 So I don't know if you want to do like a quick recap of this part. Of course. So I was just talking about the call versus nervous forecast. If you look at these pictures. So you have again as I was saying generally you have this combination of correct and random information. What do I mean by that? Your demand level might be let's say 10 units per day and this may be stable all the time. So imagine you have a product that is that always sells around 10 units per day. But in practice we will always have some randomness too. So you will never have exactly 10. Sometimes you will have 8, 9, sometimes you have 11 and 12. That deviation from 10 is what you don't want to react to is if your model is too sensitive. If you have high alpha or beta levels, your model is too sensitive. You will pick up on that noise and you will adjust your forecast every time and randomness happens. And that's what you don't want because randomness that you see tomorrow is going to be different from randomness that you see next day or you have seen before. So ideally we just want to adjust our forecast slightly when we are sure that the new information includes some real and systematic changes to your demand. Okay so that's why that's all the discussion about nervousness. And if you look at the forecast here that we have the green line is a good forecast for instance. It is trying to if you look at the gray demand changes in the background. Demand fluctuates a lot but that green line is trying to keep the middle ground. Whenever demand goes up too much it doesn't go up too much. Whenever demand goes down a lot it doesn't go down a lot. So it slightly follows demand but not too much. Still there is some correlation for instance when demand is too low at the end if our green line also goes a little bit down but not too much. It gives us some time gives the demand some time a few days to prove that actually the level is really going down before adjusting itself. Okay so just saying one observation that's too low should not impact your forecast too much because we're not sure if that's real or random. Okay that's a general concept very very high level idea about calm versus nervous forecasting and whenever you do forecasting you should always adjust your parameters play video parameters move them up and down and make sure you have the right level of sensitivity. That also needs some level of understanding about your current business. If you have too much fluctuation in your business you definitely want more calmer forecasts. If you suspect that your product will have quick changes in demand you probably want to react a little bit quickly. So there's a little bit of art to it as well. All right so we're going to solve a real example of forecasting which should be helpful make sure you should be helpful for the midterm. Once we cover this make sure you follow everything and then if you do you should be in a pretty good shape for the midterm. So you're given monthly demand data on the right you have periods from january to october they're called named period zero to nine and then you have xt which is your actual demand okay and if you look at the numbers you see a slight trend happening in there from around 28 27 we will end up at 36 so there's some level of trend in there. The company wants to use exponential smoothing approach and as I said they suspect that there should be a trend however they also say that based on their experience trends don't last forever so they they taper off over time and and they become less of a trend as they go so that that's true for a lot of trends so they just don't don't continue indefinitely there every trend will will slow down at some point so the company wants to explicitly model this and they're giving you their choices for alpha beta phi and omega okay so what would be the right model to use here given that the company wants to include trend and they also want to include the tapering off of the trend what's the best model to use it's the forecast it's the exponential smoothing with damped trend so this is an extension of exponential smoothing that includes trend but also damped trend as we go the general formula is these are just i have copied these from key concept document so you have x x hat which is your forecast for the next period you also have a hat and b hat which are the for the estimates for level and trend okay tau is basically showing you how many periods in future how many next periods in future you want to predict for okay usually in a lot of the problems we solve tau is one because just we just want to predict for the immediate next period okay so if you if you set tau one your formula gets slightly simpler and this is basically what we'll use to solve our problem okay again i want to mention Chris covers this very well in the course updating procedure that happens if you look at a hat and b hat both of them are being updated as no information comes so our previous understanding of the level of demand is x t okay which is what happened with the demand what was the actual demand in period t then we used alpha parameter for a weight so this is something again a small number so we want to weight it small we also have one minus alpha which is the weight of the new information that we get and that's the difference between the previous level level of demand and then you also add the trend to it so you know you have some idea of the previous level of the demand include you include a trend in that formula and you get some idea of where the demand should be now you also have the new information and you weight those by alpha and one minus alpha so you get an updated estimate so this is the general thing that happens in all the