In this lesson we learn how to solve a linear programming problem using the big M method. Change the setting of your youTube to HD for the best quality.
I'm used to reading cursive, so i find your handwriting legible. But I think it may indeed help others who aren't accustomed to cursive if you were to write in capitals. Nice handwriting though. Great videos too, it was a clear explanation
let's say you have 2 constraints with = and >= signs. Then, you have Max z=3x1+4x2 x1+x2=3 --> x1+x2+a1=3 x1+2x2+3x3>=1 --->x1+2x2+3x3-e2+a2=1 Note that for constraints with "=" sign we don't add any excess variable (e.g. the first constraint in the above example). You need to add both a1 and a2 with big M to the objective function. for example, in this case you have max z=3x1+4x2 ---> z=3x1+4x2-Ma1-Ma2
if there is M in the final value of Z, it means at least one of the artificial variables is still positive (basic). If you are in the optimal table, this is a sign that shows the problem does not have a feasible solution.
Thank you for the videos, they are great. I have two questions : Do we always add -M ? or we add -M for maximization problem and M for minimization problem ? Same question for the artificial variable (a) ?
we add -M for a Max and +M for a Min problem. Also, for constraints with >= signs we always add +a regardless of the objective function direction (max or min).
Mirzaei, this session was good and very useful. Did you posted any video relating Gomory's Cutting plane method and Branch & Bound method problems. Kindly give the link. Thanks
Why can't we add a positive M? I understand that we want to avoid a positive M as it's a maximization problem. But if we do add a +M to the objective function, after standardizing, it becomes -M. So by normal procedure we would automatically make that column as the pivot column because it's the MOST NEGATIVE number there?
so if the artificial variable (either a4 or 4e) are another number other than 0, does that mean that there is no optimal solution, because there is no feasible region?
no! only "a" variables are artificial variables. You have a feasible solution when e.g. e4=4. However, if any of your artificial variables (a variables) in the final optimal table are positive then you don't have a feasible solution
can you tell me how can we differ Big M method by simplex method..? by checking the constraint of inequalities ? if differ we use big M otherwise simplex . please comment.
+malayait if you have two Ms you have to add both Ms to your objective function. Example (note: this is a minimization problem): Min Z=x1+2x2 Z=X1+2X2+M1a1+M2a2 ---> Z-X1-2X2-M1a1-M2a2=0 X1>=2 X1-e1+a1=2 X1-X2>=3 X1-X2-e2+a2=3 X1,X2>=0 X1,X2>=0
+Shokoufeh Mirzaei thank you lecturer but i mean new z . mean the one which we have to use with. like you multiply M with r3 and then added to r4 to get new Z to use. sorry for bothering and last uncleare question
+malayait I see. you have to do it for both columns of a1 and a2. you can do it in two steps. first, use one of the rows to get rid of the M under a1, then use another row to get rid of the other M left in the row of Z. Note that when you are in the second step, you have to use the new row of z that you have created.
Definitely the best tutorial in between those bunch of big m videos. Thank you so much.
Fantastic tutorial!Thank you very much for your videos!I will hopefully pass my final exams thanks to you!
this will definately help me to clear my CT......thank you ma'm
i have my Operation Research exam in next 2 hrs and here I am watching this video
Thanks Great Teaching......................
Best In UA-cam For BIG M method :)
I'm used to reading cursive, so i find your handwriting legible. But I think it may indeed help others who aren't accustomed to cursive if you were to write in capitals. Nice handwriting though.
Great videos too, it was a clear explanation
Thanks for the wonderful tutorials. Best ones I've used to learn.
Brilliant, Thank you very much Shokoufeh :)
Very good job! Best tutorial of big M on youtube
thank you so much
you did great job
Very helpful, thanks!
