boot (version 1.3-27)

# simplex.object: 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.

soln

The values of `x` which optimize the objective function under the specified constraints provided those constraints are jointly feasible.

solved

This 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.

value

The value of the objective function at `soln`.

val.aux

This 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.

obj

The original coefficients of the objective function.

a

The objective function coefficients re-expressed such that the basic variables have coefficient zero.

a.aux

This 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.

A

The 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.

basic

The 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.

slack

The final values of the `m1` slack variables which arise when the "<=" constraints are re-expressed as the equalities `A1%*%x + slack = b1`.

surplus

The final values of the `m2` surplus variables which arise when the "<=" constraints are re-expressed as the equalities ```A2%*%x - surplus = b2```.

artificial

This 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.

`print.simplex`, `simplex`