lpSolve: Linear Program Solver
In RlpSolveAPI: Interface to lp_solve v. 5.5

Description Usage Arguments Value Author(s) References Examples

Solves the linear program

           min:  obj * x
    subject to:    A %*% x <= b
                 Aeq %*% x == beq
                 lb[j] <= x[j] <= ub[j]

where x is a vector of n decision variables, obj is a vector of n obective coefficients, A is an ldA by n matrix of inequality constraint coefficients, b is a vector of ldA inequality constraint values, Aeq is an ldAeq by n matrix of equality constraint coefficients, beq is a vector of ldAeq equailty constraint values, and ub and lb are respectively vectors of n upper and lower bounds on the decision variables.

1 2	lpSolveAPI(obj, A, b, Aeq = NULL, beq = NULL, lb = 0, ub = Inf, intvec = integer(0), control = list())

`obj`	a numeric vector of length `n` containing the coefficients of the linear objective function.
`A`	a numeric matrix with `ldA` rows and `n` columns containing the coefficients of the linear inequality constraints.
`b`	a numeric vector of length `ldA` containing the values for the linear inequality constraints.
`Aeq`	a numeric matrix with `n` columns containing the coefficients of the linear equality constraints.
`beq`	a numeric vector of length `ldA` containing the values for the linear equality constraints.
`lb`	a numeric vector of length `n` containing the lower bounds for the decision variables.
`ub`	a numeric vector of length `n` containing the upper bounds for the decision variables.
`intvec`	a vector of unique positive integer values from `1` to `n` indicating decision variables that are restricted to integer values.
`control`	a list containing control parameters for the MILP solver.

A list with the following components:

`objective`	a single numeric value containing the optimal value of the objective function (provided a finite optimal solution is found).
`x`	a numeric vector of length `n` containing the values of the decision variables at the optimal solution.
`status`	an integer value indicating the exit status of the MILP solver. A value of `0` indicates that an optimal solution was found. Other possibilities are given in the note below.
`message`	a character string describing the value of `status`.
`control`	a list containing the control parameters used in the MILP solver.

Possible exit statuses of the MILP solver:

0:	"optimal solution found"
1:	"the model is sub-optimal"
2:	"the model is infeasible"
3:	"the model is unbounded"
4:	"the model is degenerate"
5:	"numerical failure encountered"
6:	"process aborted"
7:	"timeout"
9:	"the model was solved by presolve"
10:	"the branch and bound routine failed"
11:	"the branch and bound was stopped because of a break-at-first or break-at-value"
12:	"a feasible branch and bound solution was found"
13:	"no feasible branch and bound solution was found"

Kjell Konis kjell.konis@epfl.ch.

lp\_solve: http://lpsolve.sourceforge.net/5.5/index.htm

  # maximize:
  #   x1 + 9 x2 +   x3 
  # subject to:
  #   x1 + 2 x2 + 3 x3 <= 9
  # 3 x1 + 2 x2 + 2 x3 <= 15

  obj <- c(1, 9, 3)
  A <- matrix(c(1, 2, 3, 3, 2, 2), 2, 3, byrow = TRUE)
  b <- c(9, 15)

  lpSolveAPI(-obj, A, b)