 Hello everybody and welcome to our second life event of AC2x supply chain design. Here is with me Akai Sregengar. Hi everyone. Hope everyone's doing great. Yeah, welcome to the second live event. We're almost reaching the mid way of the course. So excited to have you all here. Awesome. Thank you. So basically what we'd like to call in the next hour or so is the following. I'm going to start giving an overview of the meter exam. So basically I'm going to be describing what you should expect for this meter and also giving some rules about the meter. Then the main part of this life event is going to be, we're going to be solving some problems from past exam. So we're going to be solving two problems. One, it's about network design and the second one it's about a fixed planning horizon model. And after solving those problems, we're going to be opening the room for any questions that you might have regarding the content of the exam, but also any logistic questions that you might have about the meter exam. Without further ado, let's start. And for that, let me share my screen. This is the overview of the meter exam. So the meter exam is an open boot exam. So this means that you can use any material that you have for this from from the course. So this means that you can use the videos or you can use the slide, or even you can use the Excel that you have created or the transcript that you have created. So everything that you have available, you can use it during during the exam. And let me highlight that this the goal of this exam is to assess your knowledge. So basically, it's a means for us to know where you are, in terms of gaining the knowledge. So we are not providing any feedback during the test. So basically, you won't see the typical a check check or the the right the right sign that you have for the GS that won't be provided during the during the test. Okay, so no feedback will provide during the test. And also we're not going to be providing the solutions after we close the test. Remember that this exam is only for assessing your knowledge. So just to emphasize even after the exam is closed. If you got if you anyone reaches out asking for solutions or where they went wrong, please know that we will not be able to provide this on a new platform. Correct, it's not opportunity for learning is just a means for us to assess where you are. Okay, regarding the timing so the meter exam will open tomorrow. So that's December 4 at the usual time 1500 UTC and it will remain open for one week. That means that we are going to be closing this a meter exam on December 11 at the same time 1500 UTC. So this means that the meter exam is going to be available for one week, but keep in mind that this is a time exam, meaning that you will have only a limited time to complete. So basically, you're going to be having four hours to complete this test. So that means that when you click the start button, you will have only four hours to finish the test. Okay, but exam going to be open for one, one week in order to have the complete four hours, please start at least four hours before the deadline. Okay, and with that let me let me go and ask you the first the first question. What I want to ask you is when do you plan to test this exam and the options that I have for you are before the weekend weekend. So that means Wednesday, Thursday or Friday during the weekend Sunday Saturday or Sunday and finally after the weekend that will be the last Monday Tuesday or even Wednesday. Okay, so we have started collecting some of your inputs already 20, 20 responses. So some of you are saying that you're planning to take before the weekend. Some of you after the weekend, but the vast majority, at least a three quarters of you are saying that you are planning to take the exam during the weekend. Okay, I think that's a good. I would say that's a good time to take some because just keep in mind are also that if you start the exam just before the deadline will not be will not be able to help you as well. So the sooner you start the exam also that gives us opportunity to help you as well to answer any question that you have about the question that you are that we are asking. Okay, so the vast majority are planning to take the exam during the weekend, which is great. Even if you're planning taking after the weekend, try to take it on Monday and not wait till the last minute in case there's some technical issues or people's internet connection or something so I'd recommend taking it as soon as possible just to make sure none of these issues occur. Okay, great. Okay, let's talk about the content of the exam now. So what are the content that's going to be assessed during the exam. So the meter consists on four problems. So we're going to have from problem one until problem four. So you should expect the four problems in the meter exam and the content of what it will cover is all the material that is from weeks one and two weeks four. So this means the material, the two lessons of week one, two lessons of week two, two lessons of week three, and also the two lessons of week four. So we also provided you with some material in week five, a few practical consideration in able design. That's not going to be assessed during this test. Okay. Remember all the material between from week one until week four. Also, keep in mind that the meter is worth a total of 35% of your final grade so you are. That's an important piece of the final grade so please take your time to be to get prepared and do a good meter exam. Okay, a