Dear all,
I am trying to find the solution for the optimization problem focused on the
finding minimum cost.
I used the solution proposed by excel solver, but there is a restriction in
the number of variables.
My data consists of 300 rows represent cities and 6 columns represent the
centres. It constitutes a cost matrix, where the cost are distances between
each city and each of six centres.
..+ 1 column contains variables, represents number of firms.
I want to calculate the minimum cost between cities and centres. Each city
can belong only to one of the centres.
A model example:
costs: distance between municipalities and centres + plus number of firms in
each municipality
"Municipality" "Centre1" "Centre2" "Centre3" "Centre4" "Centre5" "Centre6"
"Firms"
"Muni1" 30 20 60 40
66 90 15
"Muni2" 20 30 60 40
66 90 10
"Muni3" 25 31 60 40
66 90 5
"Muni4" 27 26 60 40
66 90 30
The outcome of excel functon Solver is:
cost assigned
"Municipality" "Centre1" "Centre2" "Centre3" "Centre4" "Centre5" "Centre6"
"Solution"
"Muni1" 0 20 0 0
0 0 300
"Muni2" 20 0 0 0
0 0 200
"Muni3" 25 0 0 0
0 0 125
"Muni4" 0 26 0 0
0 0 780
objective : 1405
I used package "lpSolve" but there is a problem with variables "firms":
s <- as.matrix(read.table("C:/R/OPTIMALIZATION/DATA.TXT", dec = ",",
sep=";",header=TRUE))
[2] [3] [4] [5] [6]
[1] 30 20 60 40 66 90
[2] 20 30 60 40 66 90
[3] 25 31 60 40 66 90
[4] 27 26 60 40 66 90
row.signs <- rep ("=", 4)
row.rhs <- c(15,10,5,30)
col.signs <- rep ("=", 6)
col.rhs <- c(1,1,1,1,1,1)
lp.transport (costs, "min", row.signs, row.rhs, col.signs, col.rhs,
presolve=0, compute.sens=0)
lp.transport (costs, "min", row.signs, row.rhs, col.signs, col.rhs,
presolve=0, compute.sens=0)$solution
Outcome:
Error in lp.transport(costs, "min", row.signs, row.rhs, col.signs, col.rhs,
:
Error: We have 6 signs, but 7 columns
Does anyone know where could the problem ?
Does there exist any other possibility how to perform that analysis in R ?
I am bit confused here about how can I treat with the variables "firms".
Thanks
Pavel
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Optimization in R similar to MS Excel Solver
5 messages · Pavel_K, Hans W Borchers, Berend Hasselman
On 11-03-2013, at 23:31, Pavel_K <kuk064 at vsb.cz> wrote:
Dear all,
I am trying to find the solution for the optimization problem focused on the
finding minimum cost.
I used the solution proposed by excel solver, but there is a restriction in
the number of variables.
My data consists of 300 rows represent cities and 6 columns represent the
centres. It constitutes a cost matrix, where the cost are distances between
each city and each of six centres.
..+ 1 column contains variables, represents number of firms.
I want to calculate the minimum cost between cities and centres. Each city
can belong only to one of the centres.
