Vogel’s Approximation Method (VAM) - Business Mathematics and Statistics Video Lecture | Business Mathematics and Statistics - B Com

hi in this video I am going to explain
transportation problem so before I'm
going to explain how to solve the
transportation problem let me explain
interaction about transportation
problems transportation problem means it
is a special kind of linear programming
problem in which goods are transported
from a set of sources to set of
destination subject to or according to
supply and demand of the sources and
destination respectively such that the
total cost of transportation is
minimized the ultimate objective of this
particular technique is in order to
reduce the transportation cost we need
to apply some technique so with the help
of this we can able to minimize or
identify the method in order to avoid or
minimize the transportation cost so let
me explain two different types of
transportation problems first one is
balanced transportation problem balanced
transportation problem means both supply
and demand will be equal then it is
called as balanced transportation
problem unbalanced transportation
problem means supply is not equal to
demand means it means a unbalanced
transportation problem we cannot proceed
with unbalanced transportation problem
to balanced transportation problem we
need to add either dummy column or dummy
row according to the situation so there
are two types balance as well as
unbalanced transportation problem then
methods of transportation problem
generally there are two phases for
transportation problem first one is
finding the initial feasible solution
that is the first phase first we need to
identify or find initial feasible
solution after finding this only we can
able to check the optimality which one
is best optimum means best maximum and
finding the best among the various
natives that is the second phases so I
am going to explain with the example so
this is cornice row first row second row
third row these are the dream sources
are available okay
a B C three columns each sources and
each row you will have some supply in
each column you will have some command I
told you know balanced transportation
problem before you proceed just see or
confirm whether it is balanced
transportation problem or unbalanced
transportation problem how can you find
out this just compare the demand and
supply according to this problem just
see their demand 200 plus 400 plus 400
thousand just see the supply 200 plus
300 500 plus 500 thousand it is a
balanced transportation problem with
this problem you can proceed if it is
unbalanced means demand will note equal
to supply what will happen in that case
we need to add one more row or one more
dummy column according to demand and
supply but anyway if you want to
continue the problem you need to have
balance balance means more demand and
supply should be equal let us see the
three different methods of all three
different techniques to find the initial
basic feasible solution in phase one I
told you know there are two method of
methods of solving transportation
problems or faster phases finding the
initial basic feasible solution after
finding this only we can able to check
optimality so according to check the
initial basic feasible there are three
methods are available first one is
northwest corner cell method second one
least cost cell method
what that method it may explain each and
every one clearly first one is not miss
corner sale method so this is the
transportation problem we'll have
different sources at different
destination so foreign to this problem
there are three sources are available
sources one two and three and four
destinations are there a B C D you need
sources and each destination some value
is given this is called as supply for
sauce 1/3 hundreds of plays are
available here four hundred supplies are
available five hundred supplies are
available for each destination this is
call em know for each destination we
have some demand for a 250 demand is
there for B 354 C 440 200 before you
solve this problem first we need to
check whether the problem is balanced or
unbalanced balanced means both demand
and supply will be equal just check 250
350 400 200
what is it toten hosen 200 let's check
the supply 300 + 400 miss - thousand 200
so it is a balanced problem now we can
proceed support - northwest corner cell
method you have to start with this
corner this is a northwest corner so you
have to start with this cell each and
every element of this cell is considered
as a cost of transportation so first you
have to start from this cell this is the
northwest corner you have a start from
here just allocate before you allocate
the value we have the Compaq demand for
the particular column and supply for the
particular row here supply 300 what
demand is one D 250 so which one is
lesser value
demand is lesser so you have to allocate
only demand because demand is lesser
than the supply so based on the demand
only we can able to supply so 250 is
lesser than you know could Lucien figure
250 is allocated not just cancel put 0
this rope 300 is there we have allocated
to 50 to 53 men met remaining 50
supplies there so this column we got 0
no so then there will be get cancelled
after deleting first collar
the remaining cell yes like this now we
have to see which one is not caught not
west corner this is a not miss corner
again select this cell and see the
demand and supply of respective cell for
this particular cell demand 350 supply
50 which one is lesser value supply is
lesser than the demand so allocate 50
rupees
50 cancel we'll get zero for this 350 is
there no 15 match remaining 300 demand
is there for this rope we got 0 no the
entire row will get cancelled
shaft deleting the two thing this is the
remaining cell remaining figure
unallocated sell out of the unallocated
cell find the northwest corner which one
is not rest corner this the northwest
corner cell so start allocate for this
column 300 demand is there for this row
for hundreds of place there which one is
less demand is lesser than supply put
300 here
just cancel 0 because 300 is allocated
for hundreds of players there 300 is
allocated will have only 100 rupees here
we got 0 no just cancel this collar
after deleting all these things this is
a remaining unallocated cell with this
unallocated cell find the northwest
corner this is the northwest corner so
select this cell and allocate the value
so which one is less just come back the
row value and column value column values
400 for this cell and row value is 100
so which one is less 100 is less 100 is
lesser value just 900 here and you'll
get 0 and in out of 400 do you don't
know just can't itself this now we have
only two cells this is an odd way Scala
no allocate this cell we have got 300
demand and 500 supply which one is
lesser value demand is less so put 300
here balance 200
Kancil 0 is also get cancelled and
finally you'll have only one cell
unallocated in this unallocated cell you
have demand equal to supply just see
demand also 200 sub T also 200 it is a
balanced problem you won't get any
balancing figure everything is canceled
now just multiply the value with the
cell value in first allocated cell - 15
- 3 + 50 into 1 plus 300 into 6 plus 100
into 5 + 300 into 3 plus 200 into - just
find the value total will be remains
4400 - cause cell method according to
this method first we need to find out
least cost among the various cost we
have different sources and different
destinations know we need since we have
