I took multiple operations research classes in undergrad and I'm taking math graduate classes now. I never truly understood the connection between the primal and the dual problem until now. My mind is blown. Thank you so much!!!!!!!
just saw this after my course finished, this is good!
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The way I always understood it is that most problems are either seen as you taking up resources to maximize a profit or you are minimizing your wasted money by emptying out your storage space. In the example, you are either making potatoes/carrots to get a profit or you are essentially trying to use as much seeds and fertilizers as possible to have the least waste.
This is so interesting. I am retired now, but the last 20 years of of my working life was spent managing a dynamic truck allocation system in an opencast mine. I was mostly involved in the IT/IM side, but I knew the optimization was done with the simplex algorithm. Over the years, however, I got the impression that all the graduated industrial engineers did not understand what they were working with.I'll rewatch all of this a number of times.
@johankotze42 Interesting, i always wondered how an industrial engineer would apply Operations Research in pratice. We had to calculate the simplex by hand, but i always thought i would just use some excel plugin. I'll soon graduate in industrial engineering and am curious about key skills that you dont learn in uni. If you don't mind, what would you like to see more in upcoming IEs?
@@IxCIHAoX I mean look up the excel solver... I've learnt both doing it by hand, as well as excel, though currently I'm learning GUSEK to solve these problems!
@@IxCIHAoX I am an industrial engineer working as an operations research scientist in logistics. What I'd look for in a ie grad is decent programming skills (python/java/scala/c/c++/c# I don't care which), basic knowledge in statistics, basics in data handling and visualization and most importantly knowledge in OR and that does not mean simplex. Can you model mixed integer linear problems? Can you spot weak points in your model (big-M, symmetry, ...)? Can you write your model in your programming language of choice (for example python + pulp)? And maybe know a thing or two about heuristic solution approaches (greedy, local search, tabu search, genetic algorithms....)
Took me 2 watches on separate days while thinking about it in between to fully understand the slack loosening and tightening concept. And when it clicked, it felt really beautiful and made sense! Thanks for making it so clear.
Truly impressed by this video! As an industrial engineer, it was a challenge to learn and visualize the concept of LP and SIMPLEX. What I learned in 19 minutes from this video is comparable to my 4-month university course. Now I wish you had created this video 3 years ago. Thanks!
Wanted to say that besides your excellent knowledge on the subject, it’s an extremely rare and precious talent you have of teaching and presenting complex subjects in an accessible way. Your visuals, audio, pace and use of humour is exceptional. You have a multi-million dollar talent that I hope you benefit from!
I love your videos! It feels like you explain complex things in a way that really makes them easy to understand. Your content always triggers my interest and I find myself going into rabbit holes online lol. Keep it up!
I appreciate that you are giving the real meaning behind each step instead of just throwing some random numbers and math operations like most other creators do.
Seriously, I have not been this excited with a TH-cam channel since I discovered 3blue1brown, and that must be about 3 years ago. Sir, what a masterpiece it is. Thanks for sharing it with us.
My college professor was not bad, but this video is something else. Really utilising the technology to present complex topics in such an amazing way. I am aware of how complex and immensly time consuming these types of videos get, but please do continue making these.
Im impressed by your website and ran hours deep into a mathematical rabbit hole on Wikipedia. Thanks, I unexpectedly learned a lot today! But i noticed that on your website, the description of the maximum independent set problem and minimum vertex cover problem are wrong and mashed together
@@YTomSStating the fact that you had a correction to make and corrected it gets an extra sub from me. Thanks for the content. I’m now getting back into programming. 😊
Wow, this is awesome. The knapsack problem almost feels like it could be posed in discreet probability theory: given a random variable X, find a finite subset A of X that will maximize E[A] (=sum of p_i•x_i) and the sum of the chosen values x_i do not exceed a number k. Thanks for your website!
cannot fathom why you chose “loose” and “tight” to use for your geometric analogy of the problem. It genuinely made the pivot section 10x harder to understand in a video that was otherwise very easy to follow along with.
I didn't want to use basic/non-basic, because that was something I always mixed up when learning about the algorithm. I felt like "tight/loose" would convey the meaning of 0/anything, but perhaps something like "zeroed/free" would have been better...
that was really fun to watch. Thanks man I haven't took a math class in a while but, I was decently good at understanding math. You have a great way of explaining things and I love it! Keep up the content made me realize how much I loved math when I was taking it back then!
