Mixing
Negative cost coefficients in Transportation problem
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I have a minimum transportation cost supply demand matrix which looks like this , I dont know how to handle negative cost coefficients, since negative costs dont make any sense , should I just ignore them or add most negative value to all cells ? will it change the solution??
The literature I referred to says we should have non negative coefficients but is largely silent on what to do when we have negative coefficients
$$beginarrayc
& textS1 & textS2 & textS3 & textS4 & textS5 \ hline
textD1 & 4 & 7 & 0 & 3 & 6 \ hline
textD2 & 1 & 2 & -3 & 3 & 8 \ hline
textD2 & 3 & -1 & 4 & 0 & 5 \ hline
endarray$$
optimization optimal-transport
asked Jul 20 at 6:19
kira0705
825
 |Â
show 1 more comment
up vote
0
down vote
favorite
I have a minimum transportation cost supply demand matrix which looks like this , I dont know how to handle negative cost coefficients, since negative costs dont make any sense , should I just ignore them or add most negative value to all cells ? will it change the solution??
The literature I referred to says we should have non negative coefficients but is largely silent on what to do when we have negative coefficients
$$beginarrayc
& textS1 & textS2 & textS3 & textS4 & textS5 \ hline
textD1 & 4 & 7 & 0 & 3 & 6 \ hline
textD2 & 1 & 2 & -3 & 3 & 8 \ hline
textD2 & 3 & -1 & 4 & 0 & 5 \ hline
endarray$$
optimization optimal-transport
asked Jul 20 at 6:19
kira0705
825
How does this problem arise (other than as a school assignment)?
– Mark L. Stone
Jul 20 at 14:35
@MarkL.Stone yes it is a school assignment (college actually ) and i ask forgiveness if the question sounds very rudimentary , but I was not able to find any good source which could justify what solution one must take in such cases . I would be highly obliged and thankful if you could tell me the solution if you know it :) thanks!
– kira0705
Jul 20 at 15:03
I am not seeking at explicitly solving the problem only just a solution on how to tackle such cases , any help would be welcomed
– kira0705
Jul 20 at 15:04
1
Why not solve it as is? You could directly enter it into a general purpose LP solver. It seems to me that negative costs can make sense. For instance, maybe someone's willing to pay to move something in the form of their paying a rental fee for a one-way rental - that's a negative cost to the owner.
– Mark L. Stone
Jul 21 at 0:51
I actually got confused when I tried to cross check with this online tool , phpsimplex.com the developer has simply ignored the negative costs in finding basic feasible solution by Volge's approximation
– kira0705
Jul 21 at 13:53
 |Â
show 1 more comment
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have a minimum transportation cost supply demand matrix which looks like this , I dont know how to handle negative cost coefficients, since negative costs dont make any sense , should I just ignore them or add most negative value to all cells ? will it change the solution??
The literature I referred to says we should have non negative coefficients but is largely silent on what to do when we have negative coefficients
$$beginarrayc
& textS1 & textS2 & textS3 & textS4 & textS5 \ hline
textD1 & 4 & 7 & 0 & 3 & 6 \ hline
textD2 & 1 & 2 & -3 & 3 & 8 \ hline
textD2 & 3 & -1 & 4 & 0 & 5 \ hline
endarray$$
optimization optimal-transport
asked Jul 20 at 6:19
kira0705
825
I have a minimum transportation cost supply demand matrix which looks like this , I dont know how to handle negative cost coefficients, since negative costs dont make any sense , should I just ignore them or add most negative value to all cells ? will it change the solution??
The literature I referred to says we should have non negative coefficients but is largely silent on what to do when we have negative coefficients
$$beginarrayc
& textS1 & textS2 & textS3 & textS4 & textS5 \ hline
textD1 & 4 & 7 & 0 & 3 & 6 \ hline
textD2 & 1 & 2 & -3 & 3 & 8 \ hline
textD2 & 3 & -1 & 4 & 0 & 5 \ hline
endarray$$
optimization optimal-transport
asked Jul 20 at 6:19
kira0705
825
asked Jul 20 at 6:19
kira0705
825
asked Jul 20 at 6:19
kira0705
825
asked Jul 20 at 6:19
kira0705
825
825
How does this problem arise (other than as a school assignment)?
– Mark L. Stone
Jul 20 at 14:35
@MarkL.Stone yes it is a school assignment (college actually ) and i ask forgiveness if the question sounds very rudimentary , but I was not able to find any good source which could justify what solution one must take in such cases . I would be highly obliged and thankful if you could tell me the solution if you know it :) thanks!
