 All right, welcome back everyone. I hope you had good discussions in your breakout rooms. And so now what we wanted to do was talk about each of the ones I'll talk about the first problem that in most going to tackle the second one. But I just want to give you guys some time to put in your approaches. Remember what we're looking for is for you to describe what kind of data do you think is needed. Whether you need more than what's here. You don't need everything that's given. What methodology you recommend to use and then how will this model be used a little more description about that. Okay, so for the first one, the forklift crew break scheduling. Like I said, when Victor sent this to me what he had he had a lot more detailed data. And he showed the distribution of the transit times and all these kinds of things. And his thought was what we need to do is to use going to use first the thing he did was characterize the transit time. And he looked at this to see it doesn't fit a known distribution, because then he could use that in a simulation. And so his approach was his thought was build a simulation, whether it's in any logic or some other tool, whatever. But to simulate the behavior and then try to figure out where the best breaks are kind of like trying to train different policies. And the challenge the questions that heroes with me was, how do I make sure it's valid. How do you validate this model. And so we'll talk about this in SC 2x we do network design, but typically what you need to do is whenever you have a simulation or an optimization where you're trying to do a new prescriptive approach where you're trying to come up with a new solution. You have to test your model and make sure your model captures reality. What you do is you create what's known as a base case, and you want to use the existing data and the existing policies to see if your costs or whatever match what actually happens. Right, so that's the first thing you always do, because if your model cannot replicate reality, then you can't trust it for future recommendations. So we talked about this in SC 2x and going to great depth, because it's very important for network design, but same thing here. You need to first simulate okay am I capturing based on what they currently do is it capturing the same flow is the same number of cares is it roughly within the same ballpark. And if it is, then you can go and say okay now I'm going to tweak the policy, but if you start tweaking the policy before you validated the model, you're just wasting time. And so the way I would do it is try to model what they currently do and try to see if you can capture what they actually happening. So as I look through some people have sent some stuff in. And it looks like, let's see where am I. Yeah, so there's some breakout room one I think this is, is that where param is seeing breakout one or do we know. So do we know where he is well. Yep. So he had so problems was pretty much the same discrete event simulation, build in any logic so that's great. Victor chimed in hi Victor. And so he said he's one who suggests the problem. And he said the someone asked where the time is 30 minutes breaks per shift three ships per day warehouse capacity is 34,000 palates. So then someone else Sergio says for breakout room one, they said you need better understand the distribution of the production rate got it. That's something you get the distribution I think Victor was doing along those lines as well. And again, a discrete event simulation, take some observation doing a chi square test, because that that's how you validate if the distribution is matches is it normal is it not log normal whatever exponential. And, okay, so you guys kind of all falling on the same thing. The reason why I picked this problem is that another one came in from breakout too. Oh, was that problem too. Yeah. Oh, it is never mind. Okay. So, there's a phrase in English and I don't know if you guys have heard it for called a red herring. And a red herring is something where it's actually it's stuff that excess information that you really don't use. And for me, the first thing I would do in this problem is not set up a discrete event simulation or look at the transit time or that stuff is to understand what they're actually doing. Right. And so to me this almost looks like a management problem. And so first step is talk and see when are they taking their breaks because it might be that they don't know they're only supposed to do 30 minutes. Maybe they're just doing because no one's checking on them. So what I would recommend trying to do initially is understand what the policy is and start enforcing it. Because we don't even know if it's not being enforced and if you don't enforce something people will just naturally take their time. So maybe spend a day or two on the docs and understand what it is do a ride along. There's a famous paper in the Harvard Business Review gosh 30 years ago called staple yourself to an order you Google that you can probably find it. And the whole idea is when you solve a problem. One of the traps that we all fall into as learners in this course once you have all these methods is you solve it in the abstract. And that's very important to staple yourself to the order or to the process so do a drive along. Watch what they do and sit around I've done this and many times with I would spend a day out in Chicago a couple years back with Schneider driving in the trucks who does shuttle runs back and forth with containers. And if you've ever seen someone back into a space with a 53 foot container. It's amazing to back into a slot but you get an understanding of what's actually happening beyond just the numbers. So I put this problem first I love it because I agree that you could do some really interesting things with a simulation but job one understand what's actually happening on the ground. Don't jump into a model right away. Try to understand the people and what's happening. And it might be that if you just put in and say you know what after your third run of the day take your 30 