Thanks professor, please upload some videos about sensitivity and shadow price,
kheylii khub boodm mamnun ,goftam farsi am tashakor karde basham ;)
hello
it was a great video
thanks
excellent professor
Great Video!
the information is hard to read, please choose other font
That is my handwriting. I try to make it more legible next time. thanks for your feedback led del
+led del if you consider her handwriting as a font it means that her handwriting is beautiful hahahaha
thank you very much
you are really good, thank you professor
Thank you professor but i have one question. What we supposed to do when there is more than one > or = sign ?
let's say you have 2 constraints with = and >= signs. Then, you have
Max z=3x1+4x2
x1+x2=3 --> x1+x2+a1=3
x1+2x2+3x3>=1 --->x1+2x2+3x3-e2+a2=1
Note that for constraints with "=" sign we don't add any excess variable (e.g. the first constraint in the above example). You need to add both a1 and a2 with big M to the objective function. for example, in this case you have
max z=3x1+4x2 ---> z=3x1+4x2-Ma1-Ma2
Shokoufeh Mirzaei Thank you very much..
Thank you SO much! This was perfect.
What if all z row elements are positive but you still have M at the final value of z??
if there is M in the final value of Z, it means at least one of the artificial variables is still positive (basic). If you are in the optimal table, this is a sign that shows the problem does not have a feasible solution.
You helped a lot but I didn't understand how and why you switched from s2 to e4
thank you ma'am, you are awesome.
Thank you for the videos, they are great. I have two questions :
Do we always add -M ? or we add -M for maximization problem and M for minimization problem ?
Same question for the artificial variable (a) ?
we add -M for a Max and +M for a Min problem. Also, for constraints with >= signs we always add +a regardless of the objective function direction (max or min).
Mirzaei, this session was good and very useful. Did you posted any video relating Gomory's Cutting plane method and Branch & Bound method problems. Kindly give the link. Thanks
Excellent video!
Thank u, very helpfull
So if I get it right..if the initial problem was a minimization problem then we would have to add e's to the
regardless of your objective function direction (Max or Min) when you have
Great tutorial
thank you this is helpful 😘😗
Why can't we add a positive M? I understand that we want to avoid a positive M as it's a maximization problem. But if we do add a +M to the objective function, after standardizing, it becomes -M. So by normal procedure we would automatically make that column as the pivot column because it's the MOST NEGATIVE number there?
please watch 4:21-6:49
Yes, I have. I understood that but I don't get why we can't do it this way? Thanks ma'am.
great video !!
so if the artificial variable (either a4 or 4e) are another number other than 0, does that mean that there is no optimal solution, because there is no feasible region?
no! only "a" variables are artificial variables. You have a feasible solution when e.g. e4=4. However, if any of your artificial variables (a variables) in the final optimal table are positive then you don't have a feasible solution
thanks too much u r awesome :)
can you tell me how can we differ Big M method by simplex method..? by checking the constraint of inequalities ? if differ we use big M otherwise simplex . please comment.
If all constraints in an LP are in form of = or = signs we should use big M or two-phase method.
what if I decide to solve the min LP with the dual simplex ? do I still have to add an artificial variable in the
Hey Prof
So do we use artificial variables in Simplex too in case we have a perfect equality constraint?
+Ashwin Nair yes, in that case you only add an artificial variable and you don't add any excess variable: x1+x2=1 --> x1+x2+a1=1
ok. Thanks
In some parts it's hard to see what you wrote, wish you wrote them bigger. But thanks a lot for the video! :)
nice tutorial but what if we have two Ms in cost functions? how to get the new Z or cost function ?
+malayait if you have two Ms you have to add both Ms to your objective function. Example (note: this is a minimization problem):
Min Z=x1+2x2 Z=X1+2X2+M1a1+M2a2 ---> Z-X1-2X2-M1a1-M2a2=0
X1>=2 X1-e1+a1=2
X1-X2>=3 X1-X2-e2+a2=3
X1,X2>=0 X1,X2>=0
+Shokoufeh Mirzaei thank you lecturer but i mean new z . mean the one which we have to use with. like you multiply M with r3 and then added to r4 to get new Z to use.
sorry for bothering and last uncleare question
+malayait I see. you have to do it for both columns of a1 and a2. you can do it in two steps. first, use one of the rows to get rid of the M under a1, then use another row to get rid of the other M left in the row of Z. Note that when you are in the second step, you have to use the new row of z that you have created.
+malayait thank you so much .. :)
+malayait if you find a feasible solution, Ms will be eliminated from your objective function.
thanks so much