Thank You soo very much sir, I have an exam today and I have learnt three ours of lectures in a span of 45 minutes (All other videos). Quality content!
Thank you SIR, you are a great instructor, the video has been of great help, it has come to my understanding that a penalty cannot be zero where we have two equal integers in the same row or column; since we consider the difference of the lower cost value and the immediate highest value, my semester is becoming more brighter.
Thank u very much sirr u make my work easy and save my time.your teaching skills are too perfect and U writes too neatly that everyone can understand..
Thanks sir. Very easily explained VAM method. I have subscribed your channel and share with my classmates so that they can understand OR sub. Again Thanks sir. -a student from Gujarat
In class i couldn't really get how this subject is related to real life problems, thus i couldn't really understand the lesson (That's the way i am). But through your videos i really get it. And your balance when you explain is really commendable sir. Thank you so much
Hello sir! You are the best teacher I've ever came across. You proved to be a blessing to me during these exams. Very grateful to you sir. Thank You so much. Big thanks!
tq sir for ur amazing video... It helped me to solve the problem in the easiest way.... but one thing in our course it has been taught that if the row has same lowest no than it will be 0 but u subtract from higher to lower i.e3-2 but we learned that if the same no lies than i.e 2-2=0.... rest all i love ur video and learned well....
"The difference between the least cost and the immediately higher cost, when the least cost is subtracted form the immediately higher cost, is penalty or opportunity loss." - This is the meaning of the term "Penalty or Opportunity Loss" according to the 'Vogel's Approximation Method'. Now, it is upon you/students to follow the correct meaning and the steps accordingly or not to think out of the box and just to copy the teacher(s) or the books without applying our own mind...:)
Dear Prashant Sir, I have some questions: When I have 4 row/Column with the same highest penalties and two of them have the same lowest cost. With which one I reckon further? For example: Supply Units: S1(90)/S2(120)/S3(110) Demands D1(70)/D2(100)/D3(50)/D4(80) Costs für S1: (5/D1) - (2/D2) - (4/D3) - (4/D4) Costs for S2: (3/D2) - (8/D2) - (10/D3) - (6/D4) Costs for S3: (7/D1) - (4/D2) - (5/D3) - (9/D4) If I reckon for this 4 row/column a relation between Rows and Columns (all valid costs), I´ll see that Colum 2 are better to cancel. Other Coumns or rows must be optimized. Is my thought right? I would be glad if you help me!
1) Where there is a tie between the highest penalties, in case of VAM, it is advisable to select the row or column with the least cost out of the rows/columns involved in the tie; and 2) Where there is a tie between the cells with the same least cost, it is advisable to make allocation in a cell where you can make the highest allocation. We can also have other ways available, but so far as the matter of solving such problem in any examination, within limited time is concerned, the above suggestions stand as the best. There are lecture(s) discussing the problem(s) covering this matter in the playlist of 'Transportation Problem'... :)
Thank you ..question if we Unknown distance in one of the cell ..like M ...how i shouldd deal with it ...example if i have diiference M-number , should i consider it the max. Difference ?? ..please answer
There is a whole playlist on this topic on my channel in which there are lectures explaining all such points... Keep watching keep learning... Visit and subscribe my channel and don't forget to recommend my channel and lectures/playlists to others also... you will find so many subjects/topics... Thanks... :)
whole concept clearly understood in one example..thanks a lot sir... just one doubt sir if 1st row entries are 2,5 and 2nd row entries are 2,4 with no other rows or columns then what is the penalty in 1st column
Do you mean - 2, 5 2, 4 ? If yes, (1) In the first column there will be no penalty. So far as the allocation in this column is concerned, there is tie in least costs. But, when you are using VAM, you have to go for allocation only on the basis of the highest penalty; and (2) The highest penalty would be (5 - 2 =) 3 in the first row, then just follow the rule and select the row with the highest penalty and make allocation. There is no situation of tie... :) I have an advice for you and all other students, "Think only about the method which you are learning at present and never go for overthinking and, thus, mixing up the rules/situations/outcomes of the other alternative methods, as it creates confusion and makes one unable to understand the methods clearly... :)
Hello sir, I have a doubt on penalty I referred few books in which it is clearly mentioned that 'if there is a tie between two smallest elements in such cases the penalty should be taken as ZERO'.