minute break after something's loaded and set a policy. See how that goes. And that might solve the problem. But if that doesn't once you get that set and have people actually hearing two policies and you can start looking at things such as OK what if I change the policy they get to 15 minute breaks. Instead of a 30. That's what simulation will help you do. I'd say job one is staple yourself to a driver and see what actually happens. OK. Now I'm going to turn it over to Emma and she's going to talk about the second problem. The container loading problem. Yeah so thank you Lance for this nice problem you shared with us. This is clearly a mixed interior linear programming problem. As I'm sure all of you have figured out. So for this mixed interior linear programming problem which could be the decision variables we want to figure out. Well basically how many like box which box I or pallet I is going to container J container J being container one two three or four these four types of containers we have now. And we of course will have to build some binary variables there to decide like to say if this container is being used even if one box goes to this container that container needs to be paid for. It's going to be open and obviously reserve campaign. So this would be the decision variables. And then we will have of course volume constraint right we have the volume information for each type of container. So I will create that the constraints and of course which container am I going to use the one that gives me the cheapest value per cubic meter. However you have to notice that volume is not not the only constraint we also need to think about weight and we don't have weight data here. So that's something we will need to figure out what's the weight of its pallet or box we want to ship and also how much weight was the maximum weight we can have per container. So that would be a second type of constraints. So let me add something there because what's interesting is going from a TEU to an FEU right 20 foot to 40 foot doubles the volume. The weight doesn't double the weight only goes up by about 12%. And the reason why if anyone's a civil engineer, if I have a 20 foot member containers are only picked up on the corners. So if I pick up a 20 foot like this versus a 40 foot the 40 foot you can't handle and twice the weight because it's it's what's known as a moment. And so the further you go away it's like a think of a seesaw. Right. And so as I get further away, it's the square of the distance times the weight, I can't handle as much. So, even though the volume doubles from a TEU to an FEU, the weight you can handle does not double it only goes up by a small percentage. We'll just break, right? Yeah, I don't break. Okay, so that's something it's not in the problem and it's really, really important. So it's the data you need both for the capacity and weight for each container type and for each item, the box, the thing you're shipping. And then another thing that it's not in the problem and we should take into account is the type of product that can go into a container. So of course, there are certain products that can't be mixed up in a container. Imagine, for example, some food items mixed up with hazardous chemicals. We can't do that. So somehow we need to figure out like different types of products that can be mixed into a container or cannot be mixed. And that will be other types of constraints that need to be introduced in our model. So, as said, well, you know, probably there's some randomness here. How can a milk be used for this? And actually the randomness kind of goes away once you have the things you're doing. But, you know, some things can change in those 90 minutes. And so you had an idea, obviously, but how do you can possibly handle that in practice? Yes, we thought maybe we could reserve like some buffer space. For example, if we have a 26 cubic meter container, just fill it up until 24. So fix the maximum capacity in 24 and we have two cubic meters per container of that type, three to introduce more products that come up in the last minute. Because we were discussing also earlier that we are not sure if it will be able, this company will be able to hold or maintain this product that may come in the last minute until the next day. So if that's not possible, then you need to figure out like you need to reserve some space if it's less efficient to introduce these products and make them up late. So another way you could tweak this problem, which is more realistic is right now we said you could order them on the fly and those 90 minutes you determine how many you want to order. What if you have to place that order a week ahead of time? It changes the problem completely. And then your point parm is dead on because now I have uncertainty because I have to commit a week out. This is a problem that we'll talk about SC1 X called the news boy problem. And so we'll talk about that uses all the same tools you've already learned a probability and some optimization, but now it's a different framework. And so in that case, you try to understand, okay, what's the probability that I need three containers or two containers of a certain type. Because this goes to what the Dianon recommended by looking historical data and you can segment customers based on their variability. You need to do that if you have to commit ahead of time. If you can place your order essentially on the spot market for your containers, then you really don't care. You just don't care what the it is because you, you solve what you've got. But if I have to commit ahead of time before I know what I've got, then we have to look and get some sense of history. Then we also have this comment about how to get consolidated format format data from many different sources. And that can change in the meantime, having only one and a half hours to gather an input. So that's also challenging. Everything we've done here is pretty much spreadsheet base and you type stuff in. In practice, you won't do that. And for something like this, you need to use more structured data