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Integer Linear Programming - Graphical Method - Optimal Solution, Mixed, Rounding, Relaxation
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- Опубліковано 29 кві 2016
- 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
You've just explained in a matter of minutes something my lecturer has failed to do over several hour long lectures. THANK YOU!
One of the most perfect and intuitive explanation i ever seen. Thank you very much! Amazing!
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.
Joshua, your explanation is simply SUPERB ! .... Hats off to you.....!! ......Animation is really GREAT....!!!
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 !!
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.
i have an exam tomorrow, been studying 2-3 days like crazy saw your videos along with my course material. Thank you so much!!
Beautiful video with clear explanation and great visuals. Thanks, Joshua.
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.
best and shortest video to explain the concept. Thanks a lot !
Great vide on linear programming relaxation. Thank you so much!
Awsome!! Your video is brief but substantial enough
this was PERFECT! You're master. Thank you so much!
Thanks, Joshua! Your videos really help!
very nice finally i understand the difference between these methods....... Thank you!!!!
Really clear explanation, thank you very much!
Thanks Joshua! Very good explanation!
love watching your videos :) thank u!
Congratulations. Very good explanation, simple and direct.
Thank you for your great videos :)
amazing explanation!
Awesome stuff...
you are the absolute best!!! thank you!!
This is awesome!
Amazing video!
Thanks Emmanuel... it was amazing explanation
Great video!
Amazing work.
Much better than my lecturer, Kudos to you!
You are Great, Thank you!!!
awesome!!
Thank you for this great video!
Glad it was helpful!
that was great! thanks!
It is a great vedio.
thank you, a very informative overview
You are welcome!
Brilliant video.
Many thanks!
Thanks!
thank u so much for this video
very good video, thanks a lot
You are welcome!
amazing
Thankyou Sir 🙏🙏for this wonderful video 😇😇☺️☺️
Pls tell the book u follow for this topic , Sir .....
THANK YOU!!!!
Hey great video! Do you have the slides!?
Thanks
Thanks very much
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
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.
God bless you homie ❤️❤️❤️❤️❤️
Yo. How’d he get x & y @ 1:10 ❤️
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!
Sorry Madhukiran, I don't have a video for that.
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
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
Hello, how do you find or solve for the objective function line?
See if this helps:
ua-cam.com/video/pP0Qag694Go/v-deo.html
How do we arrive at values of X & Y. Is there any other way, rather than Graphical Trial and Error?
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:
ua-cam.com/video/1nRKsuUcNd4/v-deo.html
ua-cam.com/video/p3xxg1hynXE/v-deo.html
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
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?
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)
@@joshemman Thank you very much!
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...
Rounding down here essentially means keeping the whole number and ignoring the decimal.
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!
You can begin here: ua-cam.com/video/0TD9EQcheZM/v-deo.html
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.
2:15 2:34 4:41
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.
4:41: True, if all the coefficients are positive.
Thanks !
Welcome!
Thanks!
Welcome! Thanks for your generosity, Prasad. Much appreciated.