Version: | 0.9-4 |
Date: | 2022-03-09 |
Title: | Linear Programming / Optimization |
Author: | Arne Henningsen |
Maintainer: | Arne Henningsen <arne.henningsen@gmail.com> |
Depends: | R (≥ 2.4.0), lpSolve |
Description: | Can be used to solve Linear Programming / Linear Optimization problems by using the simplex algorithm. |
License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
URL: | http://linprog.r-forge.r-project.org/ |
NeedsCompilation: | no |
Packaged: | 2022-03-09 17:21:04 UTC; gsl324 |
Repository: | CRAN |
Date/Publication: | 2022-03-09 21:10:08 UTC |
Print Objects of Class solveLP
Description
This method prints the results of the Linear Programming algorithm.
Usage
## S3 method for class 'solveLP'
print( x, digits=6, ...)
Arguments
x |
an object returned by |
digits |
number of digits to print. |
... |
currently ignored. |
Value
print.solveLP
invisibly returns the object given in argument x
.
Author(s)
Arne Henningsen
See Also
solveLP
, summary.solveLP
,
readMps
, writeMps
Examples
## example of Steinhauser, Langbehn and Peters (1992)
## Not run: library( linprog )
## Production activities
cvec <- c(1800, 600, 600) # gross margins
names(cvec) <- c("Milk","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 ) )
## Maximize the gross margin
res <- solveLP( cvec, bvec, Amat, TRUE )
## print the results
print( res )
Read MPS Files
Description
This function reads MPS files - the standard format for Linear Programming problems.
Usage
readMps( file, solve=FALSE, maximum=FALSE )
Arguments
file |
a character string naming the file to read. |
solve |
logical. Should the problem be solved after reading it
from the file (using |
maximum |
logical. Should we maximize or minimize (the default)? |
Details
Equality constraints and 'greater than'-bounds are not implemented yet.
Value
readMps
returns a list containing following objects:
name |
the name of the Linear Programming problem. |
cvec |
vector |
bvec |
vector |
Amat |
matrix |
res |
if |
Author(s)
Arne Henningsen
See Also
Examples
## 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 ) )
## Write to MPS file
writeMps( "steinh.mps", cvec, bvec, Amat, "Steinhauser" )
## delete all LP objects
rm( cvec, bvec, Amat )
## Read LP data from MPS file and solve it.
lp <- readMps( "steinh.mps", TRUE, TRUE )
## Print the results
lp$res
## remove the MPS file
file.remove( "steinh.mps" )
Solve Linear Programming / Optimization Problems
Description
Minimizes (or maximizes) c'x
, subject to A x <= b
and x >= 0
.
Note that the inequality signs <=
of the individual linear constraints
in A x <= b
can be changed with argument const.dir
.
Usage
solveLP( cvec, bvec, Amat, maximum = FALSE,
const.dir = rep( "<=", length( bvec ) ),
maxiter = 1000, zero = 1e-9, tol = 1e-6, dualtol = tol,
lpSolve = FALSE, solve.dual = FALSE, verbose = 0 )
Arguments
cvec |
vector |
bvec |
vector |
Amat |
matrix A (of dimension |
maximum |
logical. Should we maximize or minimize (the default)? |
const.dir |
vector of character strings giving the directions of the constraints: each value should be one of "<," "<=," "=," "==," ">," or ">=". (In each pair the two values are identical.) |
maxiter |
maximum number of iterations. |
zero |
numbers smaller than this value (in absolute terms) are set to zero. |
tol |
if the constraints are violated by more than this number,
the returned component |
dualtol |
if the constraints in the dual problem are violated by more than this number, the returned status is non-zero. |
lpSolve |
logical. Should the package 'lpSolve' be used to solve the LP problem? |
solve.dual |
logical value indicating if the dual problem should also be solved. |
verbose |
an optional integer variable to indicate how many intermediate results should be printed (0 = no output; 4 = maximum output). |
Details
This function uses the Simplex algorithm of George B. Dantzig (1947)
and provides detailed results (e.g. dual prices, sensitivity analysis
and stability analysis).
If the solution x=0
is not feasible, a 2-phase procedure is
applied.
Values of the simplex tableau that are actually zero might get small
(positive or negative) numbers due to rounding errors, which might
lead to artificial restrictions. Therefore, all values that are smaller
(in absolute terms) than the value of zero
(default is 1e-10) are
set to 0.
Solving the Linear Programming problem by the package lpSolve
(of course) requires the installation of this package, which is available
on CRAN (https://cran.r-project.org/package=lpSolve).
Since the lpSolve
package uses C-code and this (linprog
)
package is not optimized for speed, the former is much faster.
However, this package provides more detailed results (e.g. dual values,
stability and sensitivity analysis).
