Linear Programming Solution Objects
Class of objects that result from solving a linear programming
problem using simplex.
This class of objects is returned from calls to the function simplex.
The class "saddle.distn" has a method for the function print.
Objects of class "simplex" are implemented as a list with the
following components.
The values of x which optimize the objective function under
the specified constraints provided those constraints are jointly feasible.
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.
The value of the objective function at soln.
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.
The original coefficients of the objective function.
The objective function coefficients re-expressed such that the basic variables have coefficient zero.
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.
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.
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.
The final values of the m1 slack variables which arise when
the "<=" constraints are re-expressed as the equalities
A1%*%x + slack = b1.
The final values of the m2 surplus variables which arise when
the "<=" constraints are re-expressed as the equalities A2%*%x -
surplus = b2.
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.
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