simplex.object {boot} | R Documentation |

## Linear Programming Solution Objects

### Description

Class of objects that result from solving a linear programming
problem using `simplex`

.

### Generation

This class of objects is returned from calls to the function `simplex`

.

### Methods

The class `"saddle.distn"`

has a method for the function `print`

.

### Structure

Objects of class `"simplex"`

are implemented as a list with the
following components.

solnThe values of `x`

which optimize the objective function under
the specified constraints provided those constraints are jointly feasible.
solvedThis indicates whether the problem was solved. A value of `-1`

indicates that no feasible solution could be found. A value of
`0`

that the maximum number of iterations was reached without
termination of the second stage. This may indicate an unbounded
function or simply that more iterations are needed. A value of
`1`

indicates that an optimal solution has been found.
valueThe value of the objective function at `soln`

.
val.auxThis is `NULL`

if a feasible solution is found. Otherwise it is
a positive value giving the value of the auxiliary objective
function when it was minimized.
objThe original coefficients of the objective function.
aThe objective function coefficients re-expressed such that the basic
variables have coefficient zero.
a.auxThis is `NULL`

if a feasible solution is found. Otherwise it is the
re-expressed auxiliary objective function at the termination of the first
phase of the simplex method.
AThe final constraint matrix which is expressed in terms of the
non-basic variables. If a feasible solution is found then this will
have dimensions `m1+m2+m3`

by `n+m1+m2`

, where the final
`m1+m2`

columns correspond to slack and surplus variables. If
no feasible solution is found there will be an additional
`m1+m2+m3`

columns for the artificial variables introduced to
solve the first phase of the problem.
basicThe indices of the basic (non-zero) variables in the solution.
Indices between `n+1`

and `n+m1`

correspond to slack
variables, those between `n+m1+1`

and `n+m2`

correspond to
surplus variables and those greater than `n+m2`

are artificial
variables. Indices greater than `n+m2`

should occur only if
`solved`

is `-1`

as the artificial variables are discarded in
the second stage of the simplex method.
slackThe final values of the `m1`

slack variables which arise when
the "<=" constraints are re-expressed as the equalities
`A1%*%x + slack = b1`

.
surplusThe final values of the `m2`

surplus variables which arise when
the "<=" constraints are re-expressed as the equalities ```
A2%*%x -
surplus = b2
```

.
artificialThis is NULL if a feasible solution can be found. If no solution
can be found then this contains the values of the `m1+m2+m3`

artificial variables which minimize their sum subject to the
original constraints. A feasible solution exists only if all of the
artificial variables can be made 0 simultaneously.
### See Also

`print.simplex`

, `simplex`

[Package

*boot* version 1.2-27

Index]