 Hello everybody, and welcome to our third live event of SC0X. So today is with me, Akash Dregengar, who is a TA for SC2X. Welcome, Akash. Hi, everyone. Great to be here. Welcome, everyone, to the third live event. Okay, awesome. So this is the plan for today. And for that, let me show you, let me share my screen. So basically what we'd like to cover today is the following. So we're going to be starting just talking about, as a reminder of the contents that you might see in order to take the exam. So we have some material about the contents and the pace. Then we will offer some options that you have to get ready for the final exam. So what are the different alternatives that you might take in order to be ready for the final exam. And finally, we're going to be discussing about one of these exam preparation section, which is going to be about optimization. So that's going to be the main part of this live event. So if you have any questions, please feel free to ask us. So we'll use the question sections that Zoom has in order to gather all the questions that you may have about optimization and about the course itself. Okay. Without further ado, let me just say as a reminder that this course is a structure in five different modules. So module one, it's about an overview of supply chain management and also about data management module two, it's about a probability module two, module three, it's about statistics. And today we're going to be talking about module four, which is optimization. And lastly, module five, which is about algorithm approximation and simulations. So these are the modules that are going to be assessed are going to be evaluated during our final final exam. So it's going to be a comprehensive final exam. So there are four weeks left to our final final exam. So it's now time for you to get ready for the final exams, only five weeks until we release the final exam. So I'm hoping that you are spending a lot of time getting ready for this final exam. So there are many options for you to prepare this final exam. So the first one is please make sure that you are taking the module, the module test. So we have one module test for each of the five modules. And there's a deadline for this module test, which is going to be December 11. So the module tests are worth 10% of the final grade. So it's not, there are not a lot, but please make sure that you prepare this module module test. Then we also have what we call the exam prep sections, prep section. And within this, this section we have three problems. So the last one, which going to be the topic of today was released last week. But additionally to this, to this problem, we have also problem, one problem about probability and one problem about, about statistics. Okay. So this, so today we will focus on the third problem of these exam prep sections. Additionally, for those that are verified, so we're going to be offering a practice exam that's going to be open on November 20 and it's going to be remain open until we open the exam. Until December 11. And this is going to be a replica of the final exam. So you will have four problems. It's going to be a time exam. You have four hours to complete this test. So the idea is to simulate all the conditions that you will experience during the life exam. So please don't, don't miss this opportunity to also take this practice exam. Okay. So, and again, the practice exam will open on November 20 and we will close this practice exam that they would release the final exam, which is going to be December 11. Please, if you have friends that are in the course and are not verified yet, please remember them that verification will close on December and November 20. And that's the last chance for them to become verified, verified learners. Okay, so as I was saying, the main focus of today is going to be problem three of the exam prep. And this is about optimizations about our module number number four. And for this particular problem we have, as you said, we have three sections. The first one is the problem statement where you can find all the details of the problem and also you can find the questions of the problem. And that's in the section that is called, in the tab that is called for you to solve. Then we have a different section that is called a step-by-step solution. And in this case we have a video and which Emma Borrella, our previous course lead will teach you or will show you a step-by-step how she approached this problem and will answer the different questions associated with this problem. So here we have the Q&A life event. So ideally you, if you had a previous questions, you have, you had the options to put your questions there. I'm going to be answered some of those questions in this live event today. So you have already this material. Okay, if something is not clear, you have the step-by-step solution where you can see how Emma approached this problem. Okay, so let's talk about the particular problem that we are trying to solve in this live event, which is this problem number three. And this problem number three, it's about this company that is called Fork Motor Company, which is an automobile manufacturing that operates in the US. This company has three different regional distribution centers, the RDCs, which are located in California, Florida, and Texas. And there's a demand in numbers of millions of automobiles that need to be satisfied to these distribution centers. Additionally, the company has two different plants that are located in Michigan and Nevada. The automobiles are shipped from these plants with a final destination as the regional distribution centers. So there is information, what you can see in the table is information about the distance between the different plants to the regional distribution centers. And those distance are measured in miles. Similarly, there is a capacity that should be met, so there is a maximum capacity at each of the plants. And that's, again, expressing millions of cars. And finally, we have a transportation cost, which is $4.86 per mile per automobile. That's all the information that was shared with us. The first question, it's about what's the minimum cost of shipping the cars and expressing millions of dollars. So how can we approach this problem? The first thing, so what I do is I will try to write the problem in the model in a piece of paper. I'm going to be showing some of my reasoning and then I'm going to be showing you how we approach this problem in Excel. So for the paper version, I need to define just the indexes. So remember that we are shipping cars from plants to the regional distribution centers, so we have two different sets. One set is going to be the eyes, so that's going to be the plants. And for this particular problem setting, we have only two plants, Michigan and Nevada. So the eyes represent the plants. The