increase capacity here by increasing the batch size, but only to a point, only to the point of the capacity of the next lowest step. So had you got batch size a line is balanced which means, as your dryer plays that's a capacity, as a function of the batch size, which in our case is B / 20 + 4 x B is exactly the same as the capacity at the next lowest step which is 5 / 30. Solve this and you get 30B after you cross multiplied = 100 + 20B, and then you see that B = 10. At B = 10, we balance those forces of the one hand the desire to increase capacity at the cutting machine. But on the other hand, not to waste capacity because it's a constraint downstream of the resource with the setup. So what is the bigger lesson here? The insight I want you to get, is that if setups are currently the bottleneck machine, you have a strong incentive to increase the batch size. After all every time that you are setting up, it's a bottleneck, it's like shutting down the entire plant. If, however, the setup occurs a non-bottleneck resource, then we have plentiful capacity at that resource since the process capacity is going to be constrained by some other resource further down the line. Now, to see this in action, consider the following example. A little while ago, I went to a place in Disneyland called The Haunted Mansion. Here's how The Haunted Mansion works. That was most Disney attraction, you have a long line of people. Standing outside, waiting to get in. Inside the haunted mansion, there's an elevator that takes people down into the basement. Here's how the elevator works. The elevator has a certain number of people that are allowed in. And then independent of whether there's one or 50 people in the elevator, it takes roughly two minutes to go down the elevator. Once you are in the basement, there is like a long line of moving chairs that take you through the dungeon, through the basement of the haunted mansion. There is basically a never-ending line of moving chairs- That make you see quite spooky stuff. Standing in line here, and the operations professor that I am. I was wondering how many people at once should these folks at Disney, let into the elevator. If they just take one person at a time, well, what's going to happen is the flow through the elevator would be rather small. In which case, many of these seats down here would be empty. If however, you're going to squeeze 50 people into the elevator at once, the result would be, that the flow through the elevator's going to be big, but at the expense of inventory of waiting people in the basement. How do you set the number of people in the elevator? You want to find exactly the balance, so that the flow through the elevator is equal to the flow of the chairs in the basement. This is the intuition how to set a batch size. It applies in my little spooky example here at Disneyland, but it is exactly the same insight I want you to take out of this session. Setups waste capacity. So what? If the resource, the machine we are setting up is not the bottleneck, capacity at that step is plentiful. So wasting a little bit of capacity in return of a lower inventory level is, actually, a pretty good idea. If, however, the setup occurs at the bottleneck machine, setting up the machine is like stopping the entire process. For this reason when we choose a good batch size on the process, we're looking for the sweet spot at which the capacity of the resource was a setup, is just at the point of the capacity of the slowest step in the rest of the process.