As an industrial engineering student who is currently studying integer LP this video has to be the best way to get a grasp of the topic. Looking forward to you getting deeper into these concepts.
this is an absolutely amazing video. It's animations are so beautiful and illustrate the essence of the method. After watching the video, I can confidently say that I have some real understanding of linear programming! Thanks a lot!
i was waiting anxtiously. for the Brilliant AD. And was pleased that the video was just pure knowledge. Thank you. For this, here is a LIKE and SUBSCRIBE!!!
This is EXACTLY what I need to learn. One problem that came up at work was how to find the intersection of N half spaces in logarithmic time, and I couldn't understand the linear programming or the simplex method to do so... Will use this vid as a starting point to get into it. Thank you!
i got confused from 5:45 the loosening and tightening, simplex method... i even got more confused with the introduction of the slack variables... I have saved this video i hope to watch it several times till i get it. Thank you very much for a great video
I struggled with linear programming when I was a student, but you explained it so well that it's easier for me to understand how it works. Thank you :)
Phenomenal video! We are going through the simplex method in my linear optimization class and it was very difficult to grasp the process, let alone the intuition behind it. Thank you for making it :)
very nice video! You really did a good job at explaining this concept very much intuitively :) actually, just a little improvement: When representing quantities or numbers with images or in this case circles, as you did at 14:56, one naturally compares the given shapes by their area they take up. Thus, a twice as heavy item having twice the height is a bit misleading, since the influence of the diameter is quadratic, and it should actually have √2 times the height. I mean, look how miniscule the 2kg circle looks in comparison to the 4kg one, even though it is just half of that, it certainly doesn't look like that - because the area is actually 1/4 of the 4kg one. And, intuitively, when thinking about them as wheights, it also makes a lot of sense to say that double the area of wheight makes for double the weight. So, just a thing for the future, when representing numbers as shapes, always think about the area, not their sidemeasures. Cheers!
Finally, an intuitive explanation of the simplex method! Your content matches that of 3blue1brown in terms of quality and ease of understanding! Subscribed Also, you might want to number the x1 and x2 tick marks
I found the answer intuitively as soon as the problem was presented (which is super simple of course) but it was interesting to see (around the 9:22 mark) that my logic to arrive to that answer is exactly the Dantzig's pivot rule. Thanks for the video it is super interesting that this intuition of mine has been reinforced by this method and that it can apply to more complex inequalities and more dimensions!
I used linear programming to solve for optimal production chains in the game Satisfactory! I made an online tool and everything. To be honest I just discovered that it was a well studied class of problems and downloaded a library to do it for me, haha. I knew vaguely there was "something, something simplex method" going on under the hood but I never truly studied the algorithm. Cool to see the geometry of how it actually works!
@@blackbriarmead1966 I made "yet another factory planner". I would post the link but TH-cam would probably eat it.
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Thank-you for this! Or should I say - děkuju? Finally someone from my country using manim and creating videos that I really enjoy watching! Keep up the great work - you have a sub from me :) Měj se!
It's pretty amazing that you summarized the most important upper level Industrial (& Systems) Engineering course in under 20 minutes. When are you going to dive deeper into the iceberg??
I hope you make more videos on this subject! We mentioned linear programming in school, but not much more other than "yeah you can plug in numbers to this library and it works" which was quite dissapointing... i want to know how and why it works.
Very nice intro to LP. I've read about slack variables, and now they make more sense. I would love to see a follow-up to N variables, which makes it less intuitive without the geometric interpretation, and a brief note on convexity. Nonconvex optimization problems require some more exotic methods :)
Great video! Just wanted to comment that most people residing in the U.S. think of a “ton” as 2000 pounds. I needed to rewind the video in your first example in order to realize that you meant a metric ton. Not a big deal, just wanted to let you know about the potential confusion. Keep up the good work!
The initial problem looks way too simple ... because it is. Of course you plant as many carrots as you can and fill the rest with potatoes. Probleme solved. To make the initial problem more complex, just add in two other factors: The amount of farmland is also limited and potatoes provide way more yield per square meter than carrots do. Yet carrots grow faster and you could sow and harvest carrots twice a season but potatoes only once. And there you have a problem you cannot solve in your head any longer, yet that is a real world problem a farmer might face.