couple of considerations as well so please keep in mind that you cannot complete a time exam using the edx mobile app. It's fine if you watch the video using the app but you have to use a web browser in order to take a time exam. Okay, so that's a technical limitation you must use a web browser browser. I really recommend you to use a computer to complete the exam. So that's also recommendation for you. And finally, you can use any, any, any optimization a software that you that you consider. The exam is designed to be sold by by Excel. So if you are using Excel, you are good to go. But also we encourage you to use sassy if you have the knowledge or even already. Okay, but keep in mind that exam is designed to be sold by Excel but it's up to you to decide the software that are going to be going to be used. I mean, there's also questions about any other software like labor office. I mean you're free to use whatever software you prefer. This is this Excel SAS and Apple are recommendations but yeah, feel free to use any software that you're comfortable with. And also, if you can, you can, you're also free to use any code or scripts that you've developed in Excel SAS ample or any other software that you develop in the past for previous problems. Feel free to use them in the exam as well. Yes, to keep in mind that this is an an open book exam. Okay, and that brings me to the second question that I have. So the second question that I have for you and the second question it's asking about what is the software the software that you're planning to use for the of the exam specifically to solve the optimization problems and the alternatives are ample Excel, Google sheets, LibreOffice or SAS study. Okay, please provide your input. Okay, we already have more than 30 responses. So the vast majority saying that's going to be using Excel, which is, which is fine. Some of you are saying inside the studio around 20% and just a few are saying they're going to be using LibreOffice. We didn't got it, we didn't get any responses of people that are going to be using ample or Google sheet, which is also also fine. Okay. I just want to clarify one more point with the time limit of the exam. It's four hours in total, not four hours per problem. So you have four hours for to complete all the four problems in the exam. Yeah, that's, that's a good point. So basically that means that on average, you have to complete each of the problems in our it roughly in one hour. Okay, so a other consideration, please remember that the work must be on your own. So there's no collaboration during the, during the exam, please don't share any comments about the content of the exam with your classmates or even our classmates, the work must be on your own. Additionally, if you have any questions about clarification, please let us know. We're going to be monitoring the email account so ac2x help at MIT that it do. But keep in mind that these are not meant to answer questions about the content. These are meant to answer questions only about clarifying what the what the question is really really ask. So a catch is going to be monitoring this email. Again, just to just to reemphasize his point that we'll only answer questions regarding clarification we want to answer questions that are asking for hints or on help and how to solve the problem the only question we answer is under better understanding what the questions asking for it. And the final consideration is please do not post any questions or any comments in the discussion forum about the exam. So we are going to be also keeping an eye on the discussion forum, please do not post any questions or comments. And also please do not do it in any other website. We're also going to be monitoring. So we encourage you to if you have any any any questions, please go to the material revise the material. And if you have any kind of kind of clarification question, please let us know and use the ac2x help at MIT that you account. Okay. And with that, let me now move into the main purpose of this life event, going to be solving one of the network design problems. So the same material was covered in the first in the first two weeks of the of the course. And the problem that I have for you is the follow up before that let me ask you the following question. And this question is asking about what are some of the challenges that you are experienced when we are solving these type of a problems. Okay, and the alternative that I'm sharing with you basically is if for you is difficult to define the variables, or maybe is how do you define the objective function was a typical objective function for this progress or even identify the different, the different type of constraints demand constraints, capacity constraints, the balance constraint linking or even the level of server constraints. I want to hear from you about what is more challenging for you when you are modeling these type of problems. Okay, I think we have a the responses spread more than 20 responses more than 25 now. So, most of you are saying that two thirds of having problems with identifying levels of service constraints. Linking constraint as well seems to be challenging. And also the conservation of flow constraint. I'm going to be talking particularly in this problem about the conservation and the linking constraint seems to be clear at the definition of the variable constraint. The conservation of the variable and the linking function, but it's something that we emphasize when I'm solving the problem. Okay, and