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Why basic feasible solution of a transportation problem always involves not more than $m+n-1$ allocations?
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I was reading Balanced transportation problem. I got stuck in the conditions of Basic Feasible solution.
If we suppose a transportation problem where $m$ number of supply points and $n$ number of demand points then why the basic feasible solution always involves not more than $m+n-1$ allocations.
My confusion --- If we consider this transportation problem as L.P.P problem then it will have $m+n$ equations and $mn$ variable. So we can get $m+n$ basic variable. i.e there can be $m+n$ allocation .
But it does not happen. Whenever we see there is $m+n$ allocations we can be confident that there is a loop.
Can anyone please help me to understand where I am missunderstanding?
Can anyone please help me ?
linear-algebra linear-programming
asked Jan 31 at 16:45
cmicmi
1,141312
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add a comment |
$begingroup$
I was reading Balanced transportation problem. I got stuck in the conditions of Basic Feasible solution.
If we suppose a transportation problem where $m$ number of supply points and $n$ number of demand points then why the basic feasible solution always involves not more than $m+n-1$ allocations.
My confusion --- If we consider this transportation problem as L.P.P problem then it will have $m+n$ equations and $mn$ variable. So we can get $m+n$ basic variable. i.e there can be $m+n$ allocation .
But it does not happen. Whenever we see there is $m+n$ allocations we can be confident that there is a loop.
Can anyone please help me to understand where I am missunderstanding?
Can anyone please help me ?
linear-algebra linear-programming
asked Jan 31 at 16:45
cmicmi
1,141312
$endgroup$
$begingroup$
did I answer your question?
$endgroup$
– LinAlg
Feb 25 at 16:29
add a comment |
$begingroup$
I was reading Balanced transportation problem. I got stuck in the conditions of Basic Feasible solution.
If we suppose a transportation problem where $m$ number of supply points and $n$ number of demand points then why the basic feasible solution always involves not more than $m+n-1$ allocations.
My confusion --- If we consider this transportation problem as L.P.P problem then it will have $m+n$ equations and $mn$ variable. So we can get $m+n$ basic variable. i.e there can be $m+n$ allocation .
But it does not happen. Whenever we see there is $m+n$ allocations we can be confident that there is a loop.
Can anyone please help me to understand where I am missunderstanding?
Can anyone please help me ?
linear-algebra linear-programming
asked Jan 31 at 16:45
cmicmi
1,141312
$endgroup$
I was reading Balanced transportation problem. I got stuck in the conditions of Basic Feasible solution.
If we suppose a transportation problem where $m$ number of supply points and $n$ number of demand points then why the basic feasible solution always involves not more than $m+n-1$ allocations.
My confusion --- If we consider this transportation problem as L.P.P problem then it will have $m+n$ equations and $mn$ variable. So we can get $m+n$ basic variable. i.e there can be $m+n$ allocation .
But it does not happen. Whenever we see there is $m+n$ allocations we can be confident that there is a loop.
Can anyone please help me to understand where I am missunderstanding?
Can anyone please help me ?
linear-algebra linear-programming
linear-algebra linear-programming
asked Jan 31 at 16:45
cmicmi
1,141312
asked Jan 31 at 16:45
cmicmi
1,141312
asked Jan 31 at 16:45
cmicmi
1,141312
asked Jan 31 at 16:45
cmicmi
1,141312
asked Jan 31 at 16:45
cmicmi
1,141312
1,141312
$begingroup$
did I answer your question?
$endgroup$
– LinAlg
Feb 25 at 16:29
add a comment |
$begingroup$
did I answer your question?
$endgroup$
– LinAlg
Feb 25 at 16:29
$begingroup$
did I answer your question?
$endgroup$
– LinAlg
Feb 25 at 16:29
$begingroup$
did I answer your question?
$endgroup$
– LinAlg
Feb 25 at 16:29
add a comment |
1 Answer
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The transportation problem only has $m+n-1$ independent constraints, see this answer. That means that there cannot be $m+n$ basic variables, but only $n+m-1$.
answered Jan 31 at 16:51
LinAlgLinAlg
10.1k1521
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I think this question it's actually a duplicate of my question. Isn't it?
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– Al t.
Feb 3 at 2:13
1
$begingroup$
@Alt. yes, although you seemed more appreciative of the answer :)
$endgroup$
– LinAlg
Feb 3 at 2:19
add a comment |
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1 Answer
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active
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1 Answer
1
active
oldest
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active
oldest
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active
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votes
$begingroup$
The transportation problem only has $m+n-1$ independent constraints, see this answer. That means that there cannot be $m+n$ basic variables, but only $n+m-1$.
answered Jan 31 at 16:51
LinAlgLinAlg
10.1k1521
$endgroup$
$begingroup$
I think this question it's actually a duplicate of my question. Isn't it?
$endgroup$
– Al t.
Feb 3 at 2:13
1
$begingroup$
@Alt. yes, although you seemed more appreciative of the answer :)
$endgroup$
– LinAlg
Feb 3 at 2:19
add a comment |
$begingroup$
The transportation problem only has $m+n-1$ independent constraints, see this answer. That means that there cannot be $m+n$ basic variables, but only $n+m-1$.
answered Jan 31 at 16:51
LinAlgLinAlg
10.1k1521
$endgroup$
$begingroup$
I think this question it's actually a duplicate of my question. Isn't it?
$endgroup$
– Al t.
Feb 3 at 2:13
1
$begingroup$
@Alt. yes, although you seemed more appreciative of the answer :)
$endgroup$
– LinAlg
Feb 3 at 2:19
add a comment |
$begingroup$
The transportation problem only has $m+n-1$ independent constraints, see this answer. That means that there cannot be $m+n$ basic variables, but only $n+m-1$.
answered Jan 31 at 16:51
LinAlgLinAlg
10.1k1521
$endgroup$
The transportation problem only has $m+n-1$ independent constraints, see this answer. That means that there cannot be $m+n$ basic variables, but only $n+m-1$.
answered Jan 31 at 16:51
LinAlgLinAlg
10.1k1521
answered Jan 31 at 16:51
LinAlgLinAlg
10.1k1521
answered Jan 31 at 16:51
LinAlgLinAlg
10.1k1521
answered Jan 31 at 16:51
LinAlgLinAlg
10.1k1521
10.1k1521
$begingroup$
I think this question it's actually a duplicate of my question. Isn't it?
$endgroup$
– Al t.
Feb 3 at 2:13
1
$begingroup$
@Alt. yes, although you seemed more appreciative of the answer :)
$endgroup$
– LinAlg
Feb 3 at 2:19
add a comment |
$begingroup$
I think this question it's actually a duplicate of my question. Isn't it?
$endgroup$
– Al t.
Feb 3 at 2:13
1
$begingroup$
@Alt. yes, although you seemed more appreciative of the answer :)
$endgroup$
– LinAlg
Feb 3 at 2:19
$begingroup$
I think this question it's actually a duplicate of my question. Isn't it?
$endgroup$
– Al t.
Feb 3 at 2:13
$begingroup$
I think this question it's actually a duplicate of my question. Isn't it?
$endgroup$
– Al t.
Feb 3 at 2:13
1
1
$begingroup$
@Alt. yes, although you seemed more appreciative of the answer :)
$endgroup$
– LinAlg
Feb 3 at 2:19
$begingroup$
@Alt. yes, although you seemed more appreciative of the answer :)
$endgroup$
– LinAlg
Feb 3 at 2:19
add a comment |
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did I answer your question?
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– LinAlg
Feb 25 at 16:29