I actually played a lot of those farm-themed diner-dash-like games that has this sort of problem. Back then, I didn't know much about how to apply linear algebra (even though I aced at all my maths subjects). I did know Excel and used it to verify hunches I had. Now that I know more, I could say that… I wish people would start with ratios and portions. Then, they know how to better do comparisons. When to do what in which order. When do we apply infinite series. When is a line a dot, a plane, or an angle. When do we use a relative scale, an informed absolute scale, or a straight-out bonkers mathematical absolute scale.
cool... it would be nice to mention that most hard problems are non-linear, non-convex, can be part of the branch of discrete decisions where it becomes computationally unscalable to use certain linear algorithms, can be multimodal (or multiobjective)... and that's where heuristic and stochastic algorithms (that have a lot of generalizations of the linear programming field) enter to even try to tackle them
Currently taking an optimisations class where we spent the first half of the semester covering the simplex method and co. I don’t mean to rush you, but if you could come out with the second video covering the dual simplex method and some of the other nuances within 8 weeks time (the final exam) that’d be greatly appreciated 😅
I took multiple operations research classes in undergrad and I'm taking math graduate classes now. I never truly understood the connection between the primal and the dual problem until now. My mind is blown. Thank you so much!!!!!!!
just saw this after my course finished, this is good!
The way I always understood it is that most problems are either seen as you taking up resources to maximize a profit or you are minimizing your wasted money by emptying out your storage space.
In the example, you are either making potatoes/carrots to get a profit or you are essentially trying to use as much seeds and fertilizers as possible to have the least waste.
EXACTLY, I just finished my finals last week and I see this video explaining the whole damn course 😂
This is so interesting. I am retired now, but the last 20 years of of my working life was spent managing a dynamic truck allocation system in an opencast mine. I was mostly involved in the IT/IM side, but I knew the optimization was done with the simplex algorithm. Over the years, however, I got the impression that all the graduated industrial engineers did not understand what they were working with.I'll rewatch all of this a number of times.
@johankotze42 Interesting, i always wondered how an industrial engineer would apply Operations Research in pratice. We had to calculate the simplex by hand, but i always thought i would just use some excel plugin. I'll soon graduate in industrial engineering and am curious about key skills that you dont learn in uni. If you don't mind, what would you like to see more in upcoming IEs?
@@IxCIHAoX I mean look up the excel solver... I've learnt both doing it by hand, as well as excel, though currently I'm learning GUSEK to solve these problems!
👀
@@IxCIHAoX I am an industrial engineer working as an operations research scientist in logistics. What I'd look for in a ie grad is decent programming skills (python/java/scala/c/c++/c# I don't care which), basic knowledge in statistics, basics in data handling and visualization and most importantly knowledge in OR and that does not mean simplex. Can you model mixed integer linear problems? Can you spot weak points in your model (big-M, symmetry, ...)? Can you write your model in your programming language of choice (for example python + pulp)? And maybe know a thing or two about heuristic solution approaches (greedy, local search, tabu search, genetic algorithms....)
This topic has to be one of the most important things I’ve seen this year. So useful. That’s crazy what you could do with this.
This is some 3Blue1Brown quality level of quality! I am genuinely shocked by how good this video and the explanation is! Thank you.
18 mins of your video is more helpful than 4 hours at my class. Thank you so much
Took me 2 watches on separate days while thinking about it in between to fully understand the slack loosening and tightening concept. And when it clicked, it felt really beautiful and made sense! Thanks for making it so clear.
Perfect pace, well thought of outline, clean and helpful visuals, good narration - what is not to love about this? You've gained a subscriber.
this is my first video of you that I've seen, and it's really amazing. i'm looking forward to seeing more videos in this series.
Truly impressed by this video! As an industrial engineer, it was a challenge to learn and visualize the concept of LP and SIMPLEX. What I learned in 19 minutes from this video is comparable to my 4-month university course. Now I wish you had created this video 3 years ago. Thanks!