Yes, in that way also we can solve the problem. This technique which I have suggested is another variant. We select the row or column with the highest penalty. Sometimes we can't select a row/column with the least cost of the entire table just because of zero penalty in that row/column because of repetition of that least cost and ultimately we lose the chance of getting the optimal solution at the initial stage itself. In the technique, which I have suggested, this kind of problem of forgoing the row/column with the least cost doesn't arise because we find the penalty as "the difference between the least cost and the immediate higher cost" and it gives a non-negative penalty and never a zero as penalty...:)
First remember our objective is to minimize the total (transportation) cost. In simple most words: Penalty means loss per unit, if we don't allocate one unit to that row/column. That means by allocating one unit to the cell with the least cost in a row/column we can reduce the total cost by the amount equal to the penalty of that row/column and if we allocate one unit to the cell with the least cost in a row/column the highest penalty we can reduce the cost by the greatest possible amount through that allocation. So, every time we make allocation on the basis of the highest penalty and try to minimize the total cost at the end of the initial solution...
So that's why they call it the penalty method. Awesome video. Thanks! But what happens when the immediate higher is also the same? just curious. Also the immediate highest in 1st row is 4. Isn't it?
sir, In S kalavathy text book they mentioned that we can use o's as penalty values unless -ve terms. what was correct? Also what if we have only two values remained in the allocated column & they were same. therefore there is no immediate higher value? plz reply sir
sir,in case of unbalanced cost table.if we add a dummy row or column with the cost values as 0's.Then in that case the penalty could become 0.Would that be correct?
Yes, but it happens only in the case of a dummy column/row where all the costs in the column/row are zero. As a result of this that column would have 'zero' penalty and, hence, it would never be selected for allocation. The allocation in the dummy column/row will be by virtue of the penalty of the other non-dummy column/row... :)
Dear Prashant Sir, At 2.30 you have mentioned that penalty can never be zero, even in the case of a tie. It must be subtracted from the "immediate higher value". Would you be able to provide some reference material which I may refer to for this? In some, or rather most, reference books, calculate the penalty as zero. I am not able to understand which method to follow. Thanking you in advance, Hope to hear from you soon, Sonal
Hi Sonal, Yes, in most of the books they take the penalty as zero. I dare to say that it is not correct. Penalty means "the difference between the least cost and the immediately higher subtracting the least cost from the immediately higher one." I, personally solved many problems in both the ways and experienced that in many cases I reached the optimal solution directly, at the stage of initial solution itself, by strictly following the definition of "penalty" as against in the reference books they had reached the same optimal solution only after applying MODI. So, I personally suggest to calculate the penalty as "the difference between the least cost and the immediately higher subtracting the least cost from the immediately higher one." The penalty will never be zero or negative... :)
highest penalty of row and column are same. we use tie breaker,---> the row or column is selected in which the cell has least cost. sir what if, both the column and row has same least cost, then which row or column is selected??
I have discussed everything but in different lectures taking different examples... There is a whole play list on Transportation Problem on my channel along with playlists on many other topics... :)
We should select the column/row where we have the cell with the least cost to which we can allocate higher quantity than the other row/column involved in tie...
Theoretically, Yes! But why should cost be negative? The meaning of negative cost is that you are getting money instead of incurring cost on transporting goods...
Sir , as you said penalty means difference the least cost & immediate higher cost in row or column..Here the term " IMMEDIATE HIGHER COST " is not clear in itself..Sir plz explain this term..
1) First find out the least/lowest cost of the row/column - (I) 2) Now find out the cost which is higher than the least cost (I) but less than all other cost amounts of the same row/column. that is the 'IMMEDIATELY HIGHER COST of the row/column - (II) 3) Penalty = (II) - (I)
I have explained everything but in different lectures taking suitable cases/examples/problems. All such lectures I have already included in the playlist of 'Transportation/Problem'. The number with the topic/chapter name in the title, e.g. Transportation Problem - 5 and VAM - 1 here in this case, suggests that this lecture is a part of series of lectures on this chapter/topic... There are many other playlists on my channel containing lectures on various topics/chapters...
