All right, time for some review questions. The first question is about batching and you see the problem described here. So, we are producing these window boxes and the window box consists out of two types of parts. There's one part A in there and there are two part Bs in there. The stamping machine that we're running, takes it a 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 360 As followed by 720 Bs. 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 have two of them, that means it takes us also one minute to B stuff done for the window box. Then downstream from the stamping machine in assembly, we have 12 workers and they put these window boxes together in 27 minutes per. As usual, I suggest you put me on pause now. Tackle the question yourself and see how you're doing. Then, press on play again and check your results. Now, the first question looks at the capacity of the stamping machine. Recall that when we have setups, we have to look at the capacity as the function of the batch size by taking the batch size and dividing it by the setup time plus the batch 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 at 360. Now the setup, I have to admit, is a little confusing, right? It's tempting to take these 120 minutes described over here, but remember there are really two set ups happening per window box, the A set up and the B set ups. And for that reason, we have to look at 240 minutes of set up time plus the batch size, 360, times the processing time per unit. And the same logic is we're going to need one minute part A, we're going to need 2 times half a minute to deal with the 2Bs. And so per unit, our processing time is two minutes. And so, we get 360 divided by 960, and that is 0.375. And I was sloppy here with the units, we should keep in mind that this is units per minute. All right, the next one. The capacity of the overall process. Recall in any process, the process capacity is driven by the minimum capacity in the process. And so that is, first we have 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 12 workers divided 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? This capacity constrained is this stamping machine and hence, the overall process is going to be operating at 0.375 window boxes per minute. All right, a 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. Are the current batches too big or too small? Now, why would they be too big? Well, if they are too big, that means the bottleneck is somewhere else in the process, and we can afford to lower the batch size, but here it's the opposite. Notice that the capacity constraint of the entire process is driven really by this set up at the stamping machine. So, we're setting up too often. We're stopping the bottleneck. We're shutting down the entire plant, and that slows us down. And so that suggests 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 + B times 2 and we have to equate this to the next lower step, which is in this case, the assembly at 12 divided by 27. Now you solve this and you're going to get 27B = 12 times 240 + 24B, and then you're going to get B = 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 who comes up with many of the questions that you see here in my Coursera course. And he has some Italian blood in him, and so his ability to pronounce terms such as fragola, chocolato and bacio 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 10 kg per hour of Fragola, 15 kilograms per hour of chocolate and 5 of Bacio. Now as you can imagine, there's going to be some set up involved in the production of the ice cream and specifically, it takes 45 minutes to set up the Fragola, 30 minutes to change over then to chocolato and 10 minutes for the Bacio. Once set up, my ice cream machine is producing at 50 kilograms per hour. All right, as usual, put me on pause, wrestle with the question, and then press on play again once you're ready to hear my answers. All right, let's take a part 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 10 kg per hour Fragola plus 15 of chocolate plus 5 of Bacio, so we need to be producing at 30 kg per hour. Next, look at the set up times. Now, don't let yourself get confused by the fact that changing over to Fragola and then to chocolato, that these times are different from each other. Really, the only thing that matters is the sum of the set up times and that is 45 minutes for Fragola, 30 for Chocolato, and then 10 for Bacio and so the total set up is 85 minutes. Now since the rest of the calculation is going to be in terms of hours, because capacity is expressed in kilograms per hour, we need to convert that into hours, and that is basically 1.41 and a bunch of 6s hours per set up. All right, now we want to solve for the batch size. We know that the flow rate in the process is going to be 30 kilograms per hour. The batch size is the unknown variable that we're going to solve for and if you'll use our equation here, the batch size divided by the set up time plus the batch size times the processing time. So the set up time here is 1.416666 plus the batch size times 1 over 50 per hour. 50 kilograms per hour is the capacity of the machine and so if you ask yourself hours per kilogram, it's a 50th of an hour per kilogram of ice cream. You cross multiply and you're going to get 42.5 plus what is that, three-fifths over B, 30 over 50 really, right equals to B. And then you simplify and that gets you a B of 106.25 and that's really the length of the batch. Now as you get, then, to 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 Fragola, you notice is 10 out of the 30 kilograms. 10 out of the 30 kilograms are Fragola. And so if you basically want to figure out how much Fragola you're going to produce in a batch, you need to just multiply with 10 over 30, and that gives you 35.41 kg of Fragola that is produced in each production cycle. Now after revealing my inability to speak Italian, let's try out my German. So, Apfel, which is actually the German word for Apple, makes smart phones and currently, they only have 64GB model. They're thinking about really segmenting the market and offering a 64 and 128 gig model. And that suggests that their margins would go up. Total sales would stay the same and so basically, we're kind of having a 50/50 allocation between those two models and there's a mild positive correlation in the variability really between those two models. Consider the following statements, put me on pause, and ask yourself which of these statements would make sense. All right, this more fragmented demand will have a different variability. So what we're doing is the opposite of pooling, we're taking an aggregate demand stream and we're splitting 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're 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. All right, now we've kind of the are really these 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, then basically carry this along all the way through. Or wouldn't it be nice to basically keep one common process and then just kind of break it up into the two models, 64, 128 at the end. This is a case here of delayed differentiational postponement. It has a beauty that up to here in the process, you're going to keep the variability in 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, 3 and 5 were the winners, which makes this here the correct answer.
