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


This is also a historic election, given that this is the first time a progressive ticket has a real possibility of winning. This Sunday, May 29th, the people of Colombia are going to the polls to vote for who will be their next president and vice president of the country. These are historic elections, given that they're taking place in a time of extreme violence and threats, not only against social leaders and human rights defenders, but against the candidates themselves. The historic PAC ticket led by Gustavo Petro and Francia Marquez have both received death threats and this past weekend during their campaign closing ceremonies, Francia Marquez was pointed at with a laser, causing her bodyguard to have to shield her with bulletproof shields. This is extremely concerning for the Colombian people and what it could mean for the guarantees to a clean electoral process and their possibility to vote in these elections. Francia Marquez, Colombian vice presidential candidate from the left-wing historic PAC coalition, once again faced a death threat on the night of May 21st. A laser was pointed at Marquez as she was on stage during a campaign rally, addressing a multitude of supporters.  She was forced to abruptly finish her speech and lead the stage in the face of the alleged danger. As she was being surrounded with the protection shields and removed from the stage, Marquez shouted, they shall not pass, we are going to liberate our people. This was the fourth and the most serious death threat that Marquez has faced since March. The historic PAC's presidential candidate, Gustavo Petro, has also faced multiple death threats since April. He carried out his election campaign under heavy security. This is not the first time electoral candidates are facing such grave threats to their lives in Colombia. In the 1990 presidential elections, three candidates were assassinated, two of whom were from the left and one was a liberal. The historic PAC presidential ticket with Petro and Marquez is favored to win the upcoming presidential elections on May 29th. Their potential victory threatens to break the decades-long rule of conservatives in the country. Since the beginning of the election campaign, they have been constantly targeted with threats by illegal paramilitary groups, allegedly supported by the Colombian right-wing oligarchy. This is also a historic election given that this is the first time a progressive ticket has a real possibility of winning. According to the recent poll by CELAG, Gustavo Petro and Marquez ticket is favored at 48% ahead of Federico Gutierrez, who is the far-right candidate in these polls. Despite the grave threats, Petro and Marquez bravely continued the campaign and closed it together with a massive rally at the historic Bolivar Square in Bogota on May 22nd. Tens of thousands of citizens joined the rally to express their support for the progressive leaders. We will be watching this election given that the key issues of agrarian development, unemployment, environmental sustainability, rights of the peasantry and many other crucial issues are up for debate. Colombia is also at a moment of extreme upheaval. Last year, there was a 10-week-long strike in which over 80 people, according to some human rights organizations, were killed due to state repression. Over 1,000 were detained and arrested. And the demands of the people have yet to be met. People are demanding an end to the structural violence against human rights defenders, social leaders. Over 1,200 human rights defenders have been killed since the signing of the peace agreements in 2016. People are demanding the full implementation of the 2016 Havana Peace Accords to this day which have not been implemented. They're also demanding the protection of former members of the guerilla who over 300 of them have been assassinated since their demobilizing in 2016. All of these issues are at play in these upcoming elections. People are very worried about their right to a free election. Gustavo Petro has rang the alarms that there's going to be an attempt to threaten the safety of these elections. In his speech, Petro vowed to build a government that prioritizes life, environment, and productive development in the country. He also promised to fight inequalities, corruption, impunity, drug trafficking, paramilitarism, and consolidate peace. At the same time, he urged people to remain alert of attempts to sabotage the electoral process by the outgoing, far-right government of President Iman Duque. Francia Marques on her part pledged to work in favor of the historically dispossessed and neglected minorities and committed to change that reality together with Petro and the people of Colombia.