In mcom sem 4, book (operation research sem-4 ch transportation problem page no 106 illustration 6) said that we can use penalty as 0 this same sum is given in book with Same answer but their are different penalty value. So my question is can we use penalty as 0?
Yes, Gatha. You can calculate the penalty in that way also and there will be the same answer. The only difference is, many a times (not every time, of course) we reach the optimal solution at earlier stage by following the path which I have suggested. I have experienced that sometimes we reach the optimal solution directly at the initial stage itself. But, it is not a matter of worry even if you follow the path suggested in the books or by your teacher, ultimately the main thing is TO LEARN.. :)
Everyone is getting, then why can't you... this is actually more logical. When you take penalty as (1 - 1), you miss the opportunity of making allocation to a cell having the least possible cost because a row/column with '0' penalty can never be selected when we need to select a row/column with the highest penalty. Moreover, under this method there are greater chances of directly reaching the optimal solution than the other alternative method... :)
That is also a tie and use the least cost as the tie-breaker, i.e. select the row out of the two the least cost of which is lower than the least cost of the other. If there is a tie in the two least costs also, then select the cell with the least cost out of the two same in which greater quantity can be allocated. The same rule is applicable in case the tie is between two columns having the same highest penalty...
Nice vedio sir and thank you so much.....for excellent vedio
excellent explanation... I am highly indebted to you for making me understand this method just in a single watch of video...
Thankuuu sooooo much sir.. U cleared my all points.. Bundle of thankxxxxx
Thank You soo very much sir, I have an exam today and I have learnt three ours of lectures in a span of 45 minutes (All other videos). Quality content!
Nice teaching sir..... Super..
become a big fan of you Sir.. Thanks alottttttt for help sir....
This is best explanation I ve had so far. I wish u were my tutor. Thanks so much for such a resourceful video
Excellent explanation
Thank you SIR, you are a great instructor, the video has been of great help, it has come to my understanding that a penalty cannot be zero where we have two equal integers in the same row or column; since we consider the difference of the lower cost value and the immediate highest value, my semester is becoming more brighter.
Sir superb exaplanation tq.....
Amazing Sir...the doubt I was looking for I found it here thts the true magic of professional and expertise 😊😊😊
Thank u very much sirr u make my work easy and save my time.your teaching skills are too perfect and U writes too neatly that everyone can understand..
Just amazing! Very helpful, Thank You
very well explained!! Thank you Sir
Thankyou sir your lectures are always easy to understand ...
Very helpful, thanks a ton Sir.
Thank you sir. it is clear & nice
your lectures are really helpful, thank-you so much for planting the seeds of knowledge.
this is becoming easier after., watching your vedio.. its too helpful nd easy understandable THANK u so much.. SIR..
You are welcome, Saurabh... :)
thanks sir.....
for detailed explanation....
Thanks sir .you are great instructor
Thank u very much sir, it is the best easy process 2 understand the Lpp...
your are the great teacher..God bless you
your lecture was awesome sir it is now easily understood by me
Thanks sir. Very easily explained VAM method.
I have subscribed your channel and share with my classmates so that they can understand OR sub.
Again Thanks sir.
-a student from Gujarat
Thank you, Adil...:)
thanks for your helpful video
In class i couldn't really get how this subject is related to real life problems, thus i couldn't really understand the lesson (That's the way i am). But through your videos i really get it. And your balance when you explain is really commendable sir. Thank you so much
thanks sir very helpful video
well done thank you
Nice teaching Sir and Thank you so much I wait to next video and next sem Thank you so much sir😙😍😆🍫
Hii sir ....your teaching very nice sir
this was really helpful thanks alot
You are the best!!!!
Sir top teaching attitude.
its amazing..thank eww sirr
Thank you sir, very nice explanation. :)
thnkuu soo mch sir.. its very helpful for me
tx u sir very much u method are very eassy
very well explained
Thank youuuu soooo muchh sir😊😊🙏🙏🙏💖
thank u sir........ from Bangladesh
Thank you for very easily learn
tq sir it was very helpful for me because am in confusion when the penalty was tie now it wa clear for me
thank u...it was very useful
Hello sir! You are the best teacher I've ever came across. You proved to be a blessing to me during these exams. Very grateful to you sir. Thank You so much. Big thanks!