second index will represent what are going to be my demand notes, which are the RDCs. And for this particular problem, we have three different RDCs located in California, Florida and Texas. So J will take these three values. So those are the indexes. So what's the data that we know? What's the information that is given to solve the problem? We have the C, which is going to be the unit transportation cost, and that is measured in dollars per mile per vehicle. So that's going to be, we're going to be charging this amount to each vehicle for each mile that is being troubled. Then we have the distance. So that's going to be the D, I, J. So the distance will depend on I and J. So that meaning that we're going to be a function on where the car is shipping and what's going to be the final destination. And that's the distance measured in miles, again from plant I to regional distribution center J. Then we have traditional pieces of information, which is the capacity, and we have a capacity at each of the plants. So that's why this S depends on the index I, because it's a value that is associated to each of the plants, so different for each of the plants. And finally, we have the demand that should be met, and this demand depends on the RDCs. We'll have one demand that is specific for each of the RDCs. That's why the D depends on J, the J. The capacity and also the demand are measured in millions of vehicles. So, okay, so any mathematical model will have, has three main parts. The first one is the decision variables. And in this case, what we're trying to decide is the number of vehicles are going to be shipped from plant I to RDC J. So basically how many vehicles will be sending from the plant to RDC? And that's going to be our XIJ, again, XIX will depend on the plant, on the origin, and it will depend on the destination. So we may have different numbers depending on the plant and depending on the RDC. So for this particular problem, for this particular question, since we have two plants and three RDCs, so we'll have two times three, so six different, different decision variables. The second part of any mathematical model is the objecting function. So now, so here for this particular problem, what we're trying to do is minimize total cost. And total cost is going to be just the product of the decision variables times the distance times the unit cost. So basically, we're going to be multiplying that the numbers are going to be shipping from plant I to RDC J by the distance between the plant and the RDC. And that's going to be, again, multiplied by the unit transportation cost. And the main objective of the mathematical model will be to minimize this total cost. Basically, that's our total transportation cost. And the third piece, the last piece of any mathematical model is the constraints. For this particular problem setting, we will have three different types of constraints. The first one is we have some capacity limits. We have some capacity constraints. And basically, each of the two plants, each of them has a capacity constraint. So basically, the first constraint, the capacity constraint is saying that the production in each of the plant should not exceed the capacity of the plant. So that's why the sum of xij over i, so this means all the production, all the vehicles that we are shipping from plant i should be less than the capacity of that plant. And we will have one of these constraints for each of the plants. Since we have two plants, we will have two different capacity constraints here. One for Michigan and other for Nevada. The second set of constraints are demand constraints. So now we need to satisfy, we need to met the demand. Basically, all the vehicles that want to be sending from different plants to a particular RDC should be equal to the end of demand. So that's what this second constraint is saying. And we will have one of these constraints for each of the RDC. Since we have three different RDCs, California, Florida and Texas, we will have three different demand constraints. And finally, the non negativity constraints will have to make sure that the number of vehicles shipped should be a greater or equal to zero. We cannot ship any negative any negative body of vehicles. So that will be all the mathematical model in the piece of paper. Let me see, let me show you now how I reflected this on an Excel. Again, I'm going to be starting with following the four steps. First, let's see what the data that we have. And all the data that we have is color in gray. So first we have the C, which is the unit transportation cost, measuring dollars per mile per vehicle. Then we have all the distances from plants to RDCs. Since we have two plants and we have three RDCs, we have six different distances. And these distances are measured in miles. Then we have the capacity, one capacity, a value for each of the plants. And these plant capacity are measuring millions of vehicles. And finally, the demand that should be met. Again, measuring number of millions of vehicles. That's all the information that was given as part of this problem. Then let's talk about now about the decision variables. And again, I'll have a table where I'm putting the decision variables, which are color in yellow. Basically, I need to decide how many units are going to be shipped from Michigan to California, from Michigan to Florida, and from Michigan to Texas. And the same thing for a value. So that's why I will have six different values for my decision variables. Then the objecting function. The objecting function now I have color in green. And this is going to be just my total transportation cost. I'm going to be multiplying these unit transportation costs. So these 4.86 times 2000, which is the distance from Michigan to California by the number of units are going to be shipping from Michigan to California. You don't have to multiply by one by one. If you're using Excel, there's a function that is called sum product that will simplify this calculation. And finally, the constraints. As mentioned before, we have three things set for constraint capacity constraint. So basically all the product, all the unit of worship from Michigan, Michigan, which is going to be the sum. So this zero, this zero represents the sum of these three cells. And this is going to be less than 2.2.5. Same thing for Nevada. We will have a demand constraints. So now the zero will represent the sum of all the vehicles that we are shipping from Michigan to Nevada with California as the destination. And this quantity of unit shift to California should be equal to the to the demand, which in this case is 1.5 million. And finally, no negative constraints. We have to make sure that all values that are color other cells that are coloring yellow should be a greater or equal to to zero. See, this is how I set up my Excel and finally just using