 Hello Global Supply Chainers and welcome to our second live event of SC2X, Supply Chain Design. I'm Sergio Caballero, the Coast Lead of this course. And here with me, I'm Ed Bilal, who is the TA for this course. Welcome to this live event. Yeah, thank you so much. Okay, so the plan for today is going to be different. So in the past, in previous rounds of SC2X, we used to have some guest speakers from industry to share about their experience about the topics that we have seen in the course. So now the focus is going to be different. We'll be just focusing on getting you ready to get the mid-term exam. So we'll still have this live event where we'll invite industry speakers, but now it's not going to be related to a course specific. It's going to be across the programs. You will see that you have three or four of these live events every year. Okay, so today, so let me, let me share my screen. What I want to present today, what we want to present today is the following. Okay, so I'm going to start giving a brief overview about the exam. Okay, so basically describing the rules and all the information that you should know about the depth coming meter exam. Then Bilal and I will be talking about solving a couple of problems from past meter example of SC2X. So in the setting, in trying to help you get ready for the exam. And after that, we'll open to any question that you might have. So we want to be as interactive as possible during this live event. So we'll be using a Slido. So please go to Slido.com, your computer or any mobile device and ask any questions that you might have during this live event. Okay, so we'll take a look to Slido and ask you or answer the questions that you might have. Okay, so this is the plan for today. So let's get started giving the brief overview about the exam. So as you know, the meter exam is an open book exam. So this means that you can access during the exam to the video lecture. You can access to the KCD, to the Key Concept document or any notes that you may have. This also means that you can use any templates, Excel templates or a system plays that you may have in order to solve the optimization problem. Okay, it's an open book exam. The main goal of this meter exam is to assess your knowledge. So we want to assess your understanding of the different methods presented in the first part of the course. So this meter exam is pure assessment. So in this sense, we won't be providing any feedback during the exams or we won't provide any solution after we close the exam. Okay, so this is the policy that is coming from the program from the master micro master program. And if you have taken a C1X in the last run, you will be familiar with this policy. Okay, so no feedback or solution will be provided during or after the meter exam. So let's talk about the timing of this exam. So the exam will open tomorrow, Wednesday, May 22nd at 1500 UTC. Then the exam will close on Wednesday, May 29th at 300 UTC. So that's the deadline of the exam. So it's a time exam. So this means that exam will be, even though that exam is available for one weekend, for one week, you will have only a limited time to complete the test. In this case, for this meeting, you will have four hours to complete the test. So once you start the exam, you will have only four hours to complete this exam. If you want to get the full four hours to do your test, you have to start the exam at least four hours before the deadline. So you have to start the exam at least four hours before Wednesday, May 29th at 1500 UTC. The second thing that we'll have to notice is try to do the exam as early as possible. As you approach the deadline, we won't be able to help you. So remember that you might know that we will receive a lot of emails and we'll try to help you. But if you are close to the deadline, so that will be really, really hard for us. Okay, so let's go now to Slido. Again, it's slido.com. And we have one question for you. So the code in order to access to the poll is sc2x-2. And the question that I have prepared for you is the following. When are you planning to take the meter exam? We have a couple of options. You're planning to take the exam before the weekend. So that's tomorrow or Thursday or Friday during the weekend or Saturday or Sunday or after the weekend. So some of you are saying that they are planning to do it during the weekend, which makes sense. So you might be working and you might find the weekend to do the test. Some of you are planning to do it before the weekend. Okay, that's also great. And some of you are saying that you are planning to do it after the weekend. Okay, we encourage you to take the exam as soon as possible. So try to do it during the week or during the weekend. Okay, because we want to help you. If you have any questions, it will be almost impossible to help you if you are doing the exam just a few hours before the deadline. Okay, awesome. So let's continue giving some instructions about the exam. And let's now talk about the content. So the exam will consist on four problems or all the problems will have exactly the same weight. So the exam will cover the material from weeks one through four. So from week one, two, three and four. Okay, so we are not considering the content that was released in week five, only from week one to week four. So as you might know, the meter exam is worth a total of 35 over your final grade. So that's an important piece of your final grade. So make sure that you are prepared and you allocate the right amount to do this exam. You might know that you cannot complete the time exam. In this case, the meter exam