got some value some on the radius value
first we need to identify which one is
listed just find out which one is least
these are these value so now I have
selected this cell then we need to find
out the supply and demand demand 350 for
this particular cell and supply free
hand so which one is lesser value supply
is lesser than demand so allocate 300
rupees get cancel 0
three-fifty allocated remaining 50
demand is there this is zero no just
cancer the entire row this is a
remaining cell unallocated self among
the unallocated cell
second step is find out the least cell
you can allocate anyone so because we
have got same value in two different
cell now we can allocate any one I
selected this cell let's find out that
demand and supply of this particular
cell so what is a demand to 50 demand
for one day supply which one is less
demand is lesser than supply just put
250 here certificate cancels 0 and here
balance 150 is a zero no this cancer
this column these are remaining
unallocated cell now find out which one
is least cost among the six cells
unallocated cell this is the least cost
demand and supply demand to Honda and
supply 500 so which one is lesser value
demand is lesser than supply so I
entered 200 yep 200 allocator will get 0
here the balancing figure is 300 this 0
no just cancel this column remaining
unallocated cell is they know so among
the unallocated cell find out which one
is least value here we have 1 2 3 so you
can allocate any one is fine or select
this one or you can select this also now
I am selecting this one and find the
value
demand 400 supply 300 so which one is
lesser value supplies lesser that demand
so enter 300 get cancer balance 100 so
this row 0 no just delete lender row now
we have only 2 cells which one is least
value Phi is least value select this
cell and allocate the value just compare
demand and supply demand 300 for this
cell
supply 150 so 100 rupees is lesser than
150 scarlet Honda will get 0 here
balance in Figure 50 0 no cancel this
and now we have only one inalca vessel
and the balancing figure that is demand
is equal to supply demand notes of if P
sub J also 50 just allocate 50
all supply-and-demand get cancer now
just multiply the value and find the
answer first one 300 into one second
cell
this is the second set plus 250 into two
plus 50 into six plus hundred into five
plus 300 into three plus 200 into two
2900 okay let us see Oh girls
approximation method according to this
method before we solve the problem
first we need to find out row difference
and column difference for each and every
row and for each and every column we
need to identify row difference and
column difference how can you find out
the row difference first select the
least cell in the first row which one is
least value one is the least value which
one is the next least value three now
find the difference between these two
please to value three to
in the same way we need to identify row
difference and call him difference for
each and every row as well as each and
every column in second row two is the
least value next value five what is the
difference between these two values
three the third row two is the least
value next to least value three what is
the difference between these two values
one now these are the row difference in
the same way you need to identify :
difference in the first column which is
the least value to next three what is
the difference
one in the second column one three
difference two in the third column three
five difference two in the fourth column
two least value mixture for what is the
difference - now we have got row
difference and column difference the
next step is select the maximum finality
these are the values called as finality
row penalty column finality among these
value you have to find out or select
maximum value so which is the maximum
value three is the maximum value three
occurs in row 2 this value occurs in Row
two find the cell with the least cost in
row two this sin has the least value now
I have selected this cell now you need
to compare demand and supply of this
particular cell demand 250 supply 400
now you have to allocate the value so
which is the least value 250 or 500 250
is the least value just allocate 250
here and subtract this you will get 0
here you will get 150 so this row 0 no
so the entire column then after this
this is the rest of the cell unallocated
cell again you have to find out row
difference and column difference with
the unallocated cell again in the first
row which one is the least value one
next four what is the difference between
these two values three in the second row
five is the least value next value six
difference one in the third row two is
the least value next two-three
difference one in the same way for
column also
so first column is enter always deleted
now let's put - in the second column
leads to value one next to value three
difference - here also - here also - so
among these value find out the maximum
value three is the maximum value just
select this occurs in row 1 again you
have to find out the least cell in this
first row 1 is the least value just
select this cell and enter a the demand
or sub play whichever is less demand 350
supply 300 software a lesser value just
put 300 here you'll get 0 here you'll
get 50 balance so this robot 0 no just
delete the entire row now one row one
column is over now we have only two
column two rows and three columns are
there with this unallocated cell again
you have to find out bro difference and
column difference in the first row
entire thing is over now just put - in a
second row Phi is the least value next
to least value 6 difference one here
also 2 3 1 in there column 3 6
difference 3 3 5 difference 2 - 9
difference 7 among these finalities
which one is the highest value
is a maximum value just select this one
this occurs in last column that is
fourth column among these two value
which is the least cell this is the DS T
cell because 9 is greater than 2 now
just compare the demand and supply which
one is lesser value demand is lesser
value just write 200 zero remaining 300
so this column what 0 no just delete
this column now we have only two rows
and two columns again you have to find
out throw difference and column
difference for this 5 and 6 difference 1
for this row 3 3-nil and for this column
3 6 3 difference for this column 3 5 2
is a difference among these values these
penalties which is a la highest value 3
it occurs in second column among the 2
value which one is least this is the
least value select this cell and here we
have only 50 but supply 300 which is the
less value demand is lesser value than
supply just put 50 here remaining 250
here you got 0 just cancel this column
now you have only two values among these
two values find out the least value 3 is
the least value select this cell and
just see demand 400 supply only 250 just
allocate 250 here he will get 0 here you
get 150 0 no cancel this row now we have
only one cell while you have last cell
you have equal value both demand and
supply will be equal always why because
it is a balanced
transportation problem both demand and
supply is equal No so the entire supply
an entire demand is exhausted now we can
find out the total transportation cost
figure allocated sell 300 into one just
multiplied with a product into one 250
into 2 plus 150 into fine plus 50 into 3
plus 250 into three 200 into two the
solution is 2008 50 the total cost of
the solution is obtained by adding a
product or cost of transportation thank
you