exponential smoothing forecasts you have old information you have new information and then your new estimate will be a linear combination of those two and then the weight you choose is going to determine whether it's calm or nervous okay so you should be very very familiar with this formula by now particularly also when you use them in gase okay so let's switch to i'm going to switch to my excel file and let's do this together okay so i have to save some time i have already built the excel file here we will try to break down the formulas for you as well okay the first thing to know is you need to be organized okay especially when you don't have too much time or in general just to avoid mistakes be organized so list all the values of alpha beta phi or omega that you have very nicely and i'll also copy and paste the data that you got from the problem have separate columns for each of the variables that are important in your calculations and make sure you approach this systematically you can get very confused there's a lot of ways to make errors and the best way to prevent that is to be extremely organized okay so we have a a hat and b which are estimates of our level we also have damped b which is the damped trend so this is something i'm introducing new when when we did it in a course we did all the calculations at once but now i just try to make it more clear and separate those we will have a first estimate of trend then we will also have a damped trend okay this is just when when you multiply phi by the the trend okay this is just this term here phi times b okay so um then you have the the estimate for the next uh next period forecast so which means you have x hat but it's using information in period t to forecast the demand in period t one so basically this 29.22 should be our forecast for for February okay and you can see the actual value that the actual demand that happened in February is 27 so we have some error here right we predict that it's going to be 29.22 it's now 27 so we have about we have an error of about two okay let me just highlight it a little bit so we have an error and estimate of minus 2.22 which means uh our actual demand is two points lower than forecast okay so as i said the forecast will automatically update itself okay so let's go back to the formula um and then we have uh in here for instance that's our formula for updating the level okay if you if you go back to the formula again you will see that x hat is a function of a hat and b hat okay so the first thing to do is compute values of a hat and b hat okay and these themselves depend on new and old information that that you get from the previous round okay so going back to my first column which is um a hat the level estimate of the level of demand okay the formula here is a linear combination of uh so i have alpha which is b1 here i have c7 which is the realization of demand in this period then on the second component i have 1 minus alpha 1 minus b1 here again times an estimate of the level of the demand based on previous information so what is that this is d6 which is my previous estimate of the level which is 28 plus b3 uh which is phi my dampening parameter and also e6 which is my uh previous estimate of trend okay but what is the logic here if i said in previous in previous month if i said the level of demand is 28 and then the trend is 1.3 1.35 okay that means that level will also be increased by the trend amount to create my new level of demand so 28 plus 135 is going to be somewhere like 29.3 that's my new that's my estimate of future demand but i also have the 27 that's the real realization so i have some old information which i calculated myself based on what i knew in january and i also have some real realization which is 27 that i see okay so i now update my forecast slightly according to this alpha factor and make create a linear combination of the old and new information which gets me to 28.66 remember we have uh basically adjusted our estimate of the level but we haven't tried to match exactly 27 because again we don't want to react too quickly okay the next thing to do is so we've covered this as well next thing to do is also update the trend okay again trend is going to be a linear combination so this is again it has two components separated with this plus sign the first component starts with b2 which is my beta in here times d7 minus d6 which is exactly the difference between the two levels that i saw okay so the best estimate of the level sorry the best estimate of the trend is to compare the previous estimate and today's estimate if previously the demand was 28 now the demand is 28.66 this means that 0.66 is my trend every month that much is added to my demand okay so that's the second piece and also remember we want to multiply that we want to dampen that a little bit too okay so again this is my first this component is my first estimate and then I also use 1 minus beta and then multiply that by f6 what is f6? f6 is the dampened dampened trend okay so once I had some idea of the old old trend which is 0.66 I also dampen my previous estimate of the trend which was 135 and then take the linear combination of the two this is again exactly following this formula so if you look at here this is beta times a hat minus a hat from previous period plus 1 minus beta times phi times beta hat from previous period okay so again I'm just here this f6 is basically the 135 times phi which I have calculated here so the formula here is basically phi times e6 which is phi times b hat okay so again this is also simple linear combination between the two once I have a and b the difference that you will see in the exponential smoothing with damp trend is that