Welcome to The God Project. Today's reading is Where Is Israel Today? By William J. Eisenman D.D., it must be remembered that The God Project is not about proselytizing, converting, or soul-saving, it's about what the Bible says. It seems there is much confusion surrounding the twelve tribes of ancient Israel and where are their modern-day descendants today. The story begins with Abraham. For his obedience, God made some unconditional promises to Abraham, Genesis 22, verse 17. God would multiply Abraham's seed as the stars in heaven. They will possess the gates of their enemies, and in Abraham's seed the earth would be blessed. Abraham was to be the father of many nations, and God gave the land of Canaan to Abraham and his seed. Genesis 17, verses 1 through 8, and Genesis 13, verses 14 through 15. These promises were passed on to Abraham's son, Isaac, Genesis 17, verses 18 through 19. Isaac passed these blessings on to his son, Jacob, Genesis 27, verses 26 through 29. Jacob's first son was Reuben by his first wife, Leah, Genesis 29, verses 32. Their second son was Simeon, Genesis 29, verses 33. Their third son was Levi, while their fourth son was Judah, Genesis 29, verses 34 through 35. Jacob also married Rachel, who had difficulty conceiving, so she convinced Jacob to have sex with her handmaid, Bilhah, who gave Jacob his fifth son Dan, Genesis 30, verses 4 through 6. Bilhah also bore Jacob's sixth son, Naphtheli, Genesis 30, verses 7 through 8. Jacob made a Zilpa, then bore Jacob's seventh son, God, Genesis 30, verses 10 through 11. Zilpa also bore Jacob's eighth son, Asher, Genesis 30, 12 through 13. Leah bore Jacob's ninth and tenth sons, Issachar and Zebulon, Genesis 30, verses 17 through 20. Rachel finally had Jacob's eleventh son, Joseph, Genesis 30, verses 22 through 24. Rachel then had Benjamin and died, Genesis 35, verses 17 through 19. God changed Jacob's name to Israel, Genesis 32, verses 27 through 28, and Genesis 35, verse 10. God promised that a nation and a company of nations was to come out of Jacob. Genesis 35, verse 11. Jacob's twelve sons were now known as the twelve tribes of Israel. Genesis 35, verse 22, Genesis 49, verse 28. Joseph had two sons, Ephraim and Manasseh. Genesis 41, verses 51 through 52, and Jacob blessed these two and said, Let his name, that is the name Israel, be on them. Genesis 48, verse 16.  Genesis 48, verse 19. After the death of King Saul, David was anointed king at Hebron over Israel. 2 Samuel, chapter 2, verse 4, and 2 Samuel, chapter 5, verses 3 through 5. However, ten tribes broke away and went with Jeroboam their king. 1 Kings 11, 30 through 33. Israel was now two nations. 1 Kings, chapter 11, verses 35 through 42. Solomon, the son of David, when he was king, was left with the tribes of Judah and Benjamin. 1 Kings, chapter 11, 35 through 36. 1 Kings, chapter 14, 7 through 11. Solomon reigned in Jerusalem, while Jeroboam ruled in the north at Samaria. Jeroboam gave the people golden calves as gods, so they wouldn't have to go to Jerusalem to worship. 1 Kings, chapter 12, 28 through 33. It must be understood now that Israel now consisted of two different nations. 2 Kings, Judah was now ruled by a Solomon's son, Rehoboam. There was war between Jeroboam and Rehoboam all their days. Tegelith Pilisar, king of Assyria, conquered Israel and took the people captive to Assyria. 2 Kings, chapter 15, verse 29. During the reign of King Ahaz of Judah, the people were called Jews. 2 Kings, chapter 16, verse 5 through 6. King Hosea was now ruling Israel when King Shalmaneser of Assyria besieged Samaria, captured it, and took away the people to Assyria. 2 Kings, chapter 17, verses 5 through 6 and verse 23. Now only the tribe of Judah, the Jews, were left. 2 Kings, chapter 17, verse 18. The birthright of Reuben, Jacob's first son, was given to the sons of Joseph, Ephraim and Manasseh. 2 Chronicles, chapter 5, verse 1. God scattered Israel to the north and other countries. Jeremiah, chapter 23, verse 8. Even after mass extermination procedures against the Jews throughout history, even the Roman Catholic Church pitched in, there are Jews in the world today. But where are the lost ten tribes of Israel? Israel disappears from history after their last captivity by Assyria. Remember that all Israelites are not Jews. Jeroboam set up Sunday worship bow over Israel when he was king. Hosea, chapter 2, verse 11. As a result of this, Israel lost sight of God's truth Sabbath the last day of the week. This would mean that the modern day descendants of the ten tribes of Israel would not be Sabbath keepers. They would be idolaters having the wrong God. The Assyrians migrated to northern Europe and settled in Germany, taking with them their Israelite slaves, which were eventually allowed to migrate northwest to northwestern Europe and the British Isles, as