The Art of Linear Programming

[@johankotze42]

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.

[@IxCIHAoX]

@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?

[@greatcanadianmoose3965]

@@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!

[@fabio.1]

👀

[@lu3tz]

@@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....)

[@mathfincoding]

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!!!!!!!

[@payrimdwein9082]

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.

[@jainickvishani5185]

EXACTLY, I just finished my finals last week and I see this video explaining the whole damn course 😂

[@prori5297]

18 mins of your video is more helpful than 4 hours at my class. Thank you so much

[@spb1179]

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.

[@Noxafurry]

This is some 3Blue1Brown quality level of quality! I am genuinely shocked by how good this video and the explanation is! Thank you.

[@puneetkumarsingh1484]

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.

[@bejoscha]

Perfect pace, well thought of outline, clean and helpful visuals, good narration - what is not to love about this? You've gained a subscriber.

[@xcoder1122]

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.

[@johankotze42]

Your example reminds me of HP's examples in their old calculator (wire bound) manuals.

[@terdragontra8900]

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

[@chamorvenigo]

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.

[@OhsoLosoo]

Ah another Harvest moon enthusiast

[@ismailchoudhury]

Wrong

[@schwaartz]

Easily the best video on linear programming

[@sanjaykrish8719]

Your work will impact generations to come and uplift the knowledge of people who are at a disadvantage. Thanks a lot

[@ehsanabbasi6218]

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!

[@TrollFunMineMafia]

i remember doing this in university and not understanding a thing, now it all makes way more sense! thank you

[@juanhbiancuzzo1490]

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.

[@pedrocolangelo5844]

Seriously, I have not been this excited with a KZbin 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.

[@macroxela]

Check out Reducible, similar to 3blue1brown but about computer science topics. He's just as good.

[@НиколайЗаднепровский]

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.

[@WavyB1]

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!!!

[@OgsLike]

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!

[@ivanperica3731]

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.

[@priyanshugoel3030]

Okay that explained slack,surplus and basic variables pretty well.

[@Alexander-oh8ry]

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

[@YTomS]

Thanks for the kind words and the comment (you're right, the definitions were incorrect), I updated the website.

[@ColinTimmins]

@@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. 😊

[@socratesphilanthropy4937]

I have heard black hole . Rabbit hole? Thanks 4 the new term from an indian

[@markgreen2170]

@@socratesphilanthropy4937 and now we have a new one 'bonus hole'

[@timelygoose]

The best explanation on this topic that I've come across, thank you sir!

[@azfarahsan]

WHERE WAS THIS VIDEO WHEN I WAS STUDYING LINEAR PROGRAMMING GOOD VIDEO CONGRATS 👏🏼👏🏼

[@VictorUn1]

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 !

[@sarkaholendova9080]

Wow, what a quality! I am blown away. The best video yet! Thank you :)

[@protiumx]

Thank you for all the work you put in these videos, I really learn a lot with them!

[@Ocara31]

Please, make about Non Linear Programming and also about Combinatorial Optimization. Your work is really fantastic!

[@demr4921]

Damn right!

[@gigantopithecus8254]

what about nonconvex instaid

[@guitarljm]

We need your next video!! Amazing stuff.

[@andrijor]

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!

[@UpsiteRealone]

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!

[@alejrandom6592]

Wow this made me realize linear programming is a lot less boring than what school makes it look like. Great video ♡

[@teodorticu2628]

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!

[@namesurname1869]

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.

[@Efesus67]

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!

[@ShashankEarth]

Excellently explained!!! What a great visualization video. Waiting for more videos on Simplex and Dual Simplex. Thank you so much.

[@kofiboamah8242]

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

[@SebastianSchwank]

I love the bot ❤ & it"s creators+intendors!

[@AlleBalle54]

great video, perfectly explained. Looking forward to the next one :)

[@feeelix]

Awesome video! I believe it's only a matter of time until your channel takes off

[@stjintje]

Wow, well explained! I struggled to get through my linear programming course for 2 years, but you make it seem so simple!

[@ajk7868]

You are amazing, I was hopping to find a mathematical channel like this

[@adolfninh23]

detail and down-to-earth explanation

[@Mayurml-e3n]

Maths with storytelling, best video I ever watch❤

[@albertn0855]

This videos is inspiring to me as I'm considering operations research as my main field of study as an applied mathematician!

[@preston7376]

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!

[@rohith9875]

What work do you do?

[@preston7376]

@@rohith9875 graphics programming for CAD systems. Basically visual tools for modelling etc.

[@rohith9875]

@@preston7376 oh damn that's sounds pretty interesting

[@white_archive]

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!

[@CarterSherman-z6n]

Phenomenal video. Very well explained. This is so helpful! Simple explanation, great work sir!.

[@giovannihernandez3208]

This is amazing. I could understand what the dual is more intuitively.

[@hot_coffee_guy]

This video is a life-saver thank you 😭🙏

[@ishungchan]

Thank you, I'm struggling with this course at my uni. Your video helps me understand it 🙏

[@Erik_The_Viking]

Beautiful video! Well done with a simple example to show the concepts.