whenever you calculate trend immediately after that you also dampen it okay so this was my estimate of 1 estimate of 1.16 but I intentionally distort that and multiply that by phi again if you look at the formula it's just phi times 1 points 116 which gives us 1.04 okay so I I use my best estimate by intentionally multiply that by phi to make it weaker that will assure me that I don't I don't over forecast for future periods okay so now I have one an updated an updated estimate for level let's just call it orange and I also have a new damp trend the only thing to do is just add them up and then and then I'll get the new forecast for the next month that's again following the formula so x is just a common addition of a and phi times b and phi times b is the damp trend that we calculated here okay so again that's what we do in this round if I want to do it for like for March again the same thing happens you have to use your previous estimate of level and your previous estimate of trend to come up with a new level estimate and then also look at what happened with the actual demand and then the linear combination of those will be your new level similar thing will happen with trend you will have a damped trend predicted in the previous period you will also have an estimate of the trend by by subtracting the previous two levels and then at the end so let's just use a maybe use a red color so you will have two levels that you subtract you will also have a previous estimate of the trend which is your dampened trend a linear combination of those two will give you new estimate of the trend again the same thing you will dampen it and then you will add it up to the level estimate so you'll get x okay so that's one piece it's just a mechanical process of following the formula and in my experience there's a lot of ways you could make mistakes make sure you approach this as clean as possible in the video Chris does not have a column for damped trend okay I just thought it's more clear to add that but feel free to use either approach that you feel is right okay lastly I want to mention we have a bunch of columns at the end that target the quality of forecast okay let me quickly just talk about those two E is as I said it's just a error it's a simple difference between the forecast and then the realization of demand okay so these are basically my my raw deviations okay then we will also need to square those for future calculations so I'll talk about that later too in another way we also want to take the absolute value so just remove the negative signs okay the reason for that is a lot of the companies just care about the absolute value of deviation you will lose money if you over forecast you will lose money if you under forecast okay so the sign doesn't matter too much you just want to look at the magnitude of magnitude of deviation okay again some some people may say okay magnitude itself is not enough you also have to compare it with the actual level of demand a deviation of two points out of a hundred deviation of two points to when your demand is a hundred is a lot less concerning compared to when your demand is like 10 okay if your demand is 10 and you're deviating by two you're 20 percent wrong okay so that percentage is also important and this ape column is taking that into account basically the way we calculated is just by dividing the absolute the absolute error term by the let's just call it blue the absolute error term by the realization of demand so sorry i should have made this one blue so three points point three errors divided by 30 gives us one percent so right now i just have one person error okay that gives us some perspective about the amount of error then we have some end of pipe calculation end of pipe metrics okay md is your mean deviation this is the average of deviations remember again these are deviations the average of these will be my md okay this tells me that on average i'm point nine above the real demand so i'm slightly over predicting maybe my dampening parameter needs to be adjusted maybe i'm adjusting too quickly to the reacting too quickly to demand okay but a better metric is this mad okay this is mean absolute deviations okay so this is this is actually the average of these absolute deviations let's just give it a different color now i might run out of color soon so what is it is it brown yeah so the average of these brown values will be mad this is telling me that on average i am i'm i'm above or below by 1.48 and this is much more valuable information for me again because i don't care about if i'm over predicting or under predicting mostly it's more about how how closely i follow the demand okay and then if you want to also look at the percentage that's mape so this mape is basically telling you it's the average of these apes that you calculate so this lighter slightly lighter blues which will give you an idea of percentage wise how much are you off okay so the right now i'm four percent about slightly above four percent of the value of demand and this is super useful information and you can directly convert this to value to money in a company setting and then we also have minus square error which is a smart use of exponential smoothing for getting an idea of your minus square basically we will start with some value whatever it is this arbitrary value and then every time you will just update that mse based on your new demand in in c seven and also your old estimate okay so this is a something i've i have seen used a little bit less in industry so just refer to your formula for more details we're just going to quickly pass over it but it's just we updated according to the exponential smoothing formula all the time so