A model example:
costs: distance between municipalities and centres + plus number of firms in
each municipality
"Municipality" "Centre1" "Centre2" "Centre3" "Centre4" "Centre5" "Centre6"
"Firms"
"Muni1" 30 20 60 40
66 90 15
"Muni2" 20 30 60 40
66 90 10
"Muni3" 25 31 60 40
66 90 5
"Muni4" 27 26 60 40
66 90 30
The outcome of excel functon Solver is:
cost assigned
"Municipality" "Centre1" "Centre2" "Centre3" "Centre4" "Centre5" "Centre6"
"Solution"
"Muni1" 0 20 0 0
0 0 300
"Muni2" 20 0 0 0
0 0 200
"Muni3" 25 0 0 0
0 0 125
"Muni4" 0 26 0 0
0 0 780
objective : 1405
I used package "lpSolve" but there is a problem with variables "firms":
s <- as.matrix(read.table("C:/R/OPTIMALIZATION/DATA.TXT", dec = ",",
sep=";",header=TRUE))
[2] [3] [4] [5] [6]
[1] 30 20 60 40 66 90
[2] 20 30 60 40 66 90
[3] 25 31 60 40 66 90
[4] 27 26 60 40 66 90
row.signs <- rep ("=", 4)
row.rhs <- c(15,10,5,30)
col.signs <- rep ("=", 6)
col.rhs <- c(1,1,1,1,1,1)
lp.transport (costs, "min", row.signs, row.rhs, col.signs, col.rhs,
presolve=0, compute.sens=0)
lp.transport (costs, "min", row.signs, row.rhs, col.signs, col.rhs,
presolve=0, compute.sens=0)$solution
Outcome:
Error in lp.transport(costs, "min", row.signs, row.rhs, col.signs, col.rhs,
:
Error: We have 6 signs, but 7 columns
Does anyone know where could the problem ?
Does there exist any other possibility how to perform that analysis in R ?
I am bit confused here about how can I treat with the variables "firms".
Please provide a reproducible example including the necessary library() statements. In the call of lp.transport you are using a variable "costs" but where is it defined? You read a file with read.table into a variable "s". Use dput. Berend
Dear Mr Hasselman,
for a better understanding I have attached an example solved in excel by
using the tool Solver.
I want to assign for each municipality one of the centres and apply it for
calculating the minimum cost as you can see in an example.
I used package lpsolve, but it does not work. I am not sure how to treat
with this part of statement, I think I made mistake in it:
row.rhs <- c(15,10,5,30) and
col.rhs <- c(1,1,1,1,1,1)
The example in R:
library(lpSolve)
costs <- as.matrix(read.table("C:/R/OPTIMIZATION/DATA.TXT", dec = ",",
sep=";",header=TRUE))
row.signs <- rep ("=", 4)
row.rhs <- c(15,10,5,30)
col.signs <- rep ("=", 6)
col.rhs <- c(1,1,1,1,1,1)
lp.transport (costs, "min", row.signs, row.rhs, col.signs, col.rhs,
presolve=0, compute.sens=0)
lp.transport (costs, "min", row.signs, row.rhs, col.signs, col.rhs,
presolve=0, compute.sens=0)$solution
Outcome:
Error in lp.transport(costs, "min", row.signs, row.rhs, col.signs, col.rhs,
:
Error: We have 6 signs, but 7 columns
Hope the example solved in excel will help you to understand my problem.
Thank you
Pavel
example.xls <http://r.789695.n4.nabble.com/file/n4661019/example.xls>
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Pavel_K <kuk064 <at> vsb.cz> writes:
Dear all, I am trying to find the solution for the optimization problem focused on the finding minimum cost. I used the solution proposed by excel solver, but there is a restriction in the number of variables. My data consists of 300 rows represent cities and 6 columns represent the centres. It constitutes a cost matrix, where the cost are distances between each city and each of six centres. ..+ 1 column contains variables, represents number of firms. I want to calculate the minimum cost between cities and centres. Each city can belong only to one of the centres.
(1) The solution you say the Excel Solver returns does not appear to be
correct: The column sum in columns 3 to 5 is not (greater or) equal
to 1 as you request.
(2) lpSolve does not return an error, but says "no feasible solution found",
which seems to be correct: The equality constraints are too strict.
(3) If you relieve these constraints to inequalities, lpSolves does find
a solution:
costs <- matrix(c(
30, 20, 60, 40, 66, 90,
20, 30, 60, 40, 66, 90,
25, 31, 60, 40, 66, 90,
27, 26, 60, 40, 66, 90), 4, 6, byrow = TRUE)
firms <- c(15, 10, 5, 30)
row.signs <- rep (">=", 4)
row.rhs <- firms
col.signs <- rep (">=", 6)
col.rhs <- c(1,1,1,1,1,1)
require("lpSolve")
T <- lp.transport (costs, "min", row.signs, row.rhs, col.signs, col.rhs,
presolve = 0, compute.sens = 0)
T$solution
sum(T$solution * costs) # 1557
Of course, I don't know which constraints you really want to impose.