software with the specific constraints. You can take a look that my objective cell is the in this case is the two, which is coloring in great. The changing variables for my decision variables are those cells that are coloring yellow. And finally, the constraints are those that I just show you. You can see that in the sub in the constraints box we have only two sets, only the capacity and demand because here I make sure that all variables are non negatives. Okay, so I don't I don't have to again add in non negativity constraints. Okay, so that's what I have to share with you. So let me stop here and start asking answering any questions that you might have. Okay, great. So one of the questions is regarding the practice exam, whether the students will be able to see the answers, the correct or not after answering the last question or what the procedure is for seeing their performance on the practice exam. Okay, that's a very good question. Yes, so after after they are done with the exam, after they tried the practice exam. So you will have you will be able to see if you get it wrong or right around, but also will we will share with you what was the right solution. So you will have the solution of that that problem. Okay, so solution will be shared for the practice problem. And also just just to point out for the final exam though, you will not receive any feedback or you won't be able to see whether the answer is correct or wrong. So you'll only be able to see a grade after the final exam has been analyzed by the staff. Correct, that's correct. So this is just for the for the practice but the final exam is going to be different. Okay. I know I also had some questions on the email and forums about the final exam rescheduling. So let me say that this will won't be possible since we have a global course. It's very hard to change deadlines for individual accommodations. So please try to do or finish the exam before the deadline between the between the two the week of the final exam. I'm assuming that the exam is going to be open for one week from December 11 to December 18. But once you start the exam once you click on the start exam, you have only four hours to complete the exam. Okay, please plan accordingly. All right, there's another question regarding the exam again referring to module four. Will the optimization part of the exam only be of LP type or other types of optimization problems also. It could be could be a different different type of optimization problems. So basically everything that is part of the content of the concept of the course could be assessing the final exam. So we can have for example milk milk as well in the final exam. Great. And there's also questions, a lot of questions about whether it's still possible to enroll in the course or verify in the course. And will, is there enough time left to finish. I think that verification deadline is a week from today or correct. Sometimes yeah. But yeah, I mean, if you're diligent enough to put the hours in before the final exam week and finish all the module tests and all the assignments on time I don't see why you won't be able to complete the course. I know it'll be a little challenging, but if you really want to finish, I think it's definitely possible. Yeah, so keep in mind also that I just showed you with you the more or less an estimation of the time that you will need to to watch all the videos and do the practice problems. Keep that out also in mind. See if you have enough time to dedicate or at least to to roughly with the corresponding to the time estimations. Please do it, but if you feel that that's going to be too much. So maybe it's it's time for you to to take the next next next next exam so next is zero X. Okay, more questions. Um, actually, there's a question about SAS, whether it's mandatory to know SAS for the exam or if it has any advantages to know for the exam or is excellent enough for the December exam. Okay, so Excel should be enough for you. So actually the exam will can be designed to be solved in Excel. However, you are free to use any software that you want. So you can use SAS, you can use Apple or any other sort of what that you are familiar with. So it's going to be again designed for Excel, but you can use the software that you that you want. Great. Yeah, so just referring to the final exam began as an open book exam. So feel free to use the resources available in the course, as well as any software that you may like. So the only constraint is you can use outside help from other people, but feel free to use any of the course material, the modules, the videos or anything like that. Correct. Yes, so that's a good, good point. So it's an open exam, you can use any material that you have, you can watch a part of the video, or even this live event during the exam so that's, that's a low, but it's not always collaboration between a partner. Thank you. And also, there was a few questions, frequently about the blended masters program, and just the structure of things of doing the master after the micro masters program. We refer you to the micro, the blended masters email address, it's scmb at MIT.edu. Again, that's scmb at MIT.edu. I'll also post it in the chat window. So you guys have access to this resource to ask me questions about the blind masters program. Yes. So we had a live event for a CCRIC last week, and we received a lot of questions about the planet. But that's a way to go, the email of the blended program. Anything else, Akash, any additional questions? Life questions? We're not, we're not having it, right? Okay, so if you have any additional questions, please use the discussion forum. Remember that we have a discussion forum section for this live event. If you have any pain in any outstanding questions, please post it there. We're going to be making sure that what we shared today is also available for you, and that's going to be available again in the sections that you use for this live event. So you can watch this video after we are done. And with that, so again, only four weeks to the final exam, so please make sure that you are dedicated enough hours to get well prepared for the final exam. And do the exam prep, the module test, but also don't miss the opportunity to take the practice exam. That's going to be a good thermometer for you to see where are you. Okay, and with that, I will say the words for you, Akash, any final remarks? Yeah, just along the similar lines, I mean, the final exam is less than a month away now. So if you've been procrastinating, I guess now is the time to start getting all the assignments together and getting prepared for the final exam. Yeah, I wish you guys all the best. And yeah, excited to work with you all further. Okay. Thank you for joining this live event, guys. I'm very lucky in the final exam. See you next time. All right, thank you.