Wanted to say that besides your excellent knowledge on the subject, it’s an extremely rare and precious talent you have of teaching and presenting complex subjects in an accessible way. Your visuals, audio, pace and use of humour is exceptional. You have a multi-million dollar talent that I hope you benefit from!
Your work will impact generations to come and uplift the knowledge of people who are at a disadvantage. Thanks a lot
I've just discovered your channel and when I finished the video I thought you would have more subscribers. The quality is mind-blowing, keep going !
I love your videos! It feels like you explain complex things in a way that really makes them easy to understand. Your content always triggers my interest and I find myself going into rabbit holes online lol. Keep it up!
Thank you for all the work you put in these videos, I really learn a lot with them!
I appreciate that you are giving the real meaning behind each step instead of just throwing some random numbers and math operations like most other creators do.
Seriously, I have not been this excited with a TH-cam channel since I discovered 3blue1brown, and that must be about 3 years ago.
Sir, what a masterpiece it is. Thanks for sharing it with us.
Check out Reducible, similar to 3blue1brown but about computer science topics. He's just as good.
i remember doing this in university and not understanding a thing, now it all makes way more sense! thank you
Please, make about Non Linear Programming and also about Combinatorial Optimization. Your work is really fantastic!
Damn right!
what about nonconvex instaid
Thank you very much!!
I can't wait to see the rest of videos in Linear Programming! Congratulations on this😃
Wow, well explained! I struggled to get through my linear programming course for 2 years, but you make it seem so simple!
Easily the best video on linear programming
My college professor was not bad, but this video is something else. Really utilising the technology to present complex topics in such an amazing way. I am aware of how complex and immensly time consuming these types of videos get, but please do continue making these.
Wow this made me realize linear programming is a lot less boring than what school makes it look like. Great video ♡
Im impressed by your website and ran hours deep into a mathematical rabbit hole on Wikipedia. Thanks, I unexpectedly learned a lot today! But i noticed that on your website, the description of the maximum independent set problem and minimum vertex cover problem are wrong and mashed together
Thanks for the kind words and the comment (you're right, the definitions were incorrect), I updated the website.
@@YTomSStating the fact that you had a correction to make and corrected it gets an extra sub from me. Thanks for the content. I’m now getting back into programming. 😊
I have heard black hole . Rabbit hole? Thanks 4 the new term from an indian
@@socratesphilanthropy4937 and now we have a new one 'bonus hole'
Wow, this is awesome. The knapsack problem almost feels like it could be posed in discreet probability theory: given a random variable X, find a finite subset A of X that will maximize E[A] (=sum of p_i•x_i) and the sum of the chosen values x_i do not exceed a number k.
Thanks for your website!
cannot fathom why you chose “loose” and “tight” to use for your geometric analogy of the problem. It genuinely made the pivot section 10x harder to understand in a video that was otherwise very easy to follow along with.
I didn't want to use basic/non-basic, because that was something I always mixed up when learning about the algorithm. I felt like "tight/loose" would convey the meaning of 0/anything, but perhaps something like "zeroed/free" would have been better...
that was really fun to watch. Thanks man I haven't took a math class in a while but, I was decently good at understanding math. You have a great way of explaining things and I love it! Keep up the content made me realize how much I loved math when I was taking it back then!
As an industrial engineering student who is currently studying integer LP this video has to be the best way to get a grasp of the topic. Looking forward to you getting deeper into these concepts.
Wow, what a quality! I am blown away. The best video yet! Thank you :)
The best explanation on this topic that I've come across, thank you sir!
This video made me like Linear Programming and helped me pass the exam, make another PLEASE
Thanks for the review
WHERE WAS THIS VIDEO WHEN I WAS STUDYING LINEAR PROGRAMMING
GOOD VIDEO CONGRATS 👏🏼👏🏼
Excellently explained!!! What a great visualization video. Waiting for more videos on Simplex and Dual Simplex. Thank you so much.
this is an absolutely amazing video. It's animations are so beautiful and illustrate the essence of the method. After watching the video, I can confidently say that I have some real understanding of linear programming! Thanks a lot!
aahhh I'm hoping there is a next video some day. It's so nice to look back at the stuff I learned at uni!
i was waiting anxtiously. for the Brilliant AD. And was pleased that the video was just pure knowledge. Thank you. For this, here is a LIKE and SUBSCRIBE!!!