demand constraint and capacity constraint seems to be as well. Okay, great. Thank you for sharing your input. Let me now move to the to the problem. Okay, and this problem is it was taken from a past meter example, a situate and it's about a company that is called a medical company that basically supplies medications. And the company has a central pharmacy. And from the central pharmacy, it shipped the goods to three different distribution centers located in New Jersey, Texas and Nevada. The goods flows from the pharmacy to these three distribution centers and from there to for a main markets located in the northeast and Midwest, south and west. Okay, so again, so the flow is going to be going from the pharmacy to these three distribution centers and from then to four potential markets. Okay, for me it's usually it's a good approach to make this diagram, because I understand how the material will flow in the problem. So I encourage you to, as a first step, please do this kind of diagram. The second thing is usually I collect, I gather all the information that is available to solve the problem in this particular situation. What we know is already what are the origin, the intermediate points and also the destinations. So we know how the material flows for this problem. But also we have information about the transportation costs. So that was given in this problem. So basically how much it will take to move one box from the pharmacy to the different distribution centers, and we can see that these costs are different. So depends where we are sending the goods. And also we have information about the transportation costs for the second piece to move the goods from the distribution centers to the final markets. Okay, and we can see that each of these transportation costs has a different transportation, unit transportation costs. Okay, so that's information that is given. We also have information about the fixed costs. This is a fixed cost that we incur every time that we open or we run a facility. So it's a, this fixed cost is link is associated with each of the distribution centers. So we have 15,000 for New Jersey, 10,000 for Texas and 20,000 in the case of Nevada. And then we're going to be incurring in each of these costs costs if we're going to be open the facility or not. And what else. Okay, so that's all the information that we what we have additional if we have a demand that we need to satisfy. Okay, so that's generally the second step so gather all relevant information for this for the problem that we are trying to solve. So I'm going to be deciding what need to be to be solved. And basically, typically for these types of problems we have two main decisions to be to be made. The first decision, it's about the flow, basically meaning how much product we're going to be shipping from the different, from the different notes. In this particular problem, we have two types of these decision variables. The first one is what is called in one flow. Basically, we need to decide how many boxes we're going to be shipping from the plants, from the pharmacy to the different distribution centers. So basically we have three of these decision variables. And also, we have what is called a ban flow, basically, the flow that goes from the different centers to the different markets. Since we have three distribution centers and we have four markets, we will have a 12 or three times for a different values for these decision variables. Okay, so we have, this is the first set of variables, the flow, and we have two types involved on a flow. So in total we will have 12 plus three 15 of these flow variables. The second decision to be made, it's about if we are keeping or reopen a facility, this in this case or not. Since we have three distribution centers, we have to make three different decisions. One for each of these different centers. And the way to incorporate this is using this binary constraint. Zero meaning that we are we are not opening the facility and one meaning that we decided to open the facility. Okay, and just to clarify, so this is the binary constraint and all the flow variables are going to be typically going to be integers because we are shipping in this case, boxes. So basically the objecting function so typically typically in this type of problems what we aim to do is to minimize total cost. And for this problem, the total cost is going to be composed for two cost component the first one is going to be the transportation cost. Remember, I just show you and share with you the transportation cost. For each of the of the legs. So basically when I be multiplying each unit transportation cost by the amount that we are shipping from the different from the different notes. So that's the first component the transportation cost, and the second component is going to be the fixed cost. Basically the cause that we're going to be incurring if we open the different distribution center. Okay, so what we have done so far we have a diagram of the of the problem we have collecting information about a different data that was available. Then we said the decision variables to types and also we said the objecting function we're trying to minimize the total the total cost, which is composed by transportation cost plus the fixed cost. Okay, and the final piece is regarding the limitation of basically trying to answer what are the constraints to solve this this problem where the limitation to solve this problem and typically we have a some constraint. The demand is associated with the demand. So