using the EDX mobile app. So there's not a big capability there. So you have to use a web browser. Okay, so keep that in mind. In order to take the meter exam, you have to use a web browser. We highly recommend you to use a computer to complete the exam. And also, so the exam is designed for you to use any software that you are familiar with. So you can use Excel, you can use SAS, or you can use Ample to solve optimization problems. Okay, so use the tool that you are most familiar with. And that brings me to the second question that I have for you. And that's related to what is the software that you're planning to use in this meter exam? So what software are you planning to use to solve optimization problems in this meter exam? Are you planning to use Excel, or maybe SAS Studio, Ample, Google Sheet, or maybe LibreOffice. Okay, just keep in mind that the exam is designed so that you can use the software of your preference. Okay, so the vast majority is saying that you will be using Excel. Some of you are saying that SAS Studio and very few are saying that we'll use Google Sheet and LibreOffice. Okay, but it's good to know what's your preference regarding the software in this for this exam. Okay, so without the final remarks about the exam. So let's talk about the owner code. Remember that the work must be your own. So there's no collaboration during the exam. If you have any questions that are related to the question itself, if you need any clarification about what the problem is asking, please reach to us. And you have the email, SC2Exceled, at MIT.edu. Just keep in mind that this is just for clarification questions. So the staff won't give any hints or any questions related to the content itself. And finally, do not pose any questions or comments on the discussion forums or any other website. So we take very seriously the meeting on final exam. So we'll be monitoring the discussion forum and also other websites. And if we find anything, we will contact you and make it. And we'll take a hard decision here. Okay, so please avoid doing these things. And with that, so I will open to any questions that you might have. Will you have any questions about the specifics about the meeting? Yeah, so there are two questions. One is on the software tool. So I think that is very relevant to the discussion that we were having before. So the question is from Anurag is asking that since CFX will allow only spreadsheet, should we stress on the same or learn SAS tool? Okay, so that's a good question. So one of the main constraints that we have during the CFX is the time limitation. So at the time we have only two hours to complete each of the exams. In the case it's impossible to ask, for example, optimization problem to model and to solve it during this time constraint, during these two hours. So that's why in the CFX we don't ask optimization questions. So that's why we're not using SAS or any other optimization software during the CFX. So if we allow it to use Excel is just to use as a calculator. Okay, so you wouldn't model, you wouldn't solve any optimization problem during CFX. The only use that you will give to Excel is going to be just as a calculator. Okay, having said that, I mean, we encourage you to learn SAS or learn ARM. Because it's something that you will need in your professional life as a supply chain of a professional. Okay, so the next question is on the support during the midterm. So this is the name of the person who asked the question is not very clear. But the question is like in the US, this is a big summer holiday. So will there be adequate support from the staff to answer discussion questions and support during the exam? Definitely. So we'll have a full support during the seven days, especially considering that we have a holiday on Monday. Okay, so Bilal and I will be monitoring permanently the email to any questions that you might have. Okay, so, but please use the right channel. So if you have any questions, don't use the discussion forum. Use the SC2x help at MIT.edu email. Okay, awesome. So with that, if we'll have more questions, let's go continue to the topics. So no more questions. So there is a question on the Mac, which is some people are saying that they're having difficulty in using Solver in Mac. So they're saying, is it fine if you use Google Sheet? Definitely. So that's one option. You can use a Google Sheet. But also in the Macs, there's an open solver that you can use. So you can download that open solver and use on your Excel as well. But so the exam is the sign in for you to use any solver that we have been commented. You can use SAS, Apple Excel, or even Google Sheet. Okay, you will have no, no, no difficulties there. Okay, so there's this one interesting question from Aziz. He's asking that once you start the exam, can you pause and take break? That's not an option. So when you start the exam, you have four hours to complete. So you cannot pause or you cannot restart the time exam. So that's not an option. So just keep that in mind. So in order, you have to allocate a time for you to take the exam in days for four hours. Okay, just please keep that in mind. Okay, so no more questions. So let's move on. So let me now talk about a problem. Okay, so in this case, so the intention and the main focus of this live event will be to solve a problem from a previous runs of SC2X. So this one was taken from a couple of rounds ago. And the first problem will focus on a network design, network design problem. Okay, and without let me ask you the third question. So let's go to the poll. And the question that I have prepared for you is a bit