Alright time for some review questions. The first question is about batching and you can see the problem described here so we are producing these window boxes and the window box consists out of, two types of parts. Is one part A in there and two part B's in there. It takes the stamping machine that we're running it takes it 120 minutes to change over from A to B but then also another 120 minutes to go from B to A. Currently, we're producing in batch sizes of 360. And so, look here at the, we're 360 A's followed by 720 B's. And so you can think of this as us producing really 360 times these entire window boxes. And that includes just 360 As and 720 Bs Once a machine is set up, you notice that it takes us one minute to produce a part A. And it takes us half a minute per part B. And so since we had, have two of them, that means it takes us also one minute to get. The B stuff done for the window box. Then downstream from the stamping machine in assembly we have twelve workers and they put these window boxes together in 27 minutes triple. As usual, I suggest you put me on pause now, tackle the questions yourself and see how you're doing then press on play again and check your results. Now the first question, Look at the capacity at the stamping machine. We call that, when we have set-ups, we have to look at the capacity of the function of the bench size by taking the bench size. And dividing it by the set up time plus the bed size times, the time per unit. Now, how does this play out in this example here? The batch size is easy right now, That's given to us as 360. Now, as a setup, I have to admit, it's a little confusing, right? It's tempting to take these 120 minutes described over here. But remember that really two setups happening per window box. The A setup and the B setups. And it was a reason we have to look at 240 minutes of setup time. Plus the batch size, 360 times a processing time per unit and the same logic as we're gonna need one minute to deal with part A. We're gonna need two times half a minute to deal with the two B's. And so, per unit our processing time is two minutes. And so we get 360 divided by 960 and that is 0.375 and our slope her was the units, we should keep in mind that this is units per minute. Alright, the next one the capacity of the old wall process. Recall in any process the process capacity is driven by the minimum capacity in the process, and so that is first here's a stamping machine which we computed as 0.375. And then the only other candidate for being the bottleneck here is the assembly operation and we learned that there it would be twelve workers be valued by 27 minutes per unit. And so if you put that into your calculator that's a number around 0.4444 and hence you see that the capacity constrained is the stamping machine. Right. There's capacity constraint. This is the stamping machine. And hence, the overall process is gonna be operating at 0.375 window boxes per minute. Alright, the last question here part C asks us to pick a batch size and so I would first ask you to think about the following questions. As a occurring batches, Too big or too small? Now, why would they be too big? well is there too big, that means well it's really, you know, the bottleneck is somewhere else in the process, and we can afford to, afford to lower the setup. The, the, the batch size. But here it's the opposite. Notice that the capacity constrain of the entire process is driven really, Buys us setup as a stamping machine. So we're setting up too often. We're, we're stopping the bottleneck, we're shutting down the entire plant and that slows us down. And so, that's just at least conceptually, we want to increase the batch size by how much? Well for that, we have to balance the line and just compute b divided by 240 plus. B times two. And we have to equate this to the next floor step, which is in this case, assembly at twelve divided by 27. Now you solve this and you're gonna get 27B is equal to twelve times 240 plus 24B and then you're gonna get B equals to 960 as a recommended batch size. So the next question is about a small local restaurant that is making ice-cream, gelato, and I want to acknowledge here my friend and co-author Gerard Causion. Who comes up with many of the questions that you see here in my Quasara course. And he has some Italian blood in him and so his ability to pronounce terms such as feragola and chocolato and batsia is a lot better than mine. Nevertheless, let me just point out that these different ice-creams have different demand rates. And, specifically, we're selling ten kg per hour of regular. Fifteen kilograms per chocolate and five of batsio. As you can imagine there is going to be some set up involved in the production of the ice cream lens specifically it takes 45 minutes to set up to formula, 30 minutes to change over then to chocolate and ten minutes for batsio. Once set up my ice cream machine is producing 50 kilograms per hour. Alright, as usual put me on pause, wrestle with the question, and then press on play again once your ready to hear my answers. All right, Let's take apart A first. In part A what we're looking at is how many kilograms should he produce in one batch? To find that out we start figuring out the production rate. We want to produce at a rate of demand, and demand is ten kilograms per hour of [FOREIGN] plus fifteen of chocolate plus five of batsio So we need to be producing at 30 kilograms per hour. Next look at the setup times. Now, don't let yourself get confused by the fact that changing over to [foreign] then to chocalate that these times are different from each other. Really the only thing that matters is the sum of the setup times. And that is 45 minutes for [foreign]. 30 for chocolato and then ten for bacio so the total setup is 85 minutes. Now since the rest of the calculation is gonna be in terms of hours because capacity is expressed in kilograms per hour. We need to convert that into hours and that is basically one. Plus four, one and a bunch of 6's hours per setup. Alright, now we want to solve for the batch size. We know that the flow rate in the process is gonna be 30 kilograms per hour. The batch size is the unknown, the variable that we're gonna solve for. And if you'll use our equation here, the batch size divided by the setup time plus the batch size times the processing time. So the setup time here is 1.416666 plus the batch size times one over 50. Per hour, right? 50 kilograms per hour is the is, is, is the capacity of the machine. And so if you ask yourself, hours per kilogram, it's a fiftieth of an hour per kilogram of ice-cream. You cross-multiply and you're gonna get 42.5 plus what is that, three-fifths. Off of B, 30 over 50 really, right? Equals two B and then you simplify and that gets you a B of a 106.25. And that's really the length of the batch. Now as you get into part B, you have to remember that the 106. .25 that's ice cream in a batch. Generic ice cream gelato across the three different flavors. Now fregola you know this is ten out of the 30 kilograms, ten out of the 30 kilo grams of fregola and so if you basically want to figure out how much fregola you're gonna produce in a batch. You need to just multiply with ten over 30 and that gives you 35.41 kilograms of [FOREIGN] that is put to use in each production cycle. Now after revealing my inability to speak Italian let's try out my German. So [foreign], which is actually the German word for apple makes smartphones and currently they only have a 64 gigabyte model. They're thinking about really segmenting the market and offering a 64 and a 128 gig model. And that said, just as their margins would go up. Total sales will stay the same. And so basically we're kind of having a 50-50 allocation between those, those two models. And there's a eh, my positive correlation in the coeffients, in the very ability really between those two models. Consider the following statements, put me on pause and ask yourself which of these statements would make sense. Alright this. More fragmented demand, will have a different variability. So what we're doing is the opposite of pulling. We're taking an aggregate demand stream and we're pulling it up. And for the reason, even with mild correlation, the coefficient of variation will actually go up. Again this is the opposite of pooling. We are taking some aggregate demand stream, and we are breaking it up, and so that increases variability as measured by the coefficient of variation. Because the coefficient of variation is a, ratio between the standard deviation and the mean. Alright. Now we have kind of set rules already those two guys over here. Then the last piece here is how should we organize the process? Should we, on the one hand, kind of, the first option is to basically have the separation between the 64 and the 128 gig happen early. And then basically carry this along all the way through. Or wouldn't it be nice to basically keep one common process. And then just kinda break it up into the two models, 64128 at the end. This is a case here of the late differentiation or postponement. It has a beauty that, up to here in the process. You're gonna keep the variability and demand low, not even to mention set-ups but also just demand variability is going to be lower. And you isolate this into this modular component namely the memory card. And so, for this reason it would be nice really, if we insert the component as late as possible. So really, three and five were the winners, which makes this here the correct answer.