that's also information that was given. So basically we need to satisfy a specific demand for each of the of the market, and these are the numbers you can see in the on the screen the numbers in the number of boxes. The first, the very first constraint we need to satisfy the demand. Okay, so basically all the, all the goods that are cheap to the different demand notes should be equal to the demand of the of the note for in this case, in the case of for example this the south, the south market, all the goods that are coming into this market should be equal, greater or equal to the demand that I have. So that's typically the first a set of constraint demand constraint how many demand constraint will have as many demand demand points as we have in this particular program we have for markets will have for a demand constraints. The second capacity, the second constraint is related to the capacity of the distribution centers that was also given in this problem we have one a maximum capacity associated with each of the three distribution centers, and that's something that we also need to satisfy. Basically, all the all the goods that are coming in to the decision centers should be less or equal to this maximum capacity. Since we have three different different distribution centers will need three of these capacity constraints. There is no capacity constraint related to the pharmacy so we are free to ship or send as many goods as we as we as we can. Okay, a third type of a typical constraint are what is called conservation of flow constraint or balance constraint, and this typically happens when we have some transmission points. Basically, when we have notes in which we receive some goods and then we send to other location. And as you can see in the in the picture in the diagram. The notes that are playing this achievement role are distribution centers. They are receiving goods from the pharmacy, and then they are sending those goods to the different markets. When we have these transmission points, we need to use this conservation of flow constraint, and this conservation of flow constraint basically what he's saying is all the goods that were that we are receiving that are coming in to each of the different center should be equal to the, to the flow that is going out. So basically, the inflow should be equal to the outflow. How many of these constraints will have as many as treatment points we have since we have three disease that act as treatment point will have three of these constraint one for each distribution centers. Then it will have the linking constraints. That's also an important piece. And this piece is basically this type of constraints we need when we have a combination of flow flow variables and also binary variables. So the, the function of these constraints as the name says is to link the variable constraint so the flow constraint with a binary constraint. So, and basically the meaning of this constraint is if we are shipping goods through each of four through a decision center is because we decided to open that that facility. So basically we're making sure that the value for the decision variable is going to be one. And that's what the linking constraint is, is, is doing. Okay, so that's the, the, the typical. So for this particular problem we have not considered the, considered the level of service constraint because the problem is not as possible. Okay, so what are the questions of the, the problem. The first one is a how many disease should the company open in order to minimize costs. So basically we have, remember that we have three distribution centers. So the problem is asking how many of these we should open and the second one is asking about what is the optimal annual cost. Okay. And let me show you a how I organize all the disinformation in a Excel spreadsheet. So basically, everything that is colored in great is the information that was given so we have from cells, the 11 to the 13 we have the fixed cost from sense the 19 to be 21 we have the unit transportation cost, the invite unit transportation cost, and from sales a C 35 to F 37. So we have the unit transportation cost for the other upon. We also have information about the capacity that is in this part in column I, and the demand that is in row 31. Okay, so everything that is coloring great is the input information that was was no. I also color in yellow, all the decision variables, the two times on one end we have the binary values in this in this part from cell C 11 to C 13. And the inbound sorry the flow variables are divided. So I have one for inbound and other for outbound. So the inbound flow variables are in sales C 19 to say a C 21. And finally, the outbound are are from C cell C 26 until a cell F 20 in 28. And as you can see also in this screenshot, you can see the main, the main constraint. So the demand constraint, capacity constraint, the linking constraint and also the balance constraint. After just using the solver the Excel solver. This is the result that that I got. Okay, so to answer the first question is how many distribution centers we should open. So the solution is saying that we should open three of them. So basically we're open all the available distribution center. And the second question was the cost, the cost. As you can see was composed by three components. First one is the fixed cost. Since we're opening the fifth, the three facilities. So the, the fixed cost is going to be the sum of the three individual fixed costs. Then we have transportation cost which is