about the challenge that you experienced when modeling a supply chain and network design. So what do you struggle most with? So to define the decision variables for maybe it's not clear for you how to define the object in function. Or maybe it's related to some of the constraints. Capacity demands constraints, conservation of flow constraints, linking constraints, or maybe the level of service constraints. Okay, we have to understand and I will try to tailor my, the solution that we'll present in order to address the main challenge that you have. So the majority is saying that is identifying a linking constraint. So all related to how to identify those linking constraints and also level of service constraints. Okay, and also a conservation of flow constraints. Okay, I will keep that in mind when I'm solving the problem. Okay. Thank you for your input. We really appreciate it. Okay, so as I was saying, this problem was taken from a couple of runs of a meter example of SC2X. So basically we have this component that is called a medical, which applies medications. And the company is interested in redesigning its supply chain, basically trying to redesign its distribution supply chain. So currently there's a pharmacy that is located in New Jersey, which supplies directly to the to the customers, but they are thinking that the company medical is thinking on introducing some distribution center. So basically the idea will be to send the products from the pharmacy to distribution centers and from there to the markets. So in regard to distribution centers, there are three options. So we have a, they can open a distribution center on a New Jersey, a Texas on Nevada. So that's a decision that they have to make where to open the distribution center. And finally, they need also to decide the quantity that they will ship. Okay, so the flow moves from the pharmacy to the distribution center. So three potentially distribution centers and from there to four different markets. So located in Northeast, Middle West, South and West. So the first thing, the first advice here will be, so when we are presented with this kind of problems. So the first thing that I usually do is I try to create a diagram. So basically just a rough diagram where you can see how the, how they move, how the goods move from the different tiers of the supply chain. In this case, it's clear that the goods are moving from the pharmacy to the distribution centers and from them to the market. Okay, first recommendation. So draw a diagram of your supply chain. Okay, then I usually divide my strategy in three parts. The first one is I'm going to be considering all the relevant information that I know about the problem. Then I will be taking a look to the decision that I have to make. So basically the decision variables and what I want to optimize the objective function. And the third piece is going to be identifying the necessary constraints to solve the problem. Okay, so let's talk about the first piece. Gathering all the information that is relevant to this problem. So basically I will try to answer the questions. What do we know about this problem? So we already know how the goods moves from pharmacy to distribution centers and from there to markets. So we have only a single pharmacy which act as the source. We have distribution centers which act as transshipment points. And finally we have four markets that act as the customers. So the demand points. What information do we have additional? So we have also transportation costs. And this is measured in dollars per box. So the units that we are moving are boxes. And in this case we have a inbound transportation costs. So basically how much is cost? That is cost to move from the plants to each of the distribution centers. In this case to seven and ten dollars per box, depending if we are going to New Jersey, Texas on Nevada. And similarly we have information about outbound transportation costs. So basically how much cost to move one box from the different distribution centers to the different markets. And those numbers are the unit transportation costs. Additionally we have information about the fixed costs. So this is the fixed cost that is needed in order to operate or to open each of the distribution centers. In the case of New Jersey that's 15,000 dollars. And we have similar numbers for Texas and Nevada. Again if we want to operate one of the distribution centers we have to pay this amount. And in this case I think this is the fixed cost is measured in dollars per year. Okay I think that's all the information that we have regarding costs. We have transportation costs and we have fixed costs. Okay so the next piece is what needs to be solved. So what are we trying to optimize? And it's typical in this kind of problems that we are trying to optimize one thing. So basically we will see that our objecting function is to minimize total cost. And usually total cost is composed of two legs. One leg is the flow. Okay so for this particular problem we are trying to decide how much we will send from the pharmacy to the different distribution centers. So we are trying to decide basically the inbound flow. Then is the outbound flow. So basically it's the flow that will be moving from the distribution centers to the markets. So how many boxes we should send from New Jersey for example to the south market. It's also something that we need to design all related to the outbound flow. Okay so this is all about talking about boxes. How many units or how many boxes we will send from the different lines. And the second thing is the second decision it's about if we are