This function has not been tested extensively and might not solve all
feasible problems (or might even lead to wrong results). However, you can
export your LP to a standard MPS file via writeMps
and check
it with other software (e.g. lp_solve
, see
http://lpsolve.sourceforge.net/5.5/).
Equality constraints are not implemented yet.
Value
solveLP
returns a list of the class solveLP
containing following objects:
opt |
optimal value (minimum or maximum) of the objective function. |
solution |
vector of optimal values of the variables. |
iter1 |
iterations of Simplex algorithm in phase 1. |
iter2 |
iterations of Simplex algorithm in phase 2. |
basvar |
vector of basic (=non-zero) variables (at optimum). |
con |
matrix of results regarding the constraints: |
allvar |
matrix of results regarding all variables (including slack variables): |
status |
numeric. Indicates if the optimization did succeed: |
lpStatus |
numeric. Return code of |
dualStatus |
numeric. Return code from solving the dual problem
(only if argument |
maximum |
logical. Indicates whether the objective function was maximized or minimized. |
Tab |
final 'Tableau' of the Simplex algorith. |
lpSolve |
logical. Has the package 'lpSolve' been used to solve the LP problem. |
solve.dual |
logical. Argument |
maxiter |
numeric. Argument |
Author(s)
Arne Henningsen
References
Dantzig, George B. (1951), Maximization of a linear function of variables subject to linear inequalities, in Koopmans, T.C. (ed.), Activity analysis of production and allocation, John Wiley \& Sons, New York, p. 339-347.
Steinhauser, Hugo; Cay Langbehn and Uwe Peters (1992), Einfuehrung in die landwirtschaftliche Betriebslehre. Allgemeiner Teil, 5th ed., Ulmer, Stuttgart.
Witte, Thomas; Joerg-Frieder Deppe and Axel Born (1975), Lineare Programmierung. Einfuehrung fuer Wirtschaftswissenschaftler, Gabler-Verlag, Wiesbaden.
See Also
Examples
## 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 ) )
## Maximize the gross margin
solveLP( cvec, bvec, Amat, 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 ) )
## Minimize the cost
solveLP( cvec, bvec, Amat )
# the same optimisation using argument const.dir
solveLP( cvec, abs( bvec ), abs( Amat ), const.dir = c( ">=", ">=", "<=" ) )
## There are also several other ways to put the data into the arrays, e.g.:
bvec <- c( Protein = -10.0,
Fat = -1.5,
Fibre = 12.0 )
cvec <- c( Feed1 = 2.5,
Feed2 = 2.0 )
Amat <- matrix( 0, length(bvec), length(cvec) )
rownames(Amat) <- names(bvec)
colnames(Amat) <- names(cvec)
Amat[ "Protein", "Feed1" ] <- -1.6
Amat[ "Fat", "Feed1" ] <- -0.5
Amat[ "Fibre", "Feed1" ] <- 2.0
Amat[ "Protein", "Feed2" ] <- -2.4
Amat[ "Fat", "Feed2" ] <- -0.2
Amat[ "Fibre", "Feed2" ] <- 2.0
solveLP( cvec, bvec, Amat )
Summary Results for Objects of Class solveLP
Description
These methods prepare and print summary results of the Linear Programming algorithm.
Usage
## S3 method for class 'solveLP'
summary(object,...)
## S3 method for class 'summary.solveLP'
print(x,...)
Arguments
object |
an object returned by |
x |
an object returned by |
... |
currently ignored. |
Value
summary.solveLP
returns an object of class summary.solveLP
.
print.summary.solveLP
invisibly returns the object given
in argument x
.
Author(s)
Arne Henningsen
See Also
solveLP
, print.solveLP
,
readMps
, writeMps
Examples
## example of Steinhauser, Langbehn and Peters (1992)
## Not run: library( linprog )
## Production activities
cvec <- c(1800, 600, 600) # gross margins
names(cvec) <- c("Milk","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 ) )
## Maximize the gross margin
res <- solveLP( cvec, bvec, Amat, TRUE )
## prepare and print the summary results
summary( res )
Write MPS Files
Description
This function writes MPS files - the standard format for Linear Programming problems.
Usage
writeMps( file, cvec, bvec, Amat, name="LP" )
Arguments
file |
a character string naming the file to write. |
cvec |
vector |
bvec |
vector |
Amat |
matrix |
name |
an optional name for the Linear Programming problem. |
Details
The exported LP can be solved by running other software on this MPS file
(e.g. lp_solve
, see http://lpsolve.sourceforge.net/5.5/).
Author(s)
Arne Henningsen
See Also
Examples
## 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 ) )
## Write to MPS file
writeMps( "steinh.mps", cvec, bvec, Amat, "Steinhauser" )
## remove the MPS file
file.remove( "steinh.mps" )