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R version 2.10.1 (2009-12-14)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> library( linprog )
Loading required package: lpSolve
>
> ## example of Steinhauser, Langbehn and Peters (1992)
> ## Production activities
> cvec <- c(1800, 600, 600) # gross margins
> names(cvec) <- c("Cows","Bulls","Pigs")
>
> ## Constraints (quasi-fix factors)
> bvec <- c(40, 90, 2500) # endowment
> names(bvec) <- c("Land","Stable","Labor")
>
> ## Needs of Production activities
> Amat <- rbind( c( 0.7, 0.35, 0 ),
+ c( 1.5, 1, 3 ),
+ c( 50, 12.5, 20 ) )
>
> ## solve the model
> result1a <- solveLP( cvec, bvec, Amat, TRUE )
>
> ## Write to a (virtual) MPS file
> mpsFile <- file()
> writeMps( mpsFile, cvec, bvec, Amat, "Steinhauser" )
>
> ## write the lines of this file to the output file
> mpsLines <- readLines( mpsFile )
> close( mpsFile )
> print( mpsLines )
[1] "NAME Steinhauser"
[2] "ROWS"
[3] " N obj"
[4] " L Land"
[5] " L Stable"
[6] " L Labor"
[7] "COLUMNS"
[8] " Cows obj 1800"
[9] " Cows Land 0.7"
[10] " Cows Stable 1.5"
[11] " Cows Labor 50"
[12] " Bulls obj 600"
[13] " Bulls Land 0.35"
[14] " Bulls Stable 1"
[15] " Bulls Labor 12.5"
[16] " Pigs obj 600"
[17] " Pigs Stable 3"
[18] " Pigs Labor 20"
[19] "RHS"
[20] " RHS Land 40"
[21] " RHS Stable 90"
[22] " RHS Labor 2500"
[23] "ENDATA"
>
> ## Write to a (virtual) MPS file again (for readMps)
> mpsFile <- file()
> writeMps( mpsFile, cvec, bvec, Amat, "Steinhauser" )
>
> ## delete all LP objects
> rm( cvec, bvec, Amat )
>
> ## Read LP data from MPS file and solve it.
> lpModel <- readMps( mpsFile, TRUE, TRUE )
> close( mpsFile )
>
> ## Print the model and its result
> lpModel
$name
[1] "Steinhauser"
$cvec
Cows Bulls Pigs
1800 600 600
$bvec
Land Stable Labor
40 90 2500
$Amat
Cows Bulls Pigs
Land 0.7 0.35 0
Stable 1.5 1.00 3
Labor 50.0 12.50 20
$res
Results of Linear Programming / Linear Optimization
Objective function (Maximum): 93600
Iterations in phase 1: 0
Iterations in phase 2: 2
Solution
opt
Cows 44
Bulls 24
Pigs 0
Basic Variables
opt
Cows 44.0
Bulls 24.0
S Land 0.8
Constraints
actual dir bvec free dual dual.reg
Land 39.2 <= 40 0.8 0.0 0.8
Stable 90.0 <= 90 0.0 240.0 15.0
Labor 2500.0 <= 2500 0.0 28.8 1375.0
All Variables (including slack variables)
opt cvec min.c max.c marg marg.reg
Cows 44.0 1800 900 2400.000 NA NA
Bulls 24.0 600 450 1200.000 NA NA
Pigs 0.0 600 -Inf 1296.000 -696.0 6.25
S Land 0.8 0 NA 731.092 0.0 NA
S Stable 0.0 0 -Inf 240.000 -240.0 15.00
S Labor 0.0 0 -Inf 28.800 -28.8 1375.00
> all.equal( result1a, lpModel$res )
[1] TRUE
>
>
> ## example 1.1.3 of Witte, Deppe and Born (1975)
> ## Two types of Feed
> cvec <- c(2.5, 2 ) # prices of feed
> names(cvec) <- c("Feed1","Feed2")
>
> ## Constraints (minimum (<0) and maximum (>0) contents)
> bvec <- c(-10, -1.5, 12)
> names(bvec) <- c("Protein","Fat","Fibre")
>
> ## Matrix A
> Amat <- rbind( c( -1.6, -2.4 ),
+ c( -0.5, -0.2 ),
+ c( 2.0, 2.0 ) )
>
> ## solve the model
> result2a <- solveLP( cvec, bvec, Amat )
>
> ## Write to a (virtual) MPS file
> mpsFile <- file()
> writeMps( mpsFile, cvec, bvec, Amat, "Steinhauser" )
>
> ## write the lines of this file to the output file
> mpsLines <- readLines( mpsFile )
> close( mpsFile )
> print( mpsLines )
[1] "NAME Steinhauser"
[2] "ROWS"
[3] " N obj"
[4] " L Protein"
[5] " L Fat"
[6] " L Fibre"
[7] "COLUMNS"
[8] " Feed1 obj 2.5"
[9] " Feed1 Protein -1.6"
[10] " Feed1 Fat -0.5"
[11] " Feed1 Fibre 2"
[12] " Feed2 obj 2"
[13] " Feed2 Protein -2.4"
[14] " Feed2 Fat -0.2"
[15] " Feed2 Fibre 2"
[16] "RHS"
[17] " RHS Protein -10"
[18] " RHS Fat -1.5"
[19] " RHS Fibre 12"
[20] "ENDATA"
>
> ## Write to a (virtual) MPS file again (for readMps)
> mpsFile <- file()
> writeMps( mpsFile, cvec, bvec, Amat, "Steinhauser" )
>
> ## delete all LP objects
> rm( cvec, bvec, Amat )
>
> ## Read LP data from MPS file and solve it.
> lpModel <- readMps( mpsFile, TRUE )
> close( mpsFile )
>
> ## Print the model and its result
> lpModel
$name
[1] "Steinhauser"
$cvec
Feed1 Feed2
2.5 2.0
$bvec
Protein Fat Fibre
-10.0 -1.5 12.0
$Amat
Feed1 Feed2
Protein -1.6 -2.4
Fat -0.5 -0.2
Fibre 2.0 2.0
$res
Results of Linear Programming / Linear Optimization
Objective function (Minimum): 10.4545
Iterations in phase 1: 2
Iterations in phase 2: 0
Solution
opt
Feed1 1.81818
Feed2 2.95455
Basic Variables
opt
Feed1 1.81818
Feed2 2.95455
S Fibre 2.45455
Constraints
actual dir bvec free dual dual.reg
Protein -10.00000 <= -10.0 0.00000 0.568182 3.60000
Fat -1.50000 <= -1.5 0.00000 3.181818 1.35000
Fibre 9.54545 <= 12.0 2.45455 0.000000 2.45455
All Variables (including slack variables)
opt cvec min.c max.c marg marg.reg
Feed1 1.81818 2.5 -3.666667 5.000000 NA NA
Feed2 2.95455 2.0 -3.000000 3.750000 NA NA
S Protein 0.00000 0.0 -0.568182 Inf 0.568182 3.60
S Fat 0.00000 0.0 -3.181818 Inf 3.181818 1.35
S Fibre 2.45455 0.0 NA 0.833333 0.000000 NA
> all.equal( result2a, lpModel$res )
[1] TRUE
>
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