we can get a better a more accurate estimate of mse over time okay that's that's not something i want to focus on right now that said i want to cover two more points here okay so imagine this is a very good forecast because my red line is the actual demand my green line is the forecast it's following closely the demand and that's good and this also shows up in my metrics if you look at md mean deviation it means on average you know i have some errors here right sometimes i'm up sometimes i'm on down but on average they all cancel out so at the end overall i i fix my errors if i'm up sometime i will just go down in the next period and overall i'm i'm okay and if you also look at mad and may you will always only one point deviated and which is 33 percent okay let's look at another estimate another forecast that is biased okay this is what we call bias why is that because i am consistently over predicting i'm always predicting too much okay even if you are just too much uh you're above your demand slightly but it's just the fact that it's consistent that's a problem that means you have not calculated things very well so you are consistently making mistakes okay and that's something that will show up in md which says your order is always on average basically two points below uh and mad is also is going to show that uh again on average your two points 265 267 deviated which is eight percent okay so when you have bias md and mad both of them will show it okay what will happen if you just have variance okay in this case uh this is not a bias this is just variance basically i uh i sometimes over forecast too sometimes under forecast too much but overall i'm you know i'm not consistently up or down okay uh the problem here is md will will uh misinform us okay this is mean deviation because the deviations cancel out md will be something close to zero okay i mean you think you're doing very well that's why uh we need to always use the absolute values if you look at the absolute values actually this forecast is now worse than previous forecast if you look at that one we had 2.67 for mad okay so this is worse and also maybe we'll also show it this tells us that we are 30% off all the time if it's on average okay so uh that's another point about variance and bias those these are two things you need to be careful about in your forecast okay so we will have about 20 more minutes let me quickly check and see if we have some uh burning questions um so we just have have a couple questions you already answered while going through the exercise maybe just how to calculate um oh that's a that's a great question yeah for January for January these are arbitrary okay you just said it sets some value and that's a great question okay um same thing is for uh alpha and beta but let's just focus on a and b for now do we have any new color left for me um green probably yes okay so the fact is over the long long run it doesn't matter what value you choose okay i could be choosing an awfully wrong value here minus 1000 okay because well minus is probably impossible so plus and then here might be 200 okay just as an experiment over time because exponential smoothing is uh updating itself okay over time it will identify that oh i'm really over over the demand i'm i'm significantly over the so it updates itself so now the next the next forecast is uh the next estimate of the level is modified significantly more than 100 units modified and then the next one similar big modification and after 10 periods we are you know we started at 1000 and then we are around 100 um so it fixes itself but the worst the worst initial values you use it will take longer for the forecast to fix okay that's why we don't worry too much about the initial values but we definitely want to choose values that are close okay so um hopefully that answers the question the nice thing about exponential smoothing it it it fixes itself okay if you start off under on the wrong foot sort of say uh it will fix itself but it will take time the accurate the more accurate use uh more accurate of a position you start from it it fixes quick more quickly okay and um similar thing goes when a sudden change happens if the market suddenly changes all your current forecasts are wrong but over time it will catch up and fix itself okay it will just be wrong for the first few periods and that's the beautiful thing about exponential smoothing okay let's quick we have I think we have 15 more minutes I'll quickly go through some inventory concepts okay we have a poll for you guys there was a lot of questions about pipeline inventory and we just want to drive that message home today we have a quick poll for you yeah that one the first one yes so we have just activated it on on slido you should be able to use uh the polling area in the slider to answer okay what is the question imagine you have a EOQ model you have an annual demand of 10 000 and your lead time is two weeks okay so basically suppliers are taking two weeks to ship this stuff to you but you only pay for this stuff once they arrive at the door of your factory okay you don't pay for it at the time of order you pay for it at the time of delivery now what is the average pipeline inventory I'll give you like 10 seconds okay and then if you look at also the kcd and also the course videos you know that there's a formula for it right so average pipeline inventory is d times l but there's also some more details to it as well okay and yeah again there was a lot of questions on the forum and different places about it and then we'll see why just as I'm looking at the answers yeah it's 36 okay so is there is there a way we could show the results I don't think we have we have set