Integer Linear Programming - Graphical Method - Optimal Solution, Mixed, Rounding, Relaxation

This video provides a short introduction to INTEGER LINEAR PROGRAMMING (ILP).
Topics Covered include:
** LP Relaxation
**All-Integer & Mixed Integer Problems
**LP Relaxation Optimal Value as Bounds
**Rounding up & down for Integer Solutions
**Maximization & Minimization Optimization models

[@bradyjamesduck]

You've just explained in a matter of minutes something my lecturer has failed to do over several hour long lectures. THANK YOU!

[@aryanabdolahi8469]

I'm a Masters student of Industrial Engineering in Iran and gonna start a course for this topic soon. This video was a nice and well explained introduction to ILP. Thanks.

[@chakravarthit.7259]

Joshua, your explanation is simply SUPERB ! .... Hats off to you.....!! ......Animation is really GREAT....!!!

[@Ziru27]

One of the most perfect and intuitive explanation i ever seen. Thank you very much! Amazing!

[@rabbilbhuiyan5666]

Very good and effective explanation to understand all integer and mixed integer LP solutions with graphical presentation. Thanks a lot! I have ended a week attempt of learning mixed integer LP solution after this materials.

[@makuruba]

wow. i have my operations research test in 6 hours.. and so, finding this playlist is the motivation i needed for the day. Thank you !!

[@snigdhamorbaita7348]

Wow!! I have been struggling to understand this for a while but with this video I now understand it very well. Thank u so much... great work.

[@SimpleMacReviews]

i have an exam tomorrow, been studying 2-3 days like crazy saw your videos along with my course material. Thank you so much!!

[@mdeliasinulislam7663]

best and shortest video to explain the concept. Thanks a lot !

[@dew01]

amazing explanation!

[@ksbalaji1287]

Beautiful video with clear explanation and great visuals. Thanks, Joshua.

[@NoctLightCloud]

this was PERFECT! You're master. Thank you so much!

[@user-pw9vn3rp6h]

thank you, a very informative overview

[@joshemman]

You are welcome!

[@mahamarooj5002]

very nice finally i understand the difference between these methods....... Thank you!!!!

[@jvbb2005]

Much better than my lecturer, Kudos to you!

[@inteligenciaartificiuau]

Congratulations. Very good explanation, simple and direct.

[@arko3822]

Awesome stuff...

[@MinhLe-xk5rm]

Great vide on linear programming relaxation. Thank you so much!

[@mnchester]

Amazing video!

[@clairelin9403]

Thank you for this great video!

[@joshemman]

Glad it was helpful!

[@user-xg9iw2ip7i]

Awsome!! Your video is brief but substantial enough

[@leizhang3329]

very good video, thanks a lot

[@joshemman]

You are welcome!

[@user-vf7wy7ub9t]

Brilliant video.

[@joshemman]

Many thanks!

[@PapercutFiles]

Thanks, Joshua! Your videos really help!

[@user-bj1nv6iq7j]

It is a great vedio.

[@abdullahalmehadi6152]

This is awesome!

[@user-db2wp1dx8k]

Really clear explanation, thank you very much!

[@BenDover-xt4tf]

you are the absolute best!!! thank you!!

[@sharmatutorials8297]

Thankyou Sir 🙏🙏for this wonderful video 😇😇☺️☺️

[@sharmatutorials8297]

Pls tell the book u follow for this topic , Sir .....

[@TotoTb]

Thanks Joshua! Very good explanation!

[@jontis123]

Just a disclaimer, I haven't studied linear programming for very long at all, so forgive me if my assumptions regarding positive coefficients here is wrong, but: You say that rounding down always results in a feasible solution for a maximization problem, but surely a rounded down solution could fall outside of your constraint functions, thus making it infeasible. For example, if your green constraint (3x + 4y >= 6) was instead >= 12, then the solution acquired by rounding down, i.e. x=1 y=2 is no longer feasible. To me at least, this seems like it keeps the mentioned requirement of positive coefficients in the constraints.

[@1DrFahad1]

Thank you for your great videos :)

[@rhe7187]

Thanks !

[@joshemman]

Welcome!

[@najeeafsanehee437]

Thanks Emmanuel... it was amazing explanation

[@UjjwalGarg09]

awesome!!