divided by inbound and about transportation cost. The three, so the sum of these three cost component is going to be the total cost. Okay, in this case, a 390,000 and a hundred dollars. Okay, and that's how we solve this, this, this problem. Okay, the second question. And with that, I'm going to be ending my, my participation in this, in this piece is saying the following. The company finds the building that is in Texas is not an option due to state regulation. So basically we cannot open a distribution center in Texas. And basically is asking what would be the optimal annual cost under this condition. Okay, and with that, I will ask this question to you. So basically what we are saying is, okay, we cannot open a facility, we cannot open a distribution center in Texas. And the question for you is going to be, okay, how do you model the situation. And we have a couple of options. The first option is to start modeling from scratch. Okay, so we have to repeat everything and create an excellent spreadsheet from from scratch. The second option is modified initial model, just removing information related to the distribution center in Texas. Okay, so remove all the information in the original spreadsheet that it's about Texas. And then the final option is add an extra constraint to make sure that the DC in Texas is not open. Okay, adding an icon strength. Let me tell you that the three options are valid. But of course they are the one that is more efficient. And let's see your answer. So we have almost a 30 responses. Some of you are saying that around 10% that start start from scratch would be a good option. 1313% is saying that modified initial model and the vast majority around 75% is saying that we need to add a constraint. I would say that that's the most efficient and efficient way to go. Just add a concern and we have a couple of options to do to do so. So typically, keep in mind that we are not allowed now to open Texas. So one way to go would be okay. So we need to force the value of this cell, the cell C 12 to be equal to zero. And that's why I'm doing here. Okay, specifically, now we are forcing to make this value zero, meaning that we are not opening this if you center located in Texas. Okay, that's one alternative using just adding a constraint. Another alternative would be instead of adding a constraint. So we might also modify the fixed cost. Okay, so now the fixed cost is 10,000. We might increase and use a really big number, for example, 1 million. Okay, if you use $1 million as a fixed call for Texas, so the model seems this is a minimization objective model will force not to open this facility. Okay, and that will be a second alternative to solve this problem. This will be the solution. So you can see that now the value for the decision variable associated with Texas is now zero. Okay, and with that, I will open to any questions. There's a few questions. One of them is back to the arc flow. I guess you can open that again. The arc flow diagram. They want to know where the balance constraints are in the arc flow diagram. You just talk over that. I'm going to be sharing my screen. The linking constraint, the conservation. The balance constraint. Okay. Okay, the balance constraints are the conservation of flow constraints. Okay, so they are synonyms. Balance or conservation flow constraints are exactly the same. Meaning that everything, so for every transshipment point, all the inflow, all the flow that is coming into the facility should go out. Okay, so the inflow should be equal to the arc flow. So basically the value of this decision variable of this arrow should be equal to the sum of these three or four hours. Okay, so that's the balance constraint. Perfect. And the other question, I think this is an interesting one. A good question is regarding constraints like capacity and demand. In some cases we see that the solution uses equal. And in some cases we see it uses less than or greater than. So what's a guideline to use for that. Okay. So typically I would recommend use to use the the equal. So we tend to use the greater or equal because that's a computationally more efficient. So meaning that the solver that are using your computer will find a solution in a more efficient way. However, particularly in this kind of problems if we use the greater or equal when we have the level of service constraint. We might we might exceed the demand. Okay, so in order to fulfill the level of service constraint. So we might say we might send more goods that are allowed. So that's why in order to have the optimal or the, yeah, the minimum cost solution. I recommend use to use the equal, the equal sign for the demand concern. Okay, perfect. Okay, one question. Let's move on. Now it's going to be the tune of a. Right. Okay. All right, so I'll be going over the fixed planning horizon model question. It's a practice question that you can use for the exam. So let's take a quick look at what the problem is. So we're looking at a problem for Alta Poli. They're a concrete electric pole manufacturer and distributor in northern in the northern city of Montreal, Mexico. They have six steps in their production process. And once their concrete poles are produced, they're sent to warehouses located in different parts of the city that are strategically located to ensure that they can reach different different markets. So one of the key decisions that they need our help with is figuring out how many, like one number of concrete poles need to be produced each week. And as a fixed