[@victormanuel8767]

This is brilliant. You really blended theory and practical application into one cohesive whole.

[@tunafllsh]

Good job! This summarizes the course I took on LP.

[@Spl3F]

bro I'd pay to watch the continuation, very well explained!

[@corlaez]

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!

[@arhamhundia3039]

Amazing video really helped me understand, thank you, please keep on making more videos.

[@skywind7449]

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.

[@YTomS]

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...

[@fawwazanvilen6625]

omg you showing duality was mindblowing

[@neobrandsainclair3407]

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 :)

[@jackgude3969]

I really like the background music. Very cosy math video.

[@tatolela1234]

I dont usually writte comments, but in this time i had to. sincerely spectacular explanation.

[@StentorCoeruleus]

This is probably the most useful thing I’ve ever learned of since learning to breathe

[@darshagarwal8307]

amazing stuff, I am working on recommender systems, and this has been quite helpful! You have just gained a subscriber :)))

[@jackninja1]

Absolutely excellent explanation!

[@samuelkhzym9442]

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 :)

[@prathameshsundaram7509]

I love how thorough your videos are! Thanks a ton.

[@lunafoxfire]

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]

satisfactorycalculator?

[@lunafoxfire]

@@blackbriarmead1966 I made "yet another factory planner". I would post the link but KZbin would probably eat it.

[@benwinstanleymusic]

Incredible video, thank you so much Tom! Helps so much with my optimisation course

[@juan.araujonog]

I just found your channel and this is so good. You should really be proud of your work!

[@andrewcpu]

Wow, just found your channel. Love it.

[@zoom8370]

Nice one! This put a smile on my face.

[@gabedarrett1301]

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

[@TheLoopesMan]

Great work as usual boss

[@DuongNguyen-dz8pb]

This is so helpful! Simple explanation, great work sir!

[@michaelangel7907]

Great! superb graphics, clear explanations. thanks

[@ojcgv21]

this is an awesome video man, congrats!

[@ridazouga4144]

Maaan thaaaanks for sharing this amazing content👏👏👏👏

[@bigjukebox3370]

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!

[@YTomS]

Makes total sense when you say it, didn't come to mind when making the video. Thanks, will keep in mind!

[@xavier4313]

12:57 from that to full video I just lost can you tell what I need to know before seen this video and the loose and tight and the s1,s2,s3. Variables doesn't comnect to me I am confused can you please explain..

[@YTomS]

The duality section is quite brief and will be covered more in-depth in an upcoming video. As for integer linear programming (ILP), we look at what happens when the variables of a linear program are restricted to integers. We show that it's NP-hard by formulating an NP-hard problem (knapsack) as an integer linear program, because if we could solve ILP quickly then we could also solve knapsack quickly. Hope this helps!

[@BrickStopLA]

"Since planting a negative amount of seeds is difficult" I love it

[@patiencebear]

0:16 - you clever bastard. Instant Like. Turned out, it's actually trivial.

[@FaffyWaffles]

I love this use of Manim. So High Quality! New Subscriber is me.

[@Ennuendo]

Saying that planting negative seeds is "difficult" rather than "impossible" made me laugh. Great video!

[@ywenp]

What would be the advantage of using simplex (and iterated pivot algorithm) compared to using gradient descent? Since the objective function is linear, it is derivable and has no local optima.

[@joelclingempeel1512]

Gradient descent wouldn't respect the constraints. For a linear objective function, the gradient is constant so it would just take you in the same direction forever - going far outside the allowed bounds.

[@ywenp]

@@joelclingempeel1512 You're right. I meant, can't you use an alternate gradient descent method where you just stop whenever you encounter a bound?

[@dsdsspp7130]

@@ywenp what you're describing is a worse version of the algorithm explained at the very beginning. The gradient is a constant vector if you move in its direction until you reach the boundary you might not get the optimal solution as the optimal solution occurs at the pivots, following the gradient most of the time gets you to the edges.

[@aglotgaming4660]

what nice video

[@innokentiyromanchenko1450]

thanks for your videos, they are excellent

[@HughJazz13]

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??

[@samarthtandale9121]

Love this video , really ❣️💯❣️

[@kameelamareen]

This video is simply art ❤

[@npan.]

Thank you so much, this video is extremely helpful.

[@polares8187]

This video was amazing. Well created 💪💪

[@nhaho1473]

Thank you for this video, it's very useful for me .

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!

[@samgould8567]

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!

[@YTomS]

Thanks for the comment, I didn't know that a ton has multiple meanings :). Will keep it in mind for future videos!

[@lucareale7161]

Phenomenal video. Very well explained

[@adamdemeter6963]

Quality work! Well done.

[@bugs-hl5jf]

Really amazing explanation. Thank you.

[@coda-n6u]

I love this, thanks so much for sharing

[@princewaesen154]

you bothered to explain the concept of duality which my university prof just didn't feel like doing. Thank you

[@iFastee]

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

[@lpi3]

That's why they are called "hard" problems. Isn't it? I would even say not "most hard problems", but _all_ hard problems ...

[@pablocasas1001]

This video is simply wonderful please keep explaining linear programming(and hopefully any convex as well)