[@marcinmich9269]

Amazing work.

[@leopd182]

amazing

[@Ryankeebs]

love watching your videos :) thank u!

[@MrBelaw]

You are Great, Thank you!!!

[@TheBreadBoard]

Great video!

[@H.sena1111]

thank u so much for this video

[@jinright695]

God bless you homie ❤️❤️❤️❤️❤️

[@dhgcrack3r111]

Yo. How’d he get x & y @ 1:10 ❤️

[@alonsojimenez8549]

Thanks very much

[@70ME3E]

that was great! thanks!

[@jiatongyu1224]

THANK YOU!!!!

[@svnsunarikani8865]

Great Sir. Will you suggest any material which includes many problems on this topic...which is easy to understand..thank you...waiting for your reply sir

[@joshemman]

You can try: *Quantitative Analysis for Management *Introduction to Management Science *Quantitative Methods for Business Here's one online: wps.prenhall.com/wps/media/objects/2234/2288589/ModB.pdf

[@madhukiranattivilli2321]

Hi Joshua Simplex LP algo (using Dantzig's pivot rule) helped me to get the max result for "x y are both real numbers" case and (max 28.636) "x y are both integers" case (max 28), but I didn't help for the 2 mixed integer cases (x integer case, y integer case). I'm unable to go beyond max value of 28. I see you got 28.4 for "x integer" case. Do u have a video where u explained the algo for mixed integer case? Thanks!

[@joshemman]

Sorry Madhukiran, I don't have a video for that.

[@agustinmariapardo9832]

Hey great video! Do you have the slides!? Thanks

[@huynguyenquoc8657]

in maximization problem, when rounding down, why the optimal solution is not (2;2) or (3;1)?? they're also inside the feasible region right...

[@joshemman]

Rounding down here essentially means keeping the whole number and ignoring the decimal.

[@akshaywani5528]

How do we arrive at values of X & Y. Is there any other way, rather than Graphical Trial and Error?

[@joshemman]

It’s really not trial and error. It’s systematic. You can also use the approach in any of these two videos to solve it: kzbin.info/www/bejne/Z5-1fKarisiBmpY kzbin.info/www/bejne/pmTbqZpnnd6hjqc

[@ayatelnabawy6696]

Hi Dr. Joshua, What if not all the coeffecients in the binding constraints are +ve ? Is the rounding can be applicable ? and Which direction for both x and y per each constraint ? Many Thanks

[@joshemman]

If 'not all' coefficients are positive, rounding could be tricky, especially when there is a negative coefficient in the objective function. The rounding rules stated here may not hold true with negative coefficients.

[@evanroycelinezo4682]

Hello, how do you find or solve for the objective function line?

[@joshemman]

See if this helps: kzbin.info/www/bejne/poGTgpSda55nfdE

[@R4G3QU1TT]

The slope of the line at 5:10, and later at 5:36, how is it determined exactly? Because it passes through X=4 and Y=6, which is the opposite of the objective function?

[@joshemman]

Take the objective function and set it equal to a number like 24 (easy number to work with because of 6&4). Then find two points that satisfy the equation -and that's your line. For 6X + 4Y = 24, two easy points are (0, 6) and (4, 0)

[@R4G3QU1TT]

@@joshemman Thank you very much!

[@timotimo9961]

Hello Joshua Thanks for the super cool awesome videos - you are the best Could you please make some videos on the following Simplex Algorithm, Duality Theory, Branch and Bound, Dijsktra, Floyd Warshall, Dynamic programming and Decision Theory?? Thanks in advance

[@axelalatorre621]

hi, could you explain me how do you determine the feasible area? I know it is related to the constraints but sometimes you divide by two and you change x by y. Thanks!

[@joshemman]

You can begin here: kzbin.info/www/bejne/ZoWnaniHmM2YkK8

[@user-bj1nv6iq7j]

Joshua,u are wrong. The best solution, the maximum of the LP relaxation is always not less than the maximum of the ILP. Your graphic method is wrong.

[@joshemman]

4:41: True, if all the coefficients are positive.

[@theprivatespeaker]

2:15 2:34 4:41

[@user-uy1sl4sk3f]

Thanks!

[@prasaddavange3837]

Thanks!

[@joshemman]

Welcome! Thanks for your generosity, Prasad. Much appreciated.