opening or not a decision. So basically for the three distribution centers we have to make a decision if we are opening or not that particular distribution center. And in this case that's going to be a binary variable. Zero if we decide to not open the facility and one if we decide to open the facility. Okay so that's all the decisions that we are making. Inbound flow, outbound flow and also the decision regarding to open or not the distribution centers. In these things what we are trying to optimize, what we're trying to minimize is in the objecting function is just the combination of the transportation costs and the fixed costs. So transportation costs will consider the unit transportation costs that I showed in the previous slide. And the inbound and the outbound flow. And the second component of the objecting function will take care of the decision of opening or not the DC plus the fixed costs. Okay so this is a typical objecting function. The last piece is related to what are the limitations or what are the constraints that we should include in our model. Okay so the first thing that we notice is that we have a demand that needs to be fulfilled. In this case the demand is again measured in boxes per year and we have a demand that is associated to each of the market. And you can see the figures there. Okay in this sense we have demand to fulfill so the model should include a constraint that is related to the demand. So we need to add demand constraints. How many of these constraints should include as many as markets as we have. In this case we have four markets. That's why we need to add four of these demand constraints. One associated to each of the markets. The second information that we have is a limitation that we have is regarding capacity. In this case each of the distribution centers has a limited capacity that is also measured in boxes per year. You can see the figures on the slide. In this sense we also need to add capacity constraints because the capacity of these centers are limited. In this case we'll be adding one of these capacity constraints for each of the distribution centers. Okay so what else? We also need to add a conservation of flow constraints. So you might remember that the distribution centers are acting as transshipment points. So basically this means that all the flow that is coming into the facility should leave the facility. And we can see here for example in New Year's that we have some goods that are coming from the pharmacy. And those goods should leave the facility as well. So in order to model that, that the inflow is equal to the inflow, we need to add the conservation of flow constraint. So in this case you should add a conservation of flow constraint every time that you have a transshipment facility. For this example we have three distribution centers that act as transshipment points. That's why we need to add three conservation of flow constraints, one for each distribution center. And finally we need to add also a linking constraints. Why do we need to add these constraints? Because we are taking a decision of opening or not a facility. So every time that you make a decision to open another facility, you need to link somehow the flow that is coming through the facility with that decision. And the way to do it is using the linking constraint. The question here will be how many of these constraints do I need? You need as many as decision variables as you have. Sorry, binary decision variables as you have. In this case we are taking, we're having, we have three different binary decisions because we have three different decisions. That's why we need to incorporate three of these linking constraints. Okay, so that's a, that's about the model. So we need, we're optimizing the total cost that is composed of the transportation cost plus the facility cost. And we are trying to achieve the demand to fulfill the demand subject to some capacity constraint, conservation of flow constraint, and also a linking, linking constraints. Okay, so let's try to solve the problem. So basically this problem is asking about how many this is a, we should open in order to minimize cost and what will be the optimal annual annual cost. And to do so, let me show you a spreadsheet and Excel spreadsheet. Let me see if I can share with you my solution. Okay, so basically this is just a template. It's similar to what you have seen in the course, in the different material that we shared with you. So we have the total cost that we are trying to, that we are trying to minimize. And this total cost is composed of three, mainly two elements. So transportation cost and the facility cost. So here we have the fixed cost, and the fixed cost is just taking into consideration the binary variables and the fixed cost of each DC. Then we have the inbound and then we have the outbound transportation. So this template is basically a group divided in three sections. The first section is related to the facilities. So I have here the decision variables which are coloring in yellow. And then I have for each of the distribution centers, I have the corresponding fixed cost. This information is about the facilities. The decision variables open or not the distribution center and the fixed cost related to each distribution center. Then I have information about the inbound transportation again. So we're making a decision about the inbound flow. This is what I have in these yellow cells. And then next to it I have the unit transportation cost for the inbound transportation. And in the last part of this spreadsheet what I have is the outbound transportation. So I have the