– kira0705
Jul 20 at 15:03
I am not seeking at explicitly solving the problem only just a solution on how to tackle such cases , any help would be welcomed
– kira0705
Jul 20 at 15:04
1
Why not solve it as is? You could directly enter it into a general purpose LP solver. It seems to me that negative costs can make sense. For instance, maybe someone's willing to pay to move something in the form of their paying a rental fee for a one-way rental - that's a negative cost to the owner.
– Mark L. Stone
Jul 21 at 0:51
I actually got confused when I tried to cross check with this online tool , phpsimplex.com the developer has simply ignored the negative costs in finding basic feasible solution by Volge's approximation
– kira0705
Jul 21 at 13:53
 |Â
show 1 more comment
How does this problem arise (other than as a school assignment)?
– Mark L. Stone
Jul 20 at 14:35
@MarkL.Stone yes it is a school assignment (college actually ) and i ask forgiveness if the question sounds very rudimentary , but I was not able to find any good source which could justify what solution one must take in such cases . I would be highly obliged and thankful if you could tell me the solution if you know it :) thanks!
– kira0705
Jul 20 at 15:03
I am not seeking at explicitly solving the problem only just a solution on how to tackle such cases , any help would be welcomed
– kira0705
Jul 20 at 15:04
1
Why not solve it as is? You could directly enter it into a general purpose LP solver. It seems to me that negative costs can make sense. For instance, maybe someone's willing to pay to move something in the form of their paying a rental fee for a one-way rental - that's a negative cost to the owner.
– Mark L. Stone
Jul 21 at 0:51
I actually got confused when I tried to cross check with this online tool , phpsimplex.com the developer has simply ignored the negative costs in finding basic feasible solution by Volge's approximation
– kira0705
Jul 21 at 13:53
How does this problem arise (other than as a school assignment)?
– Mark L. Stone
Jul 20 at 14:35
How does this problem arise (other than as a school assignment)?
– Mark L. Stone
Jul 20 at 14:35
@MarkL.Stone yes it is a school assignment (college actually ) and i ask forgiveness if the question sounds very rudimentary , but I was not able to find any good source which could justify what solution one must take in such cases . I would be highly obliged and thankful if you could tell me the solution if you know it :) thanks!
– kira0705
Jul 20 at 15:03
@MarkL.Stone yes it is a school assignment (college actually ) and i ask forgiveness if the question sounds very rudimentary , but I was not able to find any good source which could justify what solution one must take in such cases . I would be highly obliged and thankful if you could tell me the solution if you know it :) thanks!
– kira0705
Jul 20 at 15:03
I am not seeking at explicitly solving the problem only just a solution on how to tackle such cases , any help would be welcomed
– kira0705
Jul 20 at 15:04
I am not seeking at explicitly solving the problem only just a solution on how to tackle such cases , any help would be welcomed
– kira0705
Jul 20 at 15:04
1
1
Why not solve it as is? You could directly enter it into a general purpose LP solver. It seems to me that negative costs can make sense. For instance, maybe someone's willing to pay to move something in the form of their paying a rental fee for a one-way rental - that's a negative cost to the owner.
– Mark L. Stone
Jul 21 at 0:51
Why not solve it as is? You could directly enter it into a general purpose LP solver. It seems to me that negative costs can make sense. For instance, maybe someone's willing to pay to move something in the form of their paying a rental fee for a one-way rental - that's a negative cost to the owner.
– Mark L. Stone
Jul 21 at 0:51
I actually got confused when I tried to cross check with this online tool , phpsimplex.com the developer has simply ignored the negative costs in finding basic feasible solution by Volge's approximation
– kira0705
Jul 21 at 13:53
I actually got confused when I tried to cross check with this online tool , phpsimplex.com the developer has simply ignored the negative costs in finding basic feasible solution by Volge's approximation
– kira0705
Jul 21 at 13:53
 |Â
show 1 more comment
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How does this problem arise (other than as a school assignment)?
– Mark L. Stone
Jul 20 at 14:35
@MarkL.Stone yes it is a school assignment (college actually ) and i ask forgiveness if the question sounds very rudimentary , but I was not able to find any good source which could justify what solution one must take in such cases . I would be highly obliged and thankful if you could tell me the solution if you know it :) thanks!
– kira0705
Jul 20 at 15:03
I am not seeking at explicitly solving the problem only just a solution on how to tackle such cases , any help would be welcomed
– kira0705
Jul 20 at 15:04
1
Why not solve it as is? You could directly enter it into a general purpose LP solver. It seems to me that negative costs can make sense. For instance, maybe someone's willing to pay to move something in the form of their paying a rental fee for a one-way rental - that's a negative cost to the owner.
– Mark L. Stone
Jul 21 at 0:51
I actually got confused when I tried to cross check with this online tool , phpsimplex.com the developer has simply ignored the negative costs in finding basic feasible solution by Volge's approximation
– kira0705
Jul 21 at 13:53