well as Scandinavia. These people had lost their national identity and Sabbath keeping that identified them as God's people and nation. These ten tribes became lost to history. They considered themselves to be Gentiles, and in time the birthright nations, Ephraim and Manasseh, began to experience the held back promises of God. Genesis 48, verse 16. Since the early 1800s, Britain and America experienced growth like nothing before in history. The God of the Bible foretold this growth and wealth accumulation. These two nations were experiencing the promises God gave to Abraham. America is mentioned in the Bible. The descendants of Joseph's son Manasseh are those who settled America to make it clear. Ephraim was to become a company of nations. Genesis 35, verse 11. While Manasseh was to become a great nation. Genesis 49, verse 22. Now, if there are Jews in the world today, Judah, then the lost ten tribes must also exist. The real Israel must exist. Modern-day Israel in the Middle East are Jews. They are not the lost ten tribes called Israel. The ten tribes have lost their identity and their history. Along with Ephraim, Britain, they are now destined to experience God's curses for their idolatry and disobedience. The Bible says there are bad times ahead for all the modern-day descendants of the twelve tribes of Israel. God kept his unconditional promises to Abraham, and now those promises are being withdrawn. The modern-day descendants of ancient Israel are under the gun. The end.


It's her favorite season. Looks really nice, but it doesn't feel really... Just that we live in like the Arctic Circle. Feels like it. Pretty much. We get the same temperatures, so... Here's what it is. Manitoba. Not a lot of people want to move here. We like it that way. Replacing some marker lights today on the truck. On the bottom rung here. I replaced this one over here. Yesterday. Stopped working. Put a new one in. Now I've cut the wires from here. Obviously, it's not sending power to the back, but that was because of this light right here. Replacing it with this bad boy. And these are temporary, actually. I just had these extra ones, luckily. Just to get them working. I'm gonna have, like I said, I got new fender signals. They got the little visor on it, too. On both sides to match this front light. That's gonna be a clear lens. And then up there, both rows. On top of the cabin, on top of the sleeper. I've got new marker lights coming. That'll be here next week. Clear lens as well. Amber lights. But clear lens. And if anybody knows where I can get a clear lens replacement for this here. I'd be interested. I'd like to get a clear lens on there as well with orange bulbs. And these are all being replaced as well. Also with clear lens. Amber lights. But that'll be for next year. After new year sometime. They'll all have new ones. They'll be a lot brighter, too. Ned is listening to music. Jamming out here in the shop. Doing a few things. I got to install this hub cover here yet. And try and tackle this. Here's my steering wheel. And the replacement for the shifter to match it. And then, over here in this box is my train horns. That I'm going to need a little bit of help putting that on. Because we need to drill holes through the frame at some point. Or somewhere to mount it. And then we're going to figure out where I'm going to mount those bad boys. I'm going to find a spot on here. And then when you get a little help on that one. I think just make sure it's done right. You should hear me coming. Progress. That word that I like so much. Most times. Most times. As long as it's actual progress. And not like the opposite of progress. But called progress. You know, sometimes people say, hey, look at us. We're progressing when actually they're regressing. And getting worse and not better. Progress means things get better, right? Look. Look, everybody. We're going to test this light out. I got it all wired up here. I just have to do the shrink. The shrink tube on that yet. Before I do that and make it permanent. I want to make sure that these lights work. Okay. So I'm going to put you here. So you can see all the lights, right? Okay. Okay. Tell me if they're working. Nice. Very nice. Yes. Cool. But I'm seeing something going on here. Seeing something going on over here in the end. Look at this. These two dials. We're flickering a little bit just now. Do you need to be replaced too? See how those are dimmer than those? What is going on here? Well, they're working right now, right? So I'm going to leave it. I'm replacing them all soon anyway. So you can see the new one shines a little brighter. That's the new one. A little brighter than the older ones. Just got to clean up all these wires and zip tie them up underneath there. And put a little chrome cover around it. And then that's done. And then I can start looking at the steering wheel, maybe. So it took a little while to find the right tools. Thank goodness Dad's shop is right nearby. I could just run over there and find every tool known to mankind. He pointed me in the direction of his steering wheel puller. And a one inch socket that I need for the bolt. Which was right down here. This is holding the steering wheel on, right? And I have this socket. I just don't know where it is. I can't find it. It's the strangest thing. So I found that. Now I'm going to screw these in here. Oops, that's a... Let's screw in not out. Okay. And we screw this thing down. You see? Onto the steering wheel.  