decision variable regarding how much units we should send from the different decision center to the different markets. In this case we have three times four, so 12 different outflow decision, outbound decision variables. And then in gray I have all the data that was provided to solve this problem. Okay, so again we're trying to optimize the total cost which is composed of the fixed cost involved and outbound transportation cost. Fixed cost is just the multiplication of the binary variable plus the fixed cost. It's just some product. Then the inbound transportation similarly is going to be the multiplication of the flow, the units that we will send from the this from the pharmacy to the disease. And that should be multiplied by the unit transportation cost. And finally something similar with the outbound transportation cost. Just multiply the decision variables time the unit cost. And I'm using the sum product a function of Excel. Okay, so what else do we have in this spreadsheet? So the demand, so this is the demand that we have. And we have to make sure that all that is provided to the different market should be equal to the demand. So basically the sum of the columns of each column should equal to the demand. Then also the units that are supplied in each individual center should be less than the capacity. So this is the sum of all the supplied from one DC to the different market and this should be less than the capacity. And finally, I added here the balancing constraints of the conservation of one constraint and also the linking consent. Okay, so nothing new and you should be familiar with this. So then I'm going to just run the solver. And you can see that here in the solver. Not sure if you can see it, but here in the solver I'm trying to optimize the total cost subject to the user or trying to change my decision variables. And I have basically four types of constraints. I have the demand constraints that I put over here, the demand constraints. Then I have the capacity constraint in this part, conservation of flow constraints this part. And finally, the linking constraints this part. Okay, just click on solve and we'll get the solution. Okay, so in this case we are opening the three facilities. We're opening the three division centers. That's one of the answers to the problem. And this is the total cost $390,900. Okay, and that's how we will answer the question. Okay, so let's continue and let's try to solve the second question. And the second question is asking about an additional situation. And this additional situation is, let me see if I can show you is the following. Okay, so the company finds that building the DC in Texas is not longer an option due to some regulations. So in this case, Texas is not longer an option. So we are not able to open a DC there. So we have to model this and come up with the optimal annual cost under this situation. Okay, so that brings me to the last question. So how would you model this situation? So again, so we have an additional constraints that is saying that we cannot open any more the facility in Texas. How do you model this situation? And we have three options for you. Start modeling from scratch, considering only two DCs. So only considering New Jersey and Nevada, or maybe you can modify the initial model. So the template that I show you, you are removing the information that is not related to the Texas. So just removing some maybe some rows and some columns. And the last approach is just add an extra constraint to make sure that the DC is in Texas is not open. Okay, so we're starting to receive some responses. So some of you are saying that start from scratch. Others are saying that modify the existing template. And the majority, so almost took a three quarters of you are saying that you would add an extra constraint to make sure that the DC is not open. Okay, and that's the approach that we follow. Okay, so I'm going to be showing you that constraint. So here in this new tab, I have question number two. And the only difference that I have is exactly the same thing in the model itself. So the only thing that I did different is I add an additional constraint and that constraint, sorry. Sorry. I'm going to do it again. This alone. Okay, so the only constraint that I added, I won't be solving because I have some issues here. Okay, sorry, sorry about that. I cannot share with you. So but the only difference that I did is, is in this part. So when we have the decision about asking if we should open or not text us. So this particular cell, the cell C 20. In this case, I added a constraint that this value should be equal to two zero. So that's the only change that that made and I rerun the model and I got the new, the new solution. Okay, and with that, I will, I will stop and I will answer any, any questions related to this problem or related to a network design problems that you might have. Okay, Milan, do you have any questions? So there are questions related to the midterm. Do you want to answer those now? I will do that at the end. Do you have any, do we have any questions that it's related to? So there's one question on the modeling by Jay, and he's saying that sometime XO is giving hard time. It's not giving result and if you do it from the scratch, it gives a different result. So any like recommendations and how to fix that issue. Yeah, so we have, we have experienced this issue many, many times. And I think the best, the solution to this problem will be to open a, to use an open solver. So open solver is an add in. So this is completely, completely free. And I think it's more powerful than the, than the