Linear Programming Solution Objects
Class of objects that result from solving a linear programming
This class of objects is returned from calls to the function
"saddle.distn" has a method for the function
Objects of class
"simplex" are implemented as a list with the
The values of
xwhich optimize the objective function under the specified constraints provided those constraints are jointly feasible.
This indicates whether the problem was solved. A value of
-1indicates that no feasible solution could be found. A value of
0that 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
1indicates that an optimal solution has been found.
The value of the objective function at
NULLif 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.
NULLif 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
n+m1+m2, where the final
m1+m2columns correspond to slack and surplus variables. If no feasible solution is found there will be an additional
m1+m2+m3columns 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+m1correspond to slack variables, those between
n+m2correspond to surplus variables and those greater than
n+m2are artificial variables. Indices greater than
n+m2should occur only if
-1as the artificial variables are discarded in the second stage of the simplex method.
The final values of the
m1slack variables which arise when the "<=" constraints are re-expressed as the equalities
A1%*%x + slack = b1.
The final values of the
m2surplus 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+m3artificial 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.