Thank you Navneet Kaur for such nice words... May God Bless You...:)
tq sir for ur amazing video... It helped me to solve the problem in the easiest way.... but one thing in our course it has been taught that if the row has same lowest no than it will be 0 but u subtract from higher to lower i.e3-2 but we learned that if the same no lies than i.e 2-2=0....
rest all i love ur video and learned well....
"The difference between the least cost and the immediately higher cost, when the least cost is subtracted form the immediately higher cost, is penalty or opportunity loss." - This is the meaning of the term "Penalty or Opportunity Loss" according to the 'Vogel's Approximation Method'. Now, it is upon you/students to follow the correct meaning and the steps accordingly or not to think out of the box and just to copy the teacher(s) or the books without applying our own mind...:)
Infinite times THANKING YOU SIR
You are welcome...:)
Penalty can't be zero this is the new thing ,Thank you very much Sir
You are Welcome... :)
Thanku sirji, was in middle of mental breakdown, this video helped! 🤩😋😁
Are yaar ye videos milte q nhi haii aaj mera exam thaa bakwash exam huaa ...CMA ka 15 din pehle dikh Jata too ye chnnl
Thankyou sir.....
Thank uu so much sir I understood the method but what if any cost element in matrix is negative? how to solve it? plz help me..
Thank you so much sir! This really helped me a lot :)
Dear Prashant Sir,
I have some questions:
When I have 4 row/Column with the same highest penalties and two of them have the same lowest cost. With which one I reckon further?
For example:
Supply Units: S1(90)/S2(120)/S3(110)
Demands D1(70)/D2(100)/D3(50)/D4(80)
Costs für S1: (5/D1) - (2/D2) - (4/D3) - (4/D4)
Costs for S2: (3/D2) - (8/D2) - (10/D3) - (6/D4)
Costs for S3: (7/D1) - (4/D2) - (5/D3) - (9/D4)
If I reckon for this 4 row/column a relation between Rows and Columns (all valid costs), I´ll see that Colum 2 are better to cancel. Other Coumns or rows must be optimized. Is my thought right?
I would be glad if you help me!
1) Where there is a tie between the highest penalties, in case of VAM, it is advisable to select the row or column with the least cost out of the rows/columns involved in the tie; and
2) Where there is a tie between the cells with the same least cost, it is advisable to make allocation in a cell where you can make the highest allocation.
We can also have other ways available, but so far as the matter of solving such problem in any examination, within limited time is concerned, the above suggestions stand as the best.
There are lecture(s) discussing the problem(s) covering this matter in the playlist of 'Transportation Problem'... :)
Thank you ..question if we Unknown distance in one of the cell ..like M ...how i shouldd deal with it ...example if i have diiference M-number , should i consider it the max. Difference ?? ..please answer
Sir if there is c23 value = 1 then we can break tie by giving higher supply like as least cost method u delivered?
Thank you very much sir.
Welcome! Don't forget to subscribe and recommend my channel...
Sir in case question is maxamium profit so what will be the soluntion
And if in the cell the demand is negative so how to solve
There is a whole playlist on this topic on my channel in which there are lectures explaining all such points... Keep watching keep learning... Visit and subscribe my channel and don't forget to recommend my channel and lectures/playlists to others also... you will find so many subjects/topics... Thanks... :)
whole concept clearly understood in one example..thanks a lot sir...
just one doubt
sir if 1st row entries are 2,5 and 2nd row entries are 2,4 with no other rows or columns then what is the penalty in 1st column
Do you mean -
2, 5
2, 4 ?
If yes,
(1) In the first column there will be no penalty. So far as the allocation in this column is concerned, there is tie in least costs. But, when you are using VAM, you have to go for allocation only on the basis of the highest penalty; and
(2) The highest penalty would be (5 - 2 =) 3 in the first row, then just follow the rule and select the row with the highest penalty and make allocation. There is no situation of tie... :)
I have an advice for you and all other students, "Think only about the method which you are learning at present and never go for overthinking and, thus, mixing up the rules/situations/outcomes of the other alternative methods, as it creates confusion and makes one unable to understand the methods clearly... :)
thank you so much sir..I got it..