Hans Werner
A model example:
costs: distance between municipalities and centres + plus number of firms
in each municipality
"Municipality" "Centre1" "Centre2" "Centre3" "Centre4" "Centre5"
"Centre6"
"Firms"
"Muni1" 30 20 60 40 66 90 15
"Muni2" 20 30 60 40 66 90 10
"Muni3" 25 31 60 40 66 90 5
"Muni4" 27 26 60 40 66 90 30
The outcome of excel functon Solver is:
cost assigned
"Municipality" "Centre1" "Centre2" "Centre3" "Centre4" "Centre5" "Centre6"
"Solution"
"Muni1" 0 20 0 0 0 0 300
"Muni2" 20 0 0 0 0 0 200
"Muni3" 25 0 0 0 0 0 125
"Muni4" 0 26 0 0 0 0 780
objective : 1405
I used package "lpSolve" but there is a problem with variables "firms":
s <- as.matrix(read.table("C:/R/OPTIMALIZATION/DATA.TXT", dec = ",",
sep=";",header=TRUE))
[2] [3] [4] [5] [6]
[1] 30 20 60 40 66 90
[2] 20 30 60 40 66 90
[3] 25 31 60 40 66 90
[4] 27 26 60 40 66 90
row.signs <- rep ("=", 4)
row.rhs <- c(15,10,5,30)
col.signs <- rep ("=", 6)
col.rhs <- c(1,1,1,1,1,1)
lp.transport (costs, "min", row.signs, row.rhs, col.signs, col.rhs,
presolve=0, compute.sens=0)
lp.transport (costs, "min", row.signs, row.rhs, col.signs, col.rhs,
presolve=0, compute.sens=0)$solution
Outcome:
Error in lp.transport(costs, ...):
Error: We have 6 signs, but 7 columns
Does anyone know where could the problem ?
Does there exist any other possibility how to perform that analysis in R ?
I am bit confused here about how can I treat with the variables "firms".
Thanks
Pavel
On 12-03-2013, at 08:45, Pavel_K <kuk064 at vsb.cz> wrote:
Dear Mr Hasselman,
for a better understanding I have attached an example solved in excel by
using the tool Solver.
I want to assign for each municipality one of the centres and apply it for
calculating the minimum cost as you can see in an example.
I used package lpsolve, but it does not work. I am not sure how to treat
with this part of statement, I think I made mistake in it:
row.rhs <- c(15,10,5,30) and
col.rhs <- c(1,1,1,1,1,1)
The example in R:
library(lpSolve)
costs <- as.matrix(read.table("C:/R/OPTIMIZATION/DATA.TXT", dec = ",",
sep=";",header=TRUE))
row.signs <- rep ("=", 4)
row.rhs <- c(15,10,5,30)
col.signs <- rep ("=", 6)
col.rhs <- c(1,1,1,1,1,1)
lp.transport (costs, "min", row.signs, row.rhs, col.signs, col.rhs,
presolve=0, compute.sens=0)
lp.transport (costs, "min", row.signs, row.rhs, col.signs, col.rhs,
presolve=0, compute.sens=0)$solution
Outcome:
Error in lp.transport(costs, "min", row.signs, row.rhs, col.signs, col.rhs,
:
Error: We have 6 signs, but 7 columns
Hope the example solved in excel will help you to understand my problem.
You post is not available on Nabble. The excel file is inaccessible because it doesn't exist. Apart from that: show the contents of costs. Use dput(costs) and put the result in the message to R-help. That is the only way one can find out why lp.transport gives an error. And please read the posting guide (link is at the bottom of each posting to this list). Berend
Thank you Pavel example.xls <http://r.789695.n4.nabble.com/file/n4661019/example.xls> -- View this message in context: http://r.789695.n4.nabble.com/Optimization-in-R-similar-to-MS-Excel-Solver-tp4660997p4661019.html Sent from the R help mailing list archive at Nabble.com.
______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.