The size of a 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 setup. Now, consider again the process of the apparel making. Recall the four steps in the process including the cutting department, section one, section two and finally, the finishing. Recall that only the first step, the cutting department, actually had setups. Now, let's first consider and arbitrary batch size of B equals to five. With B equals to five, our capacity to cutting is, remember the formula, B divided by the setup time plus B times the processing time which turns, in this case, to five divided by twenty plus four times five, and that is five divided by 40 which is 0.125. Then, the next step we have eight divided by 40. Notice there's no set-up time here and so we can just use our good old formula, number of workers divided by the processing time. So, eight by 40 that is 0.2, five by 30 which is 0.1666. And then, one divided three which is 0.333. So, for batch size of B equals to five, we see that the bottleneck is going to be at the cutting machine, Right? You notice that the capacity here is at its minimum. Now, that was just an auditory backslash of B equals five. Let's consider another one. Say, B equals to 50. Now, at B equals to 50, here's what's going to change. At the cutting machine, we now have to look at 50 divided by twenty plus four times 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 at 0.1666 for section two, 0.333 for the finishing department. Now, look what has happened. By increasing the batch size on B equals five to be 50, we have been able to shift the bottleneck. Now, the bottleneck is at section two. Now, this is interesting in the sense that, by choosing the batch size, we determine the bottleneck.. For B equals five, it looks like all batch size currently is too small. Why is that? Because everytime we, we shut down the machine, everytime we shut down the cutting machine, we shut down the entire plant because cutting is the bottleneck.. However, for B equals to 50, The batch size seems to be too big. Why is it too big? Well, we are optimizing the capacity or we are increasing the capacity of the cutting machine that is really of no value. We are ultimately constrained by section two. 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 two. 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 bench size, but only to a point, only to the point of the capacity of the next lower step. So, at a good batch size, the line is balanced which means as you UNKNOWN there's a capacity as a function of the batch size, which in our case, is B devided by twenty plus four times B is exactly the same as the capacity at the next, lower, step, which is five divided by 30. Solve this and you get 30 b, B after you cross multiply, is equals to 100 plus twenty B and then you see that b, B has to be, equals to ten. At B equals ten, 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 there's a constrain 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 occur at the, the bottleneck machine, you have a strong incentive to increase the batch size. After all, every time that you're setting up, it's a bottleneck, it's like shutting down the entire plant. If however, the setup, the setup requires 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 is how the Haunted Mansion works. Like the most Disney attraction, you the long line of people standing outside, waiting to get in. Inside the Haunted Mansion, there is 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 is one or fifty people in the elevator, it takes roughly two minutes to go down in the elevator. Once you're in the basement, there is like a long line of moving chairs that take you through the dungeons, through the basement of the haunted mansion. There is basically a never ending line of moving chairs. They 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 the seats down here would be empty. If however, you're going to squeeze 50 people into the elevator at once, the result will be, that the force of the elevators are going to be big, but at the expense of the inventory of working 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 size. It applies in my little spooky example here at Disneyland, that is exactly the same insight I want you to take out of this session. Setups wastes capacity. So what? If the resource, the machine we're setting up is not the bottleneck, capacity at that step is plentiful. So, wasting a little bit of capacity and 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 in the process, We're looking for the sweet spot at which the capacity of the resources was a setup is just at the point of the capacity of the slowest step in the rest of the process.