Hello sir, I have a doubt on penalty I referred few books in which it is clearly mentioned that 'if there is a tie between two smallest elements in such cases the penalty should be taken as ZERO'.
Yes, in that way also we can solve the problem. This technique which I have suggested is another variant. We select the row or column with the highest penalty. Sometimes we can't select a row/column with the least cost of the entire table just because of zero penalty in that row/column because of repetition of that least cost and ultimately we lose the chance of getting the optimal solution at the initial stage itself. In the technique, which I have suggested, this kind of problem of forgoing the row/column with the least cost doesn't arise because we find the penalty as "the difference between the least cost and the immediate higher cost" and it gives a non-negative penalty and never a zero as penalty...:)
Sir, Would you mind giving another example of the same problem with the different variant ?
Sir why we allocate only the row or column which have greatest penalty? Please sir explain it.
First remember our objective is to minimize the total (transportation) cost.
In simple most words:
Penalty means loss per unit, if we don't allocate one unit to that row/column. That means by allocating one unit to the cell with the least cost in a row/column we can reduce the total cost by the amount equal to the penalty of that row/column and if we allocate one unit to the cell with the least cost in a row/column the highest penalty we can reduce the cost by the greatest possible amount through that allocation. So, every time we make allocation on the basis of the highest penalty and try to minimize the total cost at the end of the initial solution...
mast sir.
So that's why they call it the penalty method. Awesome video. Thanks! But what happens when the immediate higher is also the same? just curious. Also the immediate highest in 1st row is 4. Isn't it?
Sir.. what about cost of Matrix??.. we need to calculate cost of Matrix also
super sir thank you
sir, In S kalavathy text book they mentioned that we can use o's as penalty values unless -ve terms. what was correct? Also what if we have only two values remained in the allocated column & they were same. therefore there is no immediate higher value? plz reply sir
How to solve 6 rows and 4 columns assignment problem please explain with example sir
Sir.....
Plz explain dynamic prblm also
...
sir,in case of unbalanced cost table.if we add a dummy row or column with the cost values as 0's.Then in that case the penalty could become 0.Would that be correct?
Yes, but it happens only in the case of a dummy column/row where all the costs in the column/row are zero. As a result of this that column would have 'zero' penalty and, hence, it would never be selected for allocation. The allocation in the dummy column/row will be by virtue of the penalty of the other non-dummy column/row... :)
Sir b.com (H) ke 2nd semester ke business mathematics ke liye Konsi konsi videos Ki zaroorat hai???...plz tell me sir
plz explain decision thheory -max,min,regret criteria la place criteria etc
Thank you very much. sir
Thank you sir..
Dear Prashant Sir,
At 2.30 you have mentioned that penalty can never be zero, even in the case of a tie.
It must be subtracted from the "immediate higher value". Would you be able to provide some reference material which I may refer to for this?
In some, or rather most, reference books, calculate the penalty as zero.
I am not able to understand which method to follow.
Thanking you in advance,
Hope to hear from you soon,
Sonal
Hi Sonal,
Yes, in most of the books they take the penalty as zero. I dare to say that it is not correct. Penalty means "the difference between the least cost and the immediately higher subtracting the least cost from the immediately higher one." I, personally solved many problems in both the ways and experienced that in many cases I reached the optimal solution directly, at the stage of initial solution itself, by strictly following the definition of "penalty" as against in the reference books they had reached the same optimal solution only after applying MODI. So, I personally suggest to calculate the penalty as "the difference between the least cost and the immediately higher subtracting the least cost from the immediately higher one." The penalty will never be zero or negative... :)
Thanks a lot Sir. This explanation was very useful. :)
Hope you do not mind if I refer my lecturer to your observations , I am sure it will make up an interesting debate.
Yes sir...penalty never be zero. Because same cost cant measure the defference. To measure difference there should have a variation. Got it . Thanks.