planning horizon for six weeks that shows the demand or the forecast for the next six weeks as shown in the table. So as you can see, for the weeks one to six you have a forecasted demand of how many poles will be required by the market in these six weeks. And they also have some initial data as well. They say that the initial inventory is zero. And they also have some information on their holding cost, which is $1 per pole per week for the first three weeks, and then $1.5 per pole per week for the next three weeks. Similarly, with the setup cost, they also anticipate an increase in the last three weeks. So initially setup cost. By setup cost, we mean that each cycle of production, no matter how many they're producing that period, they have to pay 250 somewhat of a fixed cost for a given period, as long as they're producing something. So it's 250 for the first three weeks and 300 for the next three weeks. All right, so the first method they want to use, this is what they traditionally use is lot for lot, or L4L. They want to use the defined production lot sizes. And using this approach, they want to figure out what the total cost would be of manufacturing concrete poles in these next six weeks. And by total cost, we mean the sum of setup and holding costs here. We know that since we're producing lot for lot, we're only producing as much as to cover that specific weeks requirement. So if we go back here in each week, we're only producing as much as the forecast is for that week. So in week one, we're producing 1497 week 2115 week 3708 and so on. So as such, you have no holding costs, no excess inventory, which leads to no holding costs. So the cost component in the total cost equation we have here is setup cost, which as I said is $250 for the first three weeks and $300 for the next three weeks, leading to a total of 1650. So this is a quite easy problem since we're using lot for lot, there's no inventory, so no holding costs. The only thing we're looking at is setup costs and how they add up over the six weeks period. Right. So this is, it gets a little more interesting here. Now they want to look at some different methods to see what the production lot sizes should be. They want to try and see how the silver meal method looks and using this method what the total cost would be again total cost here we mean is the sum of the setup and the holding costs. And they want to know what the total cost would be across the next six weeks for manufacturing these polls. So the basic idea of the silver meal method is we look at the next periods for cats demand this period, if it reduces the average cost per period. And our goal here is to minimize the TRC per unit time, which is the TRC for a given time period divided by N. So this is the algorithm we use to go over the silver meal method. So we started T equals one, and we said n equals zero. Here we calculate the TRC per unit time. Then we add. We make n equals n plus one, so now and becomes and becomes one. And we calculate what the TRC per unit time would be at this time period. We noticed that if the TRC is greater at the next time period and the previous time period. So we place an order in the time period T for the quantity equal to the forecast demand of periods from T to T plus and minus one. And we set T equals T plus and to go back to step two and start this process again. If it doesn't if TRC per unit time at T plus and is not greater than TRC per unit time at T plus and minus one we go back to step four and continue the process. I don't want to go into them, but I'll show an example of how this is calculated. So let's start here. So we see that we have the forecast, the setup cost and the holding costs for each of the six weeks for these electric poles. And we can look at the total relevant cost here across the six time periods. So we start here at this 250 number. So this is the cost of producing forecasted poles for week one, averaged over one time period. Then according to the algorithm we could keep going. We look at time period to add that demand and also and see if we produce the demand for week one and week two together and average it over time two time periods what the total average total cost would be. That's 182.5 since so in this case since we're producing for weeks one and two. So that means that means that we are including a set of costs. No, so we would only include set of costs once since we're producing all of it together. But the week two demand that we have will incur holding costs for that one week. So basically this 182.5 that is averaged over these two weeks is basically one set of costs of 250. Plus holding costs for these 115 poles that we have to hold for one week until we enter week two, averaged over two time periods, a good clarification. But given that the TRC per unit time at two is less than one, we continue going as per the algorithm. So you can do the same thing here. So this assumes that this fine entry number basically says that we produce the forecast demand for all three time periods one, two and three in time period one. So that's one set of costs. Plus we account for a holding cost of these 115 poles for one week, and the 708 poles for two weeks, since we're producing all of that one and average that over three time periods. So now that we know that this is higher than the TRC here is higher than here. So we, that's our break point. And we say that we produce the demand for weeks one and two in time period one and start again at time period three continue with the algorithm. So