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.