Thank you so much SIR
highest penalty of row and column are same.
we use tie breaker,---> the row or column is selected in which the cell has least cost.
sir what if, both the column and row has same least cost, then which row or column is selected??
rupesh arya got solution of this?
thank you very much
Nice sir
Thanks sir
in the 3rd row 2nd column of Row Penalty, why have u subtracted 2 by 4 and not by 5, as 5 is also the immediate higher.
thnks a lot sir
Thank you Sir...........
Thanks...
very nice way
make video on dynamic programming
What will we do in the situation of equal cost also( when penalties are equal in row and column)
I have discussed everything but in different lectures taking different examples... There is a whole play list on Transportation Problem on my channel along with playlists on many other topics... :)
Thnx sir ,,,
bot sahi bataya thnku sir
You are Welcome, Vishal... :)
Very good
It is so helpful for me sir
Dear Sir,
In case of tie break, suppose we have 2 cells with the same least cost in case of equal column and row penalty. How to solve? Kindly reply.
We should select the column/row where we have the cell with the least cost to which we can allocate higher quantity than the other row/column involved in tie...
Prashant Puaar Thank u very much sir..!!
Sir if we have -1 in any of the destination, then should we write 2 -(-1) for the penalty?
Theoretically, Yes! But why should cost be negative? The meaning of negative cost is that you are getting money instead of incurring cost on transporting goods...
Sir when we have supply and demand simultaneously satisfied then we have to cut both row and column or any one of them???
Yes, cut both of them because it that row as well as column now we don't require to allocate anything...
Got that sir thanks..
Sir , as you said penalty means difference the least cost & immediate higher cost in row or column..Here the term " IMMEDIATE HIGHER COST " is not clear in itself..Sir plz explain this term..
1) First find out the least/lowest cost of the row/column - (I)
2) Now find out the cost which is higher than the least cost (I) but less than all other cost amounts of the same row/column. that is the 'IMMEDIATELY HIGHER COST of the row/column - (II)
3) Penalty = (II) - (I)
can we use U V method in least cost method to check optimality
Mehdi Hassan
Yes, to check the optimality of an initial solution obtained by any method we can use the UV method.
Superr.....
Nice
Sir if highest penalty is same and the least cost is also same but different cells are being selected which cell should be selected
You need to choose the cell with max allocation
I have explained everything but in different lectures taking suitable cases/examples/problems.
All such lectures I have already included in the playlist of 'Transportation/Problem'. The number with the topic/chapter name in the title, e.g. Transportation Problem - 5 and VAM - 1 here in this case, suggests that this lecture is a part of series of lectures on this chapter/topic...
There are many other playlists on my channel containing lectures on various topics/chapters...
In mcom sem 4, book (operation research sem-4 ch transportation problem page no 106 illustration 6) said that we can use penalty as 0 this same sum is given in book with Same answer but their are different penalty value. So my question is can we use penalty as 0?
Yes, Gatha. You can calculate the penalty in that way also and there will be the same answer. The only difference is, many a times (not every time, of course) we reach the optimal solution at earlier stage by following the path which I have suggested. I have experienced that sometimes we reach the optimal solution directly at the initial stage itself. But, it is not a matter of worry even if you follow the path suggested in the books or by your teacher, ultimately the main thing is TO LEARN.. :)
Prashant Puaar thank you sir for your reply...
using this way of solving TP
I will get marks or not...
because in other videos the penalties are calculated in same number. .
1 2 1
1-1
or
2-1
Everyone is getting, then why can't you... this is actually more logical. When you take penalty as (1 - 1), you miss the opportunity of making allocation to a cell having the least possible cost because a row/column with '0' penalty can never be selected when we need to select a row/column with the highest penalty. Moreover, under this method there are greater chances of directly reaching the optimal solution than the other alternative method... :)
Sir what if the two higher penalties lie on two rows instead of one row and one column ?
That is also a tie and use the least cost as the tie-breaker, i.e. select the row out of the two the least cost of which is lower than the least cost of the other. If there is a tie in the two least costs also, then select the cell with the least cost out of the two same in which greater quantity can be allocated. The same rule is applicable in case the tie is between two columns having the same highest penalty...
Thank you sir :)
You are welcome, Mrittika... :)
SIR IF two rows /colums have same cost at that time wt we have to do