you continue with that to figure out how much we produce in each week. And with that we can get our total cost of 1505. Okay, so basically the solution in this case would be to produce in week one for week one and two, of course, then producing week three, just for three and then producing week four, for weeks four and five and producing week six. Exactly. And that's what the total cost would also tell you. So we said that we produce for weeks one and two in week one, because your break point is here, then you continue with the algorithm starting at three, your break point becomes here because this is higher than this. So that's your break points you produce week threes production in week three or week threes demand in week three, and you continue with week four week five and week six and that's how you get your total production, which then leads to your total cost accounting for inventory cost and set of cost accordingly. Okay, great. Perfect. The last method that the company wants to try out and see is the optimal method. And in this case, they don't want to know the total cost but rather how much should be produced in each week. So there's two ways to do the optimal method we can either use a multi integer linear program or use the Wagner within method of the algorithm to solve this problem. So that's what we use here. So that's what the algorithm says. So we started time t equals one and we find the cost for ordering just enough to satisfy that given time period. And then we look at all the past orders until time equals t equals one, and find if we add those add that demand on and produce it in one order with that reduce our reduce our cost, and you keep going until t equals n, and then you can figure out what the lowest cost option would be to to meet this optimal method of algorithm. I guess so this again this will be better illustrated by an example. So, in week one as we have nothing before, and we have to cover the demand for week one, we produce all the demand for week one in week one. So that's incurred the setup cost of 250 but no holding cost, since we're satisfying all the demand for week one. Now we move on to the looking at the demand for week two, we have two options here. One is to produce the demand for week two within week one itself. So which means we would occur the incur the $250 note that this is all total cost so the cost for all the demands together. So at 365, this means that we would incur a setup cost of 250 plus a holding cost for these 115 polls for a week. That's 250 plus 365. The other option we have is produce the demand for week two in week two, which means it would incur a $250 setup cost in week one plus a $250 setup in week two leading to 500. And we noticed that 365 is the lesser of the two options, being that this is what we would go with. Now we can move to week three and keep going the same way. So in week three, we see that at 1781. This means that we're producing the demand for weeks one, two and three in week one. So here we would incur a setup cost of 250 plus a holding cost for one week for these 155 polls plus a holding cost for two weeks for these 108 polls leading to 1781. But the other option here is that we continue producing week one and week two demand in week one. And we produce these 708 units in week two and incur a holding cost for one week leading to 101208. The third and the cheapest option here with these numbers is that we produce week one and week two in week one incur the holding cost for one week, and then produce week three units in week three, leading to just an extra setup cost here with no holding cost for week units, being the 615, the cheapest option. So this is how you would go forward to see what you would produce in each week. And leading to the answers then we see that, as I mentioned, we produce week one and week two units in week one, then we move on to week three and so on and so forth. So this is an algorithm you can use to figure out the optimal method, what the optimal method or the optimal solution would be for this production, or you can also use a multi interior linear program, as mentioned in the course. Okay, great. Thank you. Thank you guys. So in this case the optimal, the optimal total cost was that value, right? So we have a 1505. So how much was it using the other one? The silver and meal. I was exactly same. Okay, which, which doesn't happen every time. So, of course, with the optimal method you will get, you will get always the best solution, the optimal solution, and the silver, silver and meal method is just an odysse sticks. Okay, meaning that you will get a good solution, sometimes going to be the optimal but not always. Okay, perfect. So I might just take a look at any questions that might have come up. Yes. Okay, so we'll open to any any questions that you have. Please now is the time about the content or about the logistics of the exam. Okay. So just a quick question about the attempts in the exam and how the creating and I guess you mentioned this but I guess let's reiterate this point. So yeah, you will have two attempts in most questions, unless it's otherwise mentioned that you only have one attempt. But again, you won't be able to see whether your first attempt was right or wrong you will receive no instant feedback. The only reason we give you two attempts is in case you make a typo the first attempt or something like that. Yeah, you won't see any feedback, but you will still have two attempts, unless otherwise mentioned. Yeah, that's correct. And whether this