This is EXACTLY what I need to learn. One problem that came up at work was how to find the intersection of N half spaces in logarithmic time, and I couldn't understand the linear programming or the simplex method to do so... Will use this vid as a starting point to get into it. Thank you!
What work do you do?
@@rohith9875 graphics programming for CAD systems. Basically visual tools for modelling etc.
@@preston7376 oh damn that's sounds pretty interesting
i got confused from 5:45 the loosening and tightening, simplex method... i even got more confused with the introduction of the slack variables... I have saved this video i hope to watch it several times till i get it. Thank you very much for a great video
This is brilliant. You really blended theory and practical application into one cohesive whole.
Awesome video! I believe it's only a matter of time until your channel takes off
I struggled with linear programming when I was a student, but you explained it so well that it's easier for me to understand how it works. Thank you :)
Okay that explained slack,surplus and basic variables pretty well.
I love how thorough your videos are! Thanks a ton.
Phenomenal video! We are going through the simplex method in my linear optimization class and it was very difficult to grasp the process, let alone the intuition behind it. Thank you for making it :)
I just found your channel and this is so good. You should really be proud of your work!
We need your next video!! Amazing stuff.
Phenomenal video. Very well explained. This is so helpful! Simple explanation, great work sir!.
very nice video! You really did a good job at explaining this concept very much intuitively :)
actually, just a little improvement: When representing quantities or numbers with images or in this case circles, as you did at 14:56, one naturally compares the given shapes by their area they take up.
Thus, a twice as heavy item having twice the height is a bit misleading, since the influence of the diameter is quadratic, and it should actually have √2 times the height.
I mean, look how miniscule the 2kg circle looks in comparison to the 4kg one, even though it is just half of that, it certainly doesn't look like that - because the area is actually 1/4 of the 4kg one.
And, intuitively, when thinking about them as wheights, it also makes a lot of sense to say that double the area of wheight makes for double the weight.
So, just a thing for the future, when representing numbers as shapes, always think about the area, not their sidemeasures.
Cheers!
Makes total sense when you say it, didn't come to mind when making the video. Thanks, will keep in mind!
Finally, an intuitive explanation of the simplex method! Your content matches that of 3blue1brown in terms of quality and ease of understanding! Subscribed
Also, you might want to number the x1 and x2 tick marks
You are amazing, I was hopping to find a mathematical channel like this
I found the answer intuitively as soon as the problem was presented (which is super simple of course) but it was interesting to see (around the 9:22 mark) that my logic to arrive to that answer is exactly the Dantzig's pivot rule. Thanks for the video it is super interesting that this intuition of mine has been reinforced by this method and that it can apply to more complex inequalities and more dimensions!
Beautiful video! Well done with a simple example to show the concepts.
great video, perfectly explained. Looking forward to the next one :)
bro I'd pay to watch the continuation, very well explained!
This videos is inspiring to me as I'm considering operations research as my main field of study as an applied mathematician!
detail and down-to-earth explanation
amazing stuff, I am working on recommender systems, and this has been quite helpful! You have just gained a subscriber :)))
I used linear programming to solve for optimal production chains in the game Satisfactory! I made an online tool and everything. To be honest I just discovered that it was a well studied class of problems and downloaded a library to do it for me, haha. I knew vaguely there was "something, something simplex method" going on under the hood but I never truly studied the algorithm. Cool to see the geometry of how it actually works!
satisfactorycalculator?
@@blackbriarmead1966 I made "yet another factory planner". I would post the link but TH-cam would probably eat it.
Thank-you for this! Or should I say - děkuju?
Finally someone from my country using manim and creating videos that I really enjoy watching!
Keep up the great work - you have a sub from me :) Měj se!
It's pretty amazing that you summarized the most important upper level Industrial (& Systems) Engineering course in under 20 minutes. When are you going to dive deeper into the iceberg??
This is amazing. I could understand what the dual is more intuitively.
Good job! This summarizes the course I took on LP.
omg you showing duality was mindblowing
I dont usually writte comments, but in this time i had to. sincerely spectacular explanation.
Thank you, I'm struggling with this course at my uni. Your video helps me understand it 🙏
Amazing video really helped me understand, thank you, please keep on making more videos.