it up no let's not change that yeah okay so I'll just tell you so right now we have 48 answers yeah you can you can probably share your screen yeah ensure that you just want you guys to to see your second one yes um entire screen is fine all right okay so you should be able to now cr poll yes okay so um yes 38 percent said you need to use the dl formula to get basically uh multiply demand by week uh by time basically and you get 384 units on the way okay so this is partially right because there is on average there's gonna be that much units 384 units on the way in trucks on the way to you okay but it's not a problem for me as a purchaser because I don't pay for it okay there's always inventory at my suppliers and suppliers of those suppliers do I need to include all of that you only include them if you pay for it okay if you own it in other way okay so because in this example we don't pay for that inventory it's not our inventory that's why our pipeline inventory has to be zero okay kudos to the two two-thirds uh that's set zero but um yeah you have to be very careful about when you own it if you own it at the time of order then the dl d times l formula is right uh you have to use that and then so you will have some inventory on your on your trucks coming to you there will also be some holding costs for it and all kinds of different things okay just because you own it you have to bear the cost of holding as well but if you don't pay for it you don't own it and then your inventory is zero your pipeline inventory is zero the cost of pipeline inventory is similarly zero okay so just be very careful about that in uh in in future a greater assignment all right okay so then let's use our remainder of the time to do two things hopefully one is a sensitivity analysis of eoq model which is very important once you learn about the formula once you know the mechanics also interpreting it is is a significantly important piece um so we want to talk a little bit about that we will also hopefully if you have time we will solve the second problem of today's session which is an inventory problem with backorder okay so um we want to look at okay imagine we calculate an exact and optimal value for eoq most companies will not be able to use that exact value for practical reasons okay if i tell you order 105.48 units of a product every time okay that's too complicated that that decimal part is hard i guess and some some products cannot be broken down right they could only be ordered in integer values and and more likely your supplier will tell you i don't care about small numbers just order in increments of 100 okay 100 200 300 i can't do 145 okay it's because practical reasons so now you have a trouble here your optimal ordering quantity is not possible so what do we do we will choose a value that's closer to it and meets our supplier requirements right but do we go up or do we go down okay that's the question we are answering here and if you look at my calculations uh again from the kcd key concept document you have that formula on the top which tells you what is a total how does total relevant cost changes if you use a q instead of q star and again to remind you q star is the optimal q that i've calculated and just the simple q is any value of q that i chose okay it could be different from the optimal so if you use that formula to calculate example one if you look at example one and two example one well both examples say that q star or the uq value is 100 so the optimal value is 100 but assume that you want to order 50 more or 50 less okay we will test those is 50 more better or 50 less if you just replace the values and calculate you will see 50 more will add about 8 percent to our cost but 50 less adds about 20 percent to our cost so definitely you want to order more in this case okay and that's the true that's true for all the cases in eoq if you go x numbers above just just reading this first line here if you go x units above it's less detrimental than going x units below the optimal value and similar thing i've just recalculated this for time similar thing happens with time because t and q go hand in hand when you order a lot when you order big amounts it also takes you longer to consume it so they have they behave the same okay i'm going to skip it for saving the time we have another poll for you guys this is another sensitivity analysis and the question is how do purchase cost shortage cost and pipeline inventory affect eoq okay let me rephrase that if my purchasing cost goes up if my shortage cost goes up or if my pipeline inventory is increased how does it affect the calculation of ordering quantity okay if supplier charges me basically for example if the lead time increases how does my optimal order quantity change okay i'll give you five more seconds and again the key here as you're solving it is the idea of relevant costs okay so going back to the key concept documents we have the separate formulas for total costs and total relevant cost okay whenever you calculate eoq you need to know for different models you need to know what costs are relevant okay there are some costs that do not impact our calculation at all it doesn't matter whatever that cost is our order quantity is not impacted by that there are other costs that impact us okay for example inventory holding cost is very important in calculation of eoq if you have large holding costs you definitely want to order small amounts and avoid too big of an inventory okay so that's an example but what about purchasing costs what about shortage costs and pipeline inventory and i'm talking specifically about eoq model the basic eoq model that does not allow short does not allow back orders and