lp {lpSolve}R Documentation

Linear and Integer Programming

Description

Interface to lp_solve linear/integer programming system

Usage

lp (direction = "min", objective.in, const.mat, const.dir, const.rhs,
        transpose.constraints = TRUE, int.vec, presolve=0, compute.sens=0)

Arguments

direction Character string giving direction of optimization: "min" (default) or "max."
objective.in Numeric vector of coefficients of objective function
const.mat Matrix of numeric constraint coefficients, one row per constraint, one column per variable (unless transpose.constraints = FALSE; see below).
const.dir Vector of character strings giving the direction of the constraint: each value should be one of "<," "<=," "=," "==," ">," or ">=."
const.rhs Vector of numeric values for the right-hand sides of the constraints.
transpose.constraints By default each constraint occupies a row of const.mat, and that matrix needs to be transposed before being passed to the optimizing code. For very large constraint matrices it may be wiser to construct the constraints in a matrix column-by-column. In that case set transpose.constraints to FALSE.
int.vec Numeric vector giving the indices of variables that are required to be integer. The length of this vector will therefore be the number of integer variables.
presolve Numeric: presolve? Default 0 (no); any non-zero value means "yes." Currently ignored.
compute.sens Numeric: compute sensitivity? Default 0 (no); any non-zero value means "yes."

Details

This function calls the lp_solve 5.5 solver. That system has many options not supported here. The current version is maintained at ftp://ftp.es.ele.tue.nl/pub/lp_solve

Value

An lp object. See lp.object for details.

Author(s)

Sam Buttrey, buttrey@nps.edu

See Also

lp.assign, lp.transport

Examples

#
# Set up problem: maximize
#   x1 + 9 x2 +   x3 subject to
#   x1 + 2 x2 + 3 x3  <= 9
# 3 x1 + 2 x2 + 2 x3 <= 15
#
f.obj <- c(1, 9, 3)
f.con <- matrix (c(1, 2, 3, 3, 2, 2), nrow=2, byrow=TRUE)
f.dir <- c("<=", "<=")
f.rhs <- c(9, 15)
#
# Now run.
#
lp ("max", f.obj, f.con, f.dir, f.rhs)
## Not run: Success: the objective function is 40.5
lp ("max", f.obj, f.con, f.dir, f.rhs)$solution
## Not run: [1] 0.0 4.5 0.0
#
# Get sensitivities
#
lp ("max", f.obj, f.con, f.dir, f.rhs, compute.sens=TRUE)$sens.coef.from
## Not run: [1] -1e+30  2e+00 -1e+30
lp ("max", f.obj, f.con, f.dir, f.rhs, compute.sens=TRUE)$sens.coef.to  
## Not run: [1] 4.50e+00 1.00e+30 1.35e+01
#
# Right now the dual values for the constraints and the variables are
# combined, constraints coming first. So in this example...
#
lp ("max", f.obj, f.con, f.dir, f.rhs, compute.sens=TRUE)$duals     
## Not run: [1]   4.5   0.0  -3.5   0.0 -10.5
#
# ...the duals of the constraints are 4.5 and 0, and of the variables,
# -3.5, 0.0, -10.5. Here are the lower and upper limits on these:
#
lp ("max", f.obj, f.con, f.dir, f.rhs, compute.sens=TRUE)$duals.from
## Not run: [1]  0e+00 -1e+30 -1e+30 -1e+30 -6e+00
lp ("max", f.obj, f.con, f.dir, f.rhs, compute.sens=TRUE)$duals.to  
## Not run: [1] 1.5e+01 1.0e+30 3.0e+00 1.0e+30 3.0e+00
#
# Run again, this time requiring that all three variables be integer
#
lp ("max", f.obj, f.con, f.dir, f.rhs, int.vec=1:3)
## Not run: Success: the objective function is 37
lp ("max", f.obj, f.con, f.dir, f.rhs, int.vec=1:3)$solution
## Not run: [1] 1 4 0
#
# You can get sensitivities in the integer case, but they're harder to
# interpret.
#
lp ("max", f.obj, f.con, f.dir, f.rhs, int.vec=1:3, compute.sens=TRUE)$duals
## Not run: [1] 1 0 0 7 0

[Package lpSolve version 5.5.8 Index]