This video is a life-saver thank you 😭🙏
Incredible video, thank you so much Tom! Helps so much with my optimisation course
Coming back to the video after a year. It feels great to finally understand it 😅
This video is simply wonderful please keep explaining linear programming(and hopefully any convex as well)
Maths with storytelling, best video I ever watch❤
I hope you make more videos on this subject! We mentioned linear programming in school, but not much more other than "yeah you can plug in numbers to this library and it works" which was quite dissapointing... i want to know how and why it works.
I love this use of Manim. So High Quality! New Subscriber is me.
This is so helpful! Simple explanation, great work sir!
Very nice intro to LP. I've read about slack variables, and now they make more sense. I would love to see a follow-up to N variables, which makes it less intuitive without the geometric interpretation, and a brief note on convexity. Nonconvex optimization problems require some more exotic methods :)
Absolutely excellent explanation!
I really like the background music. Very cosy math video.
"Since planting a negative amount of seeds is difficult" I love it
this is an awesome video man, congrats!
This is probably the most useful thing I’ve ever learned of since learning to breathe
0:16 - you clever bastard. Instant Like.
Turned out, it's actually trivial.
Great video! Just wanted to comment that most people residing in the U.S. think of a “ton” as 2000 pounds. I needed to rewind the video in your first example in order to realize that you meant a metric ton. Not a big deal, just wanted to let you know about the potential confusion. Keep up the good work!
Thanks for the comment, I didn't know that a ton has multiple meanings :). Will keep it in mind for future videos!
Great work as usual boss
what nice video
Nice one! This put a smile on my face.
"Stay tuned for the next video" its been a year wya?
Wow, just found your channel. Love it.
Saying that planting negative seeds is "difficult" rather than "impossible" made me laugh. Great video!
I love the bot ❤ & it"s creators+intendors!
Great! superb graphics, clear explanations. thanks
The initial problem looks way too simple ... because it is. Of course you plant as many carrots as you can and fill the rest with potatoes. Probleme solved. To make the initial problem more complex, just add in two other factors: The amount of farmland is also limited and potatoes provide way more yield per square meter than carrots do. Yet carrots grow faster and you could sow and harvest carrots twice a season but potatoes only once. And there you have a problem you cannot solve in your head any longer, yet that is a real world problem a farmer might face.
Your example reminds me of HP's examples in their old calculator (wire bound) manuals.
that you system described is still linear so the algorithm would still work, but it would be harder for the viewer to follow as a first example
I actually played a lot of those farm-themed diner-dash-like games that has this sort of problem. Back then, I didn't know much about how to apply linear algebra (even though I aced at all my maths subjects). I did know Excel and used it to verify hunches I had. Now that I know more, I could say that… I wish people would start with ratios and portions. Then, they know how to better do comparisons. When to do what in which order. When do we apply infinite series. When is a line a dot, a plane, or an angle. When do we use a relative scale, an informed absolute scale, or a straight-out bonkers mathematical absolute scale.
Ah another Harvest moon enthusiast
Wrong
Phenomenal video. Very well explained
Maaan thaaaanks for sharing this amazing content👏👏👏👏
cool... it would be nice to mention that most hard problems are non-linear, non-convex, can be part of the branch of discrete decisions where it becomes computationally unscalable to use certain linear algorithms, can be multimodal (or multiobjective)... and that's where heuristic and stochastic algorithms (that have a lot of generalizations of the linear programming field) enter to even try to tackle them
That's why they are called "hard" problems. Isn't it?
I would even say not "most hard problems", but _all_ hard problems ...
This video was amazing. Well created 💪💪
reminder that #SoME3 is ongoing, and this video definitely qualifies for it!
This actually is my submission for #SoME3 (tagged in the description), I'll also add a link to the SoME3 post 🙂.
Currently taking an optimisations class where we spent the first half of the semester covering the simplex method and co. I don’t mean to rush you, but if you could come out with the second video covering the dual simplex method and some of the other nuances within 8 weeks time (the final exam) that’d be greatly appreciated 😅
Quality work! Well done.
This was done so well! Thank you.
A very nice explanation about linear programming and simplex, also I'd like to add a Turkish subtitle to this video if you accept.
You're very welcome to, subtitles in any language are a great help to others 🙂.