live event is going to be recorded and can we access it's being recorded to YouTube and we'll share the link on the course very soon. Yes, and also we will be sharing the slide that we use with the recollection so there's the slides and also the Excel file. So that's going to be available for you in week number five under the tab slide event. And also, there's no feedback before or after the exam. So the folks so you won't be able to see what questions you did right or wrong. All you will be able to see is your final score at the end and we'll be able to provide no feedback or no specific question feedback for any of the exam questions, since the purpose of the exam is just to assess your knowledge and not in terms of learning or anything. Yes, so also let me let me mention that the progress bar is going to be disabled during the during the week that the exam is. Okay. There's another question asking whether there'll be resources available over the weekend to answer questions about the exam. Yes, I'll be monitoring the email. Many times or a few times at least over the weekend. Obviously, I won't be able to respond immediately. But yeah, send the question as soon as possible. I'd recommend sending looking through the exam first seeing what questions you may have and sending so that you still have those four hours instead of waiting to the last question to send me an email and then you don't have much time to wait for the response. And yeah, there's another question about time constraint for any particular problem. No, there's no time constraint per problem. The current constraint is for the whole exam is four hours. You're free to spend as much time as you want on each problem as long as the total costs for problems does not exceed four hours. Yes. Will this case study be available in PDF form for practice. Yes, I will upload it very shortly this like the slides. Yes. Will there be provided some of the checks in the questions. No, I feel we don't have any sanity checking the questions for this particular exam. No, we don't have. Yeah, and will any model data be provided in spreadsheets or will be inputting in all. I think all the data, you would need to make your own spreadsheet model and input all of it in the spreadsheet. I don't think. Yeah, but we don't have programs that that involves a lot of data. You will see that we have many matrix with a two times five, so good 10 values. Yeah, but no more than that. And a lot of it is already in table format so you can just copy paste it. I think what we recommend to you, just copy and paste what you have in the, in the website. Yeah, do we get hints at the beginning with zero points that we got in the practice problems. No, I think there are no sanity check questions, just still straight. And regarding your last comments over meal miss optimal. Isn't it that they give the both the same minimum cost but the decision variables could be different. So, so if the decision variables are different. So that means that the, the total cost might be also different right. Okay, so but just keep in mind again so the optimal methods or the what we think will, or the, the meal formulation will give you the optimal solution, meaning that's going to be the least total cost. So in the case of silver silver and new, that's a new districts, meaning that is, I've got in that will provide a good response a good answer, but not always the case when I be the optimal. Okay, so typically, so they optimal or they wasn't this is going to be always getting always getting the solution, and see what I mean it's going to be something close to the optimal solution a good solution. And be all model based or will it be conceptual questions as well. I think there's conceptual questions as well. Yes, so we'll have one problem is going to be for these type of questions concept of problem so one of problem of conceptual and the other three is going to be a more a qualitative calculations. So data provided if it contains decimal values can also be provided also with a comma as separator. I think with Excel with using a comma separator it might take that differently versus a decimal so I think all our data provided will be an actual decimal point when it uses a decimal. Yes, we have for I think we have for the for the distances might might have some, but also for the cost so we're providing just the decimal point. I mean, it's not really the recommendation that they just do a copy and paste just to copy and paste and I mean if your Excel you as commas as decimals. Either you can recognize or if it doesn't recognize you can just manually change so there's not many data points I mean the exam is. I think if I remember correctly, the number of data points is much smaller than what you see on GS or. Yeah, that's correct. So, yeah, it's meant to test your knowledge not meant to do tedious reptile work. So right. So that's all the questions. If you guys have any more questions, please feel free to reach out via email. That's C2x help at MIT.edu, or you can have any conceptual questions that are not relating to something rated please feel free to use the discussion forums and one of the ones you were there. Okay, awesome. Thank you. Thank you guys. Yeah, thank you. Great seeing everyone here and good luck on the exam. Thank you all for attending this life event so one more time. So this material is going to be the video and also the slides and the except going to be available for you after we finish this life event. And the best of luck in the MIT exam. All right.