It pushes down onto the steering post. And it pulls the steering wheel up. See if I can do this. I've never done this before, so... Disclaimer. He know not what he does. Make sure that that gets actually screwed in. Thread it in down there. Come on. There we go. There we go. Oh, no. It doesn't want to thread in. Come on now. Don't do this to me. I can tell this has been used before. The threads are a little bit warped on these things. I'm going to do what we can here. Okay. Let's see if we can get this thing to pull up. Need a little bit of a bigger socket now again. Bigger. 11-16th. Come on. Winner, winner. That's the one. All right. Oops, going to need a bigger wrench. Seems I need to replace all my tool sets. I am running low on tools and I don't know where they are. Just like that. Okay. Now I want to mark it. I said I know. Well, I'm not going to move the truck, right? So straight up should be straight. Really should have checked that before I pulled this up. The steering wheel was straight, right? Yes. The wheels are straight. My first time. Cut me some slack. Okay. There's that. The new one. Oh, this one's a lot lighter. Wow. Wow. Okay. Comes through up here. Here. That'll be straight. If not, I am going to have to readjust it later, right? Okay. That's perfect. It worked just perfect. It had the same adapter as the other one. Everything went on here just fine. So now screw this on here again. Oh, new steering wheel installed. All right. All right. All right. There's this onto here. Oops. This is the wrong one. That belongs with the other one. Where's this? Where's the new one? Here you are. Here you are. There we go. Not bad, eh? That's awesome. Just got to wipe the fingerprints off it now. But I now know how to install steering wheels. I've run out of time. I've got to run home. So I'll have to do the shifter another day. And the hub cover. That's not going to take too long. That's easy. Just got to flop it in there. I'm being summoned to the house. It's time to go. I've got to bring Dad's tools back and head back. What's going on, Frank? Holding the fort? Holding it? I need something like that. I don't know. I'm old. I don't know what's going on. Who are you? Yeah, I know you. You're that guy that visits every weekend, right? Frank, hey. I'm your dad. You're not my real dad. Chevy? Oh, Chevy? You have anything else to say to the vlog? Wait till you see my new steering wheel, man. Wait till you see it. Diesel. Anything you want to say to them, Chevy? It looked like you wanted to say something before in the last clip. It seemed like there was something you wanted to tell them. I just wanted to say Merry Christmas, everybody. This is a very special day. So you're probably watching this either on or after Christmas. I won't be offended if you just watch it after Christmas. Christmas is about spending time with your family, so no need to watch Trucker Josh on Christmas Day. We can catch up on the 26th, which is boxing day for us.  I got that new steering wheel installed. That was a gift from Jim along with the matching shifter knob. Mine was cracked, and he sent me a replacement for that as well. That I'm going to replace after Christmas, because once again, I'm not going to be doing any work. In the next few days, we have lots of family gatherings to attend, lots of food to eat, presents to give, presents to open, and good times to be had. So after Christmas sometime, I'll install that shifter knob. I've been meaning to get those horns on there. I'm going to wait until one of the services on my truck and get the guys at my shop that I go to at PBX there to help me out with that, I think. At least ask them about it. I want to make sure that they're mounted correctly. I don't want to mess that up. It's very important for the kids. When you give me the arm pump, you know? They won't expect that. Hey, Chevy. So anyways, hope you guys had a merry Christmas, and we'll see you in my next video. For us, it's not Christmas here yet when I'm filming this. We have our first gathering later today. I'm filming this on the 23rd, so we still have the 24th, 25th, and 26th every day Christmas stuff going on. It's going to be good. We'll talk to you later.