models. And that's why we'll use relational databases. We introduce those in this forex when we talk about how you scale these problems to real size systems. And so you'll spend a lot of time learning SQL structure query language and understand how to formally handle large amounts of data. Because what you'd need is a data upload, some kind of API where the format and format is set, you know, all the detailed information coming in. You probably have to tie that to what's known as a skew master table that says this skewer this shipment weighs, you know, 300 pounds, and it takes this much volume and it's on a palette. You need to know that information to combine things together. Because essentially as we were talking, this is what's known as a form of a knapsack problem. And so I've got this knapsack and everything I'm trying to put in it. I've got it has a certain value, and it has certain dimensions and only certain ones fit together like a puzzle. And so the problem is, which items do I put into which box. And that's, it's a complicated problem, but you can solve it and you can solve using a mixed injury. What else? Did you talk about the compatibility of different items? Yeah, of different items. Yeah, we mentioned that. And then we had a last comment about, like right now, you can't mix products from different retailers in the same container. So that's a constraint. So what would happen if we were allowed to mix the products from different retailers in the same container? So what will happen in that case? So this is the, so the question is, let's say you're doing this and you're doing your job and you have your mixed injury program and it does it for each retailer. If you have an idea that you know what, I think I could save more money. How would you do this? Well, you could just loosen the constraint, run your data back through and see what is the difference in the solutions, and you could build the case. And so you would use an optimization on a new, you essentially relax a constraint instead of solving, let's say I have 10 retailers I'm solving for solving 10 problems, I solve one problem. And I allow mixing if needed, not everyone makes, but some mixed. See what the savings is. And then you want to see, does this justify me going to the retailers and see if they want to change their policy. You only want to go to some of the retailers that have comfortable or, or compatible equipment or compatible product. So you don't want to get someone who's shipping refrigerated things with someone shipping, you know, light bulbs. Right, but maybe you can make something where they fit together. And then part of what we've shown you in these tools, you can make the case that maybe it makes sense to change this policy. And that's the beauty of all these tools that we showed you and the rest of the courses will show you how to use these methodologies to make better decisions. And with that, I think we're just about done. So I think what we wanted to do now, kind of wrap things up. So any reminders for them for SC zero X. Yes, I would like to remind you that we are almost at the end of the course and the final exam will be released next week on Wednesday, December the sixth. I know you're all very excited out of the final exam. We've been working a lot on it. And I hope it's going to be nicely crafted. And you enjoy solving it. So please make sure you review all the concepts from all the previous week, because all the contents from week one to week 10 will be included in this exam. Please remember that once we release the exam on December the sixth at 1500 UTC, it will be available during one week until December the 13th. But once you begin to solve the exam, you only have four hours to complete it because it's a timed exam. Right. And so this is going to wrap up SC zero X but let me just tell you just quickly what you'll do in one X because I hope you take that next. It starts, I want to say 27 December week zero. So you can you can get Christmas off. You can start in the new year. So in SC one X, we do three things. And they're all tied to the idea of a trade off. You might trade off because you have competing demands. The first is demand forecasting. How do you understand or how do you model the what the for the demand is going to be for your product your service for your company. And we'll go over a bunch of different techniques to include using regression again for causal analysis but we'll talk about exponential smoothing moving average all these different techniques to better forecast your demand. They will switch gears and spend a lot of time on inventory because that's a really costly part of supply chain management and you use all those probabilistic models that we talked about before when you look at inventory. And so you try to understand how much inventory to have to avoid stocking out what is the probability of stocking out what's my level of service. And then we'll finish up with transportation and for transportation is really all about understanding mode choice. And so should I take a ship or should I fly by air. Should I go by rail or by truck. Should I pick different providers and because the transit time gives me lead time of the average as well as the variability. And so we'll show you through what's known as a total cost equation how to make these different trade offs because you're making trade off between level of service and cost you're making trade off between the overage having too much and having too little underage. And you're making trade off between a fixed cost and the variable cost will go through all of these, but all the tools you're going to be using, you've already mastered. So you've done them in zero X now we're going to apply now we'll do the fun stuff. So as you want X, I encourage you to take that next. And I hope, hope we'll see you there. Yeah, I think it's super fun. Yeah, I, I love as you want X is the most fun course. Yes. And Chris will be the instructor again for a C1 X. So we really hope to see you there. And good luck with the final exam. Good luck. Take care. Bye bye.