shortage okay we have 46 answers do you want to check them or yes yeah let's check okay i want to share my screen all right there are a lot of good answers so this seems to be less of a difficulty so 61 percent said no impact and and the answer is no impact because again you can refer to the key concept document again and i see some folks changing their answers that's too late guys so again the idea is eoq model the basic eoq model only uses the cost of inventory holding and the cost of ordering in calculation of the optimal order quantity okay it doesn't matter how expensive your product is it doesn't matter whether you have pipeline inventory or not and so on okay so these values and also the shortage costs because we you don't allow shortage at all in an eoq so these doesn't matter and then here i just want to emphasize that in every model you need to separate the relevant cost and irrelevant cost okay irrelevant cost is not going to impact your calculation of ordered quantity but it matters for business so you just keep it separate but you don't include that in your derivations and your calculations okay so this was another trick question for you and then let's see how much time we have six more minutes okay so let's see what we can cover should we do the actual problem or some more sensitivity analysis okay so let's look at the more high level stuff because what i have for you next after this is a simple calculation of eoq with back order you probably can can nicely follow your graded assignments as well for that but here i have some things that we probably have not talked about a lot okay so the question here is if we allow for back order does the order quantity get smaller or larger what about t what about total relevant cost okay so imagine i have a basic eoq that does not allow for back orders now if i suddenly you know the CEO says okay now we are going to allow for back orders what is going to happen to my order quantity does it increase or decrease think about it for a few seconds also what happens to my time periods my cycle time okay does it increase or decrease and also does my cost go up and down and this is a very very important question if you are able to solve that that means you have a very good understanding of the whole mechanics of inventory management here okay so think a few seconds about that and i also have the formulas there for you so this should also be very helpful okay so let's see let's start with q just looking at the formula i see that q star of plan back order model is q star of eoq times uh square root of one over cr or critical ratio okay critical ratio if you remember was some value between zero and one okay so when that's in denominator it will make the final value bigger because one over a value that's less than one is going to be a value that's bigger than one okay we can simply replace point nine for cr and see what happens okay is square root of a value that's bigger than one is still going to be bigger than one okay again you can verify that by by a number okay so q star times a bigger something that's bigger than one is going to increase our order quantity okay so basically if you allow for back order you will order bigger uh bigger lots okay if you order bigger lots they will last longer too right uh because i we haven't said anything changes with the demand so demand is stable you're just ordering more it will last longer too so your t will go up as well you can also verify that by the formula so t is just q divided by d if q goes up t goes up too all right now what happens to total relevant cost and this is a very hard question to answer from the formula you know on the formula you have for example in the middle you see q minus b right q goes as i just said q goes up in the planned back order model you also have b which is my back order amount which is a positive value so which one is bigger both of them are increasing uh we don't know which way will go at the end but we can infer it from uh just the logic okay imagine uh previously ceo was telling me hey you're not allowed to allow any back order and then the cost i realized what let's say one thousand dollars okay today the ceo tells me you can't allow for back order but it's your choice i just i'm just letting you do it uh if it helps okay when i model that problem and minimize cost the total cost that comes out of it should not be any worse than eoq why is that because i'm just giving my mathematical model more flexibility more freedom to search for better answers okay so it should never get worse if it's worse it will just set our uh back order level to zero i would say that okay even though you can use any back order back orders are not economical right now so zero back order will be chosen so anyways the model will adjust itself so it's never worse if anything it will it will get better because now you have the option you have more options uh if the cost of back order is not too much you can allow for a little back order and and save uh some money there okay so the so total relevant cost should stay the same or go up okay if you if you have that if you have a lot of time and a lot of patients and a lot of mathematical skills you can replace all the new q and new b in that formula and and verify it yourself but i'm just giving you a simpler logical explanation whenever you allow your model more flexibility you give yourself more options you can't be worse okay uh okay and if in the time that's left or maybe i will just cover that last piece too okay how does an all unit discount impact your eoq analysis okay this is again the same process imagine you have the basic eoq that does not have any discount does not have any back order and everything just the basic eoq and suddenly your supplier says if you order above thousand a thousand units i will give you this much discount okay how does it impact your eoq analysis this is just a reminder okay i'm still going to stay imagine my optimal order quantity was more than a thousand like 1200 okay i'm already in the discount region and i'm enjoying the discount that supplier gives me so this discount will only drive my cost out it will not affect my optimal order quantity i will still stick with the 1200 and enjoy the discount okay but if i am below that 1000 okay imagine my e my basic eoq was 800 now the supplier says okay if you order more than 1000 i will give you this much discount so i will save that 800 separate and calculate the total cost with it okay so that's one thing now i also want to see if i will save any money if i order up to that discount level so instead of 800 if i order 1000 which is the lowest level i can do to realize the discount and the savings okay so i will order a little bit more and reach to 1000 and see now what happens to the total cost if total cost cost doesn't doesn't go below what i originally had with 800 i will stick with 800 if not i will order 1000 so the only thing that happens is you will also have a second value of order second order quantity to compare so you take your eoq you look at the cost you also look at the second order quantity that you have chosen to take the discount and compare the cost okay that's how it impacts our eoq analysis and then i want to stop at here and take a quick look at our questions okay all right so we will switch to the poll's view and we don't have much questions on this mother okay we have some about pipeline inventory but because of time we will answer them offline yes yeah so any questions you asked and any reasonable questions you asked will be answered afterwards because we just couldn't get to them uh feel we don't have questions about sensitivity analysis okay no problem so um all right let me come back to screen all right so um hopefully this uh review helped today um we wish you the best of luck in the midterm feel free to ask uh any clarification questions through the helpline email again we want to remind you that no questions are allowed on the forum about the midterm and and then you will you should have six more days to take the meter and i strongly encourage you to take it as early as possible um but we will always have we always have examples of people who left the exam to the last few days and something really happened they lost internet connection or something happened uh with the platform and and they couldn't uh take the exam and i also want to remind me we don't have the capability to extend the deadline for anyone the system does not allow us to do okay the deadlines are set in the beginning and so we can't really extend it so that's why taking it as early as possible is our recommendation again it's always wise to test your system and use a computer to taking the exam and then um i just want to thank you all for joining uh to this live event our goal was to help you have a more smooth exam and i'm sure if you followed our calculations and our problems you will have a a bitter grasp of this stuff and easier time in the midterm let us know again how we did let us know if you uh you know had more troubles with other concepts um and then we will take that into account and hopefully we'll address them better in future and that's all do you have anything else to add yeah so there was this question are we going to share these problems with them uh yes i will share the spreadsheet and um and the slides and the slides with you uh it's also important to know the recording will be available on youtube channel so you can go over it again um yeah so that should be you know that should give you the flexibility if you can't if you couldn't follow us yeah so there was this uh poll that was open from the beginning that said in one word what concept in sc1x was most valuable to you should we show that that's a nice thing yeah so um i am sharing my screen and i really also want to thank you guys for your patience in the beginning of the session um as we were fixing the audio problem yeah we had also quite a complex questions there so the the exam is four hours it usually doesn't take students four hours to complete it it depends on the expertise um just to grab like to say it again the level of difficulty is similar to the ga and we're covering one week one to four it's not one problem for each week but we're making sure like we have um we're testing all the concepts that are being thought from one to four um just for those who couldn't hear what Sina was explaining and these are the results for the poll yeah we also asked you in one word what concept in sc1x is most valuable to you so forecasting jumps as the biggest thing then inventory eoq i also seen something about heuristics that's interesting we will have some heuristics about inventory management again uh sometimes it's hard to use all this formula in practice so heuristics are great they're quick calculations and and great mathematicians have shown that these heuristics will give us answers that are close to the optimal answer and they're much simpler so these are great things to learn as well and and yeah yeah i also see optimization modeling that kind of thing yeah okay great well if you have any more questions we'll answer them offline on the slido or just send us an email to sc1x help um mit.edu and we'll be happy to help just don't post anything regarding the exams or the ga's in the forum please all right we wish you the best of luck and see you maybe in the next live event thank you