normal Excel Excel. So my recommendation will be to download this open solver and use it with within Excel. And that's a, how you can avoid this, this issue. Okay, so no more questions? I'm not related to this question. Okay, so we'll take some of the questions at the end of the slides. Okay, so let's move on and talk about now the fixed planning horizon model. Okay, let me share the screen. So you can take it over. Okay, so here's the question. Let's take like a few, like seconds just to read this question. So, so the question is about I'll top only manufacturers and they basically manufacture and distribute electrical poles. And there's a couple of information mentioned in the top it is not very relevant to the question. The important thing really in the question is that they are the you is that we need to figure out how many poles we need to produce each week. So that's that's sort of it seemed it's objective of the question. And then the good thing about this question is that explicitly lays down the matter that has been using which is fixed planning horizon. And the other thing that is important is six weeks. So we need to figure out the plan for the next six weeks. And then you have this table. And there's a couple of things information mentioned below the table. Again, you can read through it, but all that stuff is already in the table. So really the table is the most important thing that you need to focus on. So it's a it's a relatively straightforward question in that we have been very explicitly told what is the objective and what method they have been using. And if you look at the table basically the first thing is the week. This is time period. Then we have the forecast that is the number of the poles in each time period. Then below that is a set of cost. And again, note the unit here, which is a dollar per set up. So one set up needs like $250. And then we have the holding cost below it. Again, look at the unit which is the dollar per pole per week. So it basically means that if you look at this number, it you have to pay $1. To hold like one pole for one week. And one important thing is that at the end of third time period, the set of cost and the holding cost increases. So this is really the context. Again, like I said, it's a pretty straightforward question. So let's see what we need to do about this question. So this is the first part to it. So the first part basically says that the company has traditionally used the lot for a lot approach to define the production lot sizes. Using this approach, what would be the total cost of manufacturing the concrete poles in the next six weeks? Now, okay, I mean, I really like these sort of questions because very explicitly it has been laid down what we need to do. So that is we need to use lot for lot approach and need to figure out the total cost, which is again the sum of setup and holding cost in this case. So let's stop this thing and I'm going to move to the Excel sheet. Now, again, this is something you could also do it with like a with a page and pen, but I mean Excel, I think is the best way to go about it. So let me switch the screen and go to the Excel sheet. You have to stop first. So again, this is the same table that you saw in the in the question. And so we're doing this for lot for lot. So really the whole concept of lot for lot is that I tell you that the demand for next period is let's say 100 units and then you produce 100 units in that time period. Then I tell you, let's say the demand for period two is 120 units, you produce 120 units in period two. So whatever the demand is, you produce exactly the same units. So this is pretty straightforward. So let's, we need to figure out a couple of things here. The first is the production, which is how many units to put to produce. And like I said, for lot for lot, it's really straightforward. So it is equal to the demand. In first time period, this will be equal to 1497. In second time period, it will be equal to 115. And then we can extrapolate it to all the relevant cells. Yep. So this is basically the number of units that needs to be produced. And remember that this is something that we are doing for for lot. The next thing that we need to do is the inventory on hold. Now really, you don't have to do the calculation for this case, because you know the inventory will be zero. But just for the sake of learning how to enter the formula will do it in this case. So we know like the initial inventory is zero. And so the inventory in any period can be determined by the inventory change formula, which is incoming inventory, which in this case is the number of holds being produced in that time period. Plus the existing inventory, which in this case is zero minus the stuff that we are selling, which is the demand in this case. And then again, we can extrapolate this formula to all the relevant cells. And like I said, we don't have to really do this thing. But just I want to show the formula to you. So this comes out to the zero. So the last thing that we need to do is to the last two things to determine the total cost. The first will calculate the setup cost. And it's very straightforward in this case. So we are producing and we are manufacturing units in every time period. So we'll have to pay set of costs in all of these six time periods. So and that will be equal to the set of costs that we have been provided in the question. Okay. So this is the set of cost and the unit here is the dollars. And then the last thing that we need to figure out is the inventory cost and which is really zero in this case. So we don't have to do anything. A good technique will be to just to apply the formula because we will need this formula in the next part. So which is inventory cost will be the inventory on hold multiplied by the holding cost in extrapolating it to all the relevant fields. And finally, the last thing that we need to do is to really sum up the cost for the setup and inventory cost. And once I do that, I have my final answer, which is 1650. So if we use lot for lot, the answer comes out of the 1650. So now let's move to the next part. I'm going to switch back to the PowerPoint. So the next part basically says that Eltopol is now considering different methods to determine the production lot sizes. The company wants to use a silver meal method to plan this production instead, using this method, what would be the total cost to manufacture the concrete poles in the next six weeks. Again, like I said, I really like this type of questions in that they really explicitly lay out what method to use and what are the things that we need to figure out. So here in this case, we need to apply the silver meal method. So again, let's move to the Excel sheet and see if we can actually apply the silver meal method in the data that we have been provided. So actually we will see one of the questions. So Sachini is asking, we can explain the silver meal method. Okay, awesome. So we'll answer his or her question. Yes, so I'm going to switch back to the Excel sheet. And we can share this actual sheet with you also later on. Okay. So again, this is the same data that has been provided. Now the whole, the simple idea of silver meal method is that while to figure out like what to produce, we want to look into the forecast of the next period. And really this is still a heuristic approach, but a little bit more sophisticated than what we did for a lot for a lot. And this is the algorithm. And really what this question is asking is that can you read this thing and apply it. So it's a very useful skill to learn like reading algorithms and being able to apply it on your data set. And what I will do in this case is that actually I'll go through the algorithm and apply the silver meal method on this data set. So let's actually start doing that thing. One important thing that you need to know before you basically start this algorithm is this, the concept of total relevance cost, which in this case is basically your set of this inventory and holding cost. And then there's another term which is total relevant course per unit time. So you take the total cost and you divide it by the number of periods. This sounds, this might sound a little bit abstract, but let's do it and I think things will be very clear. So let's start applying this algorithm. So we'll start with basically step one, which is we need to start at the one. Okay. So, so you can see like these is T. Okay. And then we need to set n is equal to zero. Let's set n is equal to zero here. This will be clear why I'm doing it in this way. There are many other ways of going about it, but this is like one way that you guys can follow. Then we can need to calculate the total relevant cost per unit time. So we'll do it for T is equal to one. So which in this case, you can see where I'm entering is just equal to the setup cost. So if we order, if you produce in like time period one, we'll only have to pay the setup cost because there will be no inventory. Okay. Now let's set n is equal to two. So we are basically incrementing n. And now we need to calculate the total relevant cost for both these time periods. So setup cost will show the 250. But since we are ordering, since we are producing for time period one and time period two, there will be some inventory on hold at the end of time period one. And that inventory will be equal to 115. So we'll have to pay some invent, inventory charges at the end of time period one, which will be equal to 115 into the holding cost, which is one in this case. And then since this is per unit time, so we need to divide it by the number of time period, which is two in this case. So next part of the step, so we're at now step six, we need to compare these two numbers. Okay, so we need to compare 182 with 250. We will stop once this number is greater than this number. So which is, so in this case 182 is less than 250, which means we can continue. But if let's say this number 182 was greater than 250, we would have stopped at that point. But since it's less, we will continue with and start again with step number four, which is the increment and again, and is equal to three. And again, we'll have to use the for the same process. So now what we are doing, we are ordering for these three, these three time period at time is equal to one. So which is a set of costs will remain the same. Okay, and this is a little bit tricky, but if you're a little bit concentrated will be clear. Like if you please, if you if you produce in time period one, they will be inventory for time period two and time period three. So the inventory at the end of time period one will be equal to 115 plus 708 into the holding cost. And the inventory and the end of second period will be equal to 708 into the holding cost. Okay, sorry. So this since this is per unit time, so we need to divide it by three. Now this number comes out to be greater than 182. So this is the time where we stop. So what, so now we can use information to at least fill in the data for the first two time period. So what this is saying is that at time period one, you should produce enough for the first two time periods, which is 1497 plus 115. These are the number of polls you should use are the number of. It's something an area. So these are the number of polls that you should manufacture at time period one, then at time period two, you know, don't need to manufacture anything. Okay. The inventory holding costs you already figured out how to calculate this thing. And the setup cost will be 250. The inventory holding cost will be the inventory on hold multiply by the holding cost. And we can just extrapolate this to all the relevant cells thing will be getting short on time so really what you have to do is to continue with this step. So the next step after this will be to start now from T is equal to three can remove this end. I just want to show what the next step will be and then I can show you the final solution. You start from step, step number three, and again, do the same process and continue with the same algorithm that we did for the first that we did in this role. So the final solution will look something like this you can see here. And what you see this is the part which which I showed you, and this is the stuff which you can figure out yourself. And then based on this information you need to fill the table, and that will give you an idea of when to produce and what amount of polls to produce in that time period. And then you if you sum up the setup cost and inventory cost, you would have the total cost here, which comes out to be 1505 which is less than the simple heuristic method of lot for lot. Okay. So, I think you're getting short on time but if we have time I can quickly tell them the next question or do you think we should answer the equation. I feel have some some some questions so let me try to answer answer there. Okay, so we have some some questions. So let me find one that is related more related to the topic that you presented. So lean is asking about saying from the previous years what are the common mistakes people tended to make when solving a fixed planning horizon problem. Do you have a sense, or maybe when you were solving this problem where where may the key things that they should be be careful. Yeah, I think so the important thing is that so there's this method and there's other method that you didn't have time to show which is the optimal method in both the method. The important thing is that algorithm is already there. So you should be able to very rigorously follow the algorithm. What happens is that while following the algorithm you might like get like lost with some of the steps and that can lead to errors. So I think it's a very useful art to be able to read an algorithm and follow it. So this is something that you want to practice and not being able to not having enough practice can lead to sort of misrepresentation on how to implement that algorithm. So that's probably the biggest mistake that you can make. Okay, awesome. So we have some some general questions about the meter, the meter exam. So SJ is saying during the exam, will we know the answer is correct or not when we submitted. So I mentioned during my intervention in this case, the answer is no. So we won't provide any feedback during the exam. So you won't know if you are right or wrong in each of the questions. Okay, so no feedback during the exam and not feedback or solutions after the exam. So the only thing that will provide is your grade. So how much did you score in the meter exam? So no feedback. So that answers the questions. Order is how much harder will the meter be compared to the assignments? So I would say a bit harder. So there's not a big difference between the meter and the GAs. So if you did the GAs and you have a clear understanding of the GAs and you solve them, I mean, you should be in a good position to take the meter exam. So Rolando is saying, are you going to share the slides for this presentation? Yes. So we'll share the slides. We'll share also the Excel files. And we also will make sure that you have the link to the YouTube video. In case you want to take a look or you want to watch it again or maybe a specific session, so you will have the link. All of this information will be displayed, will be available in week number five under the life event tab. So okay, so you can find the resources there. So what else? So let me see. Can I watch the webinar later? Yes, we mentioned that. And the slides also we covered that. So let me see if we have new life questions. Can Silver Millen be modeling in SAS? I mean, it could be. But you will need to know some coding in SAS. So it's not straightforward. It's not like an optimization problem when you set the objective, decision variables and constraints. In this case, you just need to follow as Bilal was saying the algorithm. So basically you want to use SAS, you have to code that for how to, the computer should follow the different steps of the algorithm. Would we have checkpoints like we had on the homeworks? So the answer is no. You won't have any feedback. So no checkpoints on any questions in the middle. And the same thing will apply to the final exam. Okay. And with that, I think we covered all the questions that you had. If you have final question, please let us know. Also please feel free to send us an email to ac2x help at MIT. If you have any questions or any concern about the meeting. So we are here to help. Any final words to the students below? Best of luck for the midterm. And I agree with what you said. I recommend you to start early in case you have any problems or anything with the midterm. You can at least send an email to the support and get that support earlier. Okay. So from my side, the best of luck. So be prepared for